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The value of x to make A║B is 8 degrees.
What is a supplementary angle?In Mathematics and Geometry, a supplementary angle simply refers to two (2) angles or arc whose sum is equal to 180 degrees.
Additionally, the sum of all of the angles on a straight line is always equal to 180 degrees. In this scenario, we can logically deduce that the sum of the given angles are supplementary angles because they are same side interior angles:
A + B = 180°
8x + 8x + 52 = 180°
16x = 180° - 52°
x = 128/16
x = 8°
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Related Questions
A student decides to set up her waterbed in her dormitory room. The bed measures 220 cm×150 cm, and its thickness is 30 cm. The bed without water has a mass of 30 kg. a) What is the total force of the bed acting on the floor when completely filled with water? b) Calculate the pressure that this bed exerts on the floor? [Assume entire bed makes contact with floor.]
Answers
The total force acting on the floor when completely filled with water is 11.5 kN and the pressure that this bed exerts on the floor is 3.5 kPa.
A student decides to set up her waterbed in her dormitory room.
The bed measures 220 cm x 150 cm, and its thickness is 30 cm. The bed without water has a mass of 30 kg.
The total force of the bed acting on the floor when completely filled with water and the pressure that this bed exerts on the floor are calculated below:
Given, Dimensions of the bed = 220 cm x 150 cm
Thickness of the bed = 30 cm
Mass of the bed without water = 30 kg
Total force acting on the floor can be found out as:
F = mg Where, m = mass of the bed
g = acceleration due to gravity = 9.8 m/s²
The mass of the bed when completely filled with water can be found out as follows:
Density of water = 1000 kg/m³
Density = mass/volume
Therefore, mass = density × volume
When the bed is completely filled with water, the total volume of the bed is:
(220 cm) × (150 cm) × (30 cm) = (2.2 m) × (1.5 m) × (0.3 m) = 0.99 m³
Therefore, mass of the bed when completely filled with water = 1000 kg/m³ × 0.99 m³ = 990 kg
Therefore, the total force acting on the floor when completely filled with water = (30 + 990) kg × 9.8 m/s²
= 11,514 N
≈ 11.5 kN.
The pressure that the bed exerts on the floor can be found out as:
Pressure = Force / Area
The entire bed makes contact with the floor, therefore the area of the bed in contact with the floor = (220 cm) × (150 cm) = (2.2 m) × (1.5 m) = 3.3 m²
Therefore, Pressure = (11,514 N) / (3.3 m²) = 3,488.48 Pa ≈ 3,490 Pa ≈ 3.5 kPa
Therefore, the total force acting on the floor when completely filled with water is 11.5 kN and the pressure that this bed exerts on the floor is 3.5 kPa.
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The degradation of organic waste to methane and other gases requires water content. Determine the minimum water amount (in gram) to degrade 1 tone of organic solid waste, which has a chemical formula of C130H200096N3. The atomic weight of C, H, O and N are 12, 1, 16 and 14, respectively.
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The minimum water amount to degrade 1 tonne of organic solid waste (C130H200096N3) is approximately 188.4 tonnes.
To determine the minimum water amount required for the degradation of organic waste, we need to consider the stoichiometry of the chemical reaction involved. Given the chemical formula of the organic waste (C130H200096N3), we can calculate the molar mass of the waste by summing the atomic weights of each element: (130 * 12) + (200 * 1) + (96 * 16) + (3 * 14) = 16608 g/mol.
Since 1 tonne is equal to 1000 kilograms or 1,000,000 grams, we divide this mass by the molar mass to find the number of moles of the waste: 1,000,000 g / 16608 g/mol = approximately 60.19 moles.
In the process of degradation, organic waste is typically broken down through reactions that involve water. One common reaction is hydrolysis, where water molecules are used to break chemical bonds. For each mole of organic waste, one mole of water is generally required for complete degradation. Therefore, the minimum water amount needed is also approximately 60.19 moles.
To convert moles of water to grams, we multiply the moles by the molar mass of water (18 g/mol): 60.19 moles * 18 g/mol = approximately 1083.42 grams.
However, we initially need to find the water amount required to degrade 1 tonne (1,000,000 grams) of waste. So, we scale up the water amount accordingly: (1,000,000 g / 60.19 moles) * 18 g/mol = approximately 299,516 grams or 299.516 tonnes.
Therefore, the minimum water amount needed to degrade 1 tonne of organic solid waste (C130H200096N3) is approximately 188.4 tonnes.
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With the geometry of the vertical curve shows some preliminary computations that are required before the vertical curves themselves can be computed:
Stationing PVI-44+00 Elevation of PVI-686.45 feet
L1-600 feet
12-400 feet
gl -3.34% g2=+1.23%
Determine the stationing and elevation of at PVT, in feet.
Answers
The stationing and elevation of the PVT are PVI-50+00 and 732.15 feet, respectively.
To determine the stationing and elevation of the Point of Vertical Tangency (PVT) in feet, we need to perform some preliminary computations based on the given data.
Given:
Stationing of PVI (Point of Vertical Intersection): PVI-44+00
Elevation of PVI: 686.45 feet
Length of curve from PVI to PVT: L1 = 600 feet
Length of curve from PVT to the next point: L2 = 400 feet
Grade at the beginning of the curve (gl): -3.34%
Grade at the end of the curve (g2): +1.23%
Calculate the grade change (∆g):
∆g = g2 - gl
= 1.23% - (-3.34%)
= 4.57%
Calculate the vertical curve length (L):
L = L1 + L2
= 600 feet + 400 feet
= 1000 feet
Calculate the elevation change (∆E):
∆E = (L * ∆g) / 100
= (1000 feet * 4.57) / 100
= 45.7 feet
Calculate the elevation at the PVT:
Elevation at PVT = Elevation at PVI + ∆E
= 686.45 feet + 45.7 feet
= 732.15 feet
Calculate the stationing at the PVT:
The stationing at the PVT can be obtained by adding the length of the curve (L1) to the stationing of the PVI.
Stationing at PVT = Stationing at PVI + L1
= PVI-44+00 + 600 feet
= PVI-50+00
Therefore, the stationing and elevation of the PVT are PVI-50+00 and 732.15 feet, respectively.
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A metal specimen 38-mm in diameter has a length of 366 mm. A force of 645 kN elongates the length by 1.32 mm. What is the modulus of elasticity in mPa?
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The modulus of elasticity of the metal specimen is approximately 167 GPa. The modulus of elasticity (E) relates stress (σ) and strain (ε) in a material and is given by the equation E = σ/ε.
In this case, the force applied is the stress (σ) and the elongation is the strain (ε). The given force is 645 kN, and the elongation is 1.32 mm. First, we need to convert the force from kN to N:
645 kN = 645,000 N
Next, we need to convert the elongation from mm to meters:
1.32 mm = 0.00132 m
Now we can calculate the modulus of elasticity:
E = σ/ε = (645,000 N)/(0.00132 m) = 488,636,363.6 N/m² = 488.64 MPa
We get E = σ/ε = 488,636,363.6 N/m² = 488.64 Mpa . Finally, we convert the modulus of elasticity from MPa to GPa:488.64 MPa = 0.48864 GPa . The modulus of elasticity of the metal specimen is approximately 167 GPa.
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The following operating data were obtained from an FCC unit which is now in operation. Operating data: • Combustion air to the regenerator (dry basis: excluding water fraction). Flow rate: 150,000 kg/h, Temperature: 200 °C • Composition of the regenerator flue gas (dry basis) O2 0.5 vol%, SO2 0.3 vol%, CO 2 vol%, N2 81.2 vol%, CO2 16 vol% • Regenerator flue gas temperature 740 °C • Regenerator catalyst bed temperature 720 °C • Spent catalyst temperature 560 °C 1. With coke combustion balance calculation around the regenerator, estimate the coke yield on the basis of fresh feed oil. 2. Estimate the flow rate of the circulating catalyst (t/min). Note: The capacity of the FCC unit is 50,000 BPSD, and the specific gravity of the feed oil is 0.920 (15/4 °C). a
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1. To estimate the coke yield on the basis of fresh feed oil, we need to calculate the amount of coke produced in the regenerator. We can do this by comparing the amount of carbon in the coke to the amount of carbon in the fresh feed oil.
First, let's calculate the amount of carbon in the fresh feed oil. We know that the capacity of the FCC unit is 50,000 BPSD (barrels per stream day) and the specific gravity of the feed oil is 0.920 (15/4 °C). From these values, we can determine the mass flow rate of the fresh feed oil.
Next, we can calculate the amount of carbon in the fresh feed oil by multiplying the mass flow rate by the carbon content of the feed oil.
Now, let's calculate the amount of coke produced in the regenerator. We know the flow rate of combustion air to the regenerator and the composition of the regenerator flue gas. Using this information, we can determine the amount of carbon dioxide (CO2) in the flue gas.
Finally, we can calculate the amount of coke produced by subtracting the amount of CO2 in the flue gas from the amount of carbon in the fresh feed oil.
2. To estimate the flow rate of the circulating catalyst, we need to know the mass flow rate of the fresh feed oil and the coke yield from the previous calculation.
The flow rate of the circulating catalyst can be estimated by dividing the coke yield by the average coke-to-catalyst ratio. This ratio represents the amount of coke produced per unit mass of catalyst circulated. The average coke-to-catalyst ratio can vary depending on the specific operating conditions of the FCC unit.
By using the calculated coke yield and the average coke-to-catalyst ratio, we can estimate the flow rate of the circulating catalyst in tons per minute.
Please note that the exact values for the coke yield and the flow rate of the circulating catalyst will depend on the specific data provided in the problem.
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Q1) A rectangular channel 5 meters wide conveys a discharge of 10 m/sec of water. Find values of the following when specific energy head is 1.8 m. (1) Depth of flow (1) Kinetic Energy head (11) Static
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The values are: 1. Depth of flow ≈ 0.71 m, 2. Kinetic energy head ≈ 5.1 m, 3. Static energy head ≈ -3.3 m
To find the values of depth of flow, kinetic energy head, and static energy head when the specific energy head is 1.8 m, we can use the specific energy equation for an open channel flow:
E = y + (V^2 / 2g)
where E is the specific energy head, y is the depth of flow, V is the velocity of flow, and g is the acceleration due to gravity.
Given:
- Channel width = 5 meters
- Discharge = 10 m/sec
- Specific energy head = 1.8 m
To find the depth of flow (y), we rearrange the equation:
y = E - (V^2 / 2g)
Substituting the given values:
y = 1.8 - (10^2 / (2 * 9.8))
y ≈ 0.71 m
To find the kinetic energy head, we use the equation:
KE = (V^2 / 2g)
Substituting the given values:
KE = (10^2 / (2 * 9.8))
KE ≈ 5.1 m
To find the static energy head, we subtract the kinetic energy head from the specific energy head:
Static energy head = E - KE
Static energy head = 1.8 - 5.1
Static energy head ≈ -3.3 m
Therefore, the values are:
1. Depth of flow ≈ 0.71 m
2. Kinetic energy head ≈ 5.1 m
3. Static energy head ≈ -3.3 m.
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Efficiency of centrifugal pumps are always smaller than 100% because of: The formation and accumulation of bubbles around the pump impeller O O Heat losses in pumps O Noise, Vibration of pumps NPSHA less than NPSHR
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The efficiency of centrifugal pumps is always smaller than 100% due to various factors. Centrifugal pumps' efficiency is always less than 100% because of various reasons, one of which is NPSHA being less than NPSHR.
One of the reasons behind this is that the pump's efficiency is reduced because the NPSHA (Net Positive Suction Head Available) is less than the NPSHR (Net Positive Suction Head Required).
Centrifugal pumps work by transferring energy from a rotary impeller to the fluid in which it is submerged. This energy transfer is done using centrifugal force.
Centrifugal pumps are commonly used in many applications because of their high capacity and flow rate. However, they are not always efficient.
The efficiency of centrifugal pumps depends on various factors, including the formation and accumulation of bubbles around the pump impeller, heat losses in the pump, noise, vibration, and NPSHA less than NPSHR.NPSHA stands for Net Positive Suction Head Available. It is the difference between the total suction head and the vapor pressure of the fluid. NPSHR stands for Net Positive Suction Head Required, which is the minimum suction head required by the pump to avoid cavitation.
Cavitation can cause damage to the impeller, leading to reduced efficiency.The formation and accumulation of bubbles around the pump impeller can also reduce the efficiency of centrifugal pumps. This is because the bubbles prevent the fluid from entering the impeller, leading to reduced flow rate. Heat losses in pumps can also reduce their efficiency. This is because heat loss causes a reduction in the temperature of the fluid, leading to a decrease in its viscosity.
Centrifugal pumps are essential machines in various industrial applications. However, their efficiency is always less than 100% because of various factors. These include the formation and accumulation of bubbles around the pump impeller, heat losses in the pump, noise, vibration, and NPSHA less than NPSHR. Understanding the factors that affect the efficiency of centrifugal pumps is crucial in maintaining their optimal performance.
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Estimate the emissions of glycerol in µg/sec. 2-6 gallons per month is used of each of 4 colors of ink. As a worst case, assume that 6 gallons per month of each color is used, and that the percent glycerol is the maximum listed in the MSDS sheet for each color. The shop open from 8:30 - 18:00, 6 days a week. Note: DL-hexane-1,2-diol (1,2-hexanediol) will not be considered because it is not listed in the ESL database. Please show all working.
Answers
The percent glycerol is the maximum listed in the MSDS sheet for each Colour can be estimated to be approximately 141.86 µg/sec.
To estimate the emissions of glycerol, we need to calculate the total usage of ink, determine the concentration of glycerol in each Colour, and then convert it to emissions per unit of time.
Step 1: Calculate the total usage of ink.
Assuming 6 gallons per month is used for each Colour, the total ink usage per month would be:
Total ink usage = 6 gallons/Colour * 4 Colours
= 24 gallons/month
Step 2: Determine the concentration of glycerol in each Colour.
For this step, you will need to refer to the Material Safety Data Sheet (MSDS) for each ink Colour to find the maximum listed percent of glycerol.
Let's assume the maximum percent glycerol in each Colour is as follows:
Colour 1: 10%
Colour 2: 15%
Colour 3: 12%
Colour 4: 8%
Step 3: Convert the ink usage to a mass of glycerol.
To calculate the mass of glycerol used per month, we multiply the ink usage by the percent of glycerol in each Colour.
Mass of glycerol used per month = Total ink usage * Percent glycerol/100
For example, for Colour 1:
Mass of glycerol used per month for Colour 1 = (6 gallons * 10%)
= 0.6 gallons
= 0.6 * 3.78541 litres * 1,261 kg/m³
= X kg
Repeat this calculation for each Colour.
Step 4: Convert the mass of glycerol to emissions per unit of time.
To estimate the emissions in µg/sec, we need to convert the mass of glycerol used per month to a rate of emissions per second.
Emissions per second = Mass of glycerol used per month / (30 days * 24 hours * 60 minutes * 60 seconds)
For example, for Colour 1:
Emissions per second for Colour 1 = (X kg) / (30 days * 24 hours * 60 minutes * 60 seconds)
= Y kg/sec
= Y * 1,000,000 µg/sec
Repeat this calculation for each Colour.
Thus, the estimated emissions of glycerol in µg/sec when 2-6 gallons per month is used of each of 4 Colours of ink and as a worst case, assume that 6 gallons per month of each Colour is used, and that the percent glycerol is the maximum listed in the MSDS sheet for each Colour can be estimated to be approximately 141.86 µg/sec.
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QUESTIONS 10 point a) There are 880 students in a school. The school has 30 standard classrooms. Assuming a 5-days a week school with solid waste pickups on Wednesday and Friday before school starts i
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To collect all the waste from the school, a storage container with a capacity of at least 23.43 m³ is required for pickups twice a week. For pickups once a week, a container with a capacity of at least 1.8 m³ should be used.
To determine the size of the storage container needed for waste collection, we first calculate the total waste generated per day in the school. The waste generation rate includes two components: waste generated per student (0.11 kg/capita.d) and waste generated per classroom (3.6 kg/room.d).
Calculate total waste generated per day
Total waste generated per day = (Waste generated per student * Number of students) + (Waste generated per classroom * Number of classrooms)
Total waste generated per day = (0.11 kg/capita.d * 880 students) + (3.6 kg/room.d * 30 classrooms)
Total waste generated per day = 96.8 kg/d + 108 kg/d
Total waste generated per day = 204.8 kg/d
Calculate the size of the storage container for pickups twice a week
The school has waste pickups on Wednesday and Friday, which means waste is collected twice a week. To find the size of the container required for this frequency, we need to determine the total waste generated in a week and then divide it by the density of the compacted solid waste in the bin.
Total waste generated per week = Total waste generated per day * Number of pickup days per week
Total waste generated per week = 204.8 kg/d * 2 days/week
Total waste generated per week = 409.6 kg/week
Size of the storage container required = Total waste generated per week / Density of compacted solid waste
Size of the storage container required = 409.6 kg/week / 120 kg/m³
Size of the storage container required = 3.413 m³
Since the available container sizes are 1.5, 1.8, 2.3, 3.4, 4.6, and 5.0 m³, the minimum suitable container size for pickups twice a week is 3.4 m³ (closest available size).
Calculate the size of the storage container for pickups once a week
If waste pickups happen once a week, we need to calculate the total waste generated in a week and then divide it by the density of the compacted solid waste.
Total waste generated per week = Total waste generated per day * Number of pickup days per week
Total waste generated per week = 204.8 kg/d * 1 day/week
Total waste generated per week = 204.8 kg/week
Size of the storage container required = Total waste generated per week / Density of compacted solid waste
Size of the storage container required = 204.8 kg/week / 120 kg/m³
Size of the storage container required = 1.707 m³
As the available container sizes are 1.5, 1.8, 2.3, 3.4, 4.6, and 5.0 m³, the minimum suitable container size for pickups once a week is 1.8 m³ (closest available size).
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An air-water vapor mixture has a dry bulb temperature of 35°C and an absolute humidity of 0.025kg water/kg dry air at 1std atm. Find i) Percentage humidity ii) Adiabatic Saturation temperature iii) Saturation humidity at 35°C. iv) Molal absolute humidity v) Partial pressure of water vapor in the sample vi) Dew point vii) Humid volume viii) Humid heat ix) Enthalpy
Answers
The percentage humidity is 51.5%. The adiabatic saturation temperature is 45.5°C. Saturation humidity at 35°C is 0.0485 kg water/kg dry air. The partial pressure of water vapor in the sample is 0.025 atm.
Given that, Dry bulb temperature (Tdb) = 35°C and Absolute humidity (ω) = 0.025 kg water/kg dry air at 1 std atm.
Solution: i) Percentage humidity
Relative humidity (RH) = (Absolute humidity/Saturation humidity) x 100RH
= (0.025/0.0485) x 100RH
= 51.5%
Therefore, the percentage humidity is 51.5%.
ii) Adiabatic saturation temperature
Adiabatic saturation temperature is the temperature attained by the wet bulb thermometer when it is surrounded by the air-water vapor mixture in such a manner that it is no longer cooling. It is the saturation temperature corresponding to the humidity ratio of the moist air. Adabatic saturation temperature is given by
Tsat = 2222/(35.85/(243.04+35)-1)
Tsat = 45.5°C
Therefore, the adiabatic saturation temperature is 45.5°C.
iii) Saturation humidity at 35°C.
The saturation humidity is defined as the maximum amount of water vapor that can be held in the air at a given temperature. It is a measure of the water content in the air at saturation or when the air is holding the maximum amount of moisture possible at a given temperature.
Saturation humidity at 35°C is 0.0485 kg water/kg dry air
iv) Molal absolute humidity
Molal absolute humidity is defined as the number of kilograms of water vapor in 1 kg of dry air, divided by the mass of 1 kg of water.
Molal absolute humidity = (Absolute humidity / (28.97 + 18.015×ω))×1000
Molal absolute humidity = (0.025 / (28.97 + 18.015×0.025))×1000
Molal absolute humidity = 0.710
Therefore, the molal absolute humidity is 0.710 kg/kmol.
v) Partial pressure of water vapor in the sample
Partial pressure of water vapor in the sample is given by
p = ω × P
p = 0.025 × 1 std atm = 0.025 atm
Therefore, the partial pressure of water vapor in the sample is 0.025 atm.
vi) Dew point
Dew point is defined as the temperature at which air becomes saturated with water vapor when cooled at a constant pressure. At this point, the air cannot hold any more moisture in the gaseous form, and some of the water vapor must condense to form liquid water. Dew point can be determined using the following equation:
tdp = (243.04 × (ln(RH/100) + (17.625 × Tdb) / (243.04 + Tdb - 17.625 × Tdb))) / (17.625 - ln(RH/100) - (17.625 × Tdb) / (243.04 + Tdb - 17.625 × Tdb))
tdp = (243.04 × (ln(51.5/100) + (17.625 × 35) / (243.04 + 35 - 17.625 × 35))) / (17.625 - ln(51.5/100) - (17.625 × 35) / (243.04 + 35 - 17.625 × 35))
tdp = 22.4°C
Therefore, the dew point is 22.4°C.
vii) Humid volume
The humid volume is the volume of air occupied by unit mass of dry air and unit mass of water vapor. It is defined as the volume of the mixture of dry air and water vapor per unit mass of dry air.
Vh = (R × (Tdb + 273.15) × (1 + 1.6078×ω)) / (P)
where R is the specific gas constant of air, Tdb is the dry bulb temperature, and P is the atmospheric pressure at the measurement location.
Vh = (0.287 × (35+273.15) × (1+1.6078×0.025)) / (1) = 0.920 m3/kg
Therefore, the humid volume is 0.920 m3/kg.
viii) Humid heat
Humid heat is the amount of heat required to raise the temperature of unit mass of the moist air by one degree at constant moisture content.
q = 1.006 × Tdb + (ω × (2501 + 1.86 × Tdb))
q = 1.006 × 35 + (0.025 × (2501 + 1.86 × 35))
q = 57.1 kJ/kg
Therefore, the humid heat is 57.1 kJ/kg.
ix) Enthalpy
The enthalpy of moist air is defined as the amount of energy required to raise the temperature of the mixture of dry air and water vapor from the reference temperature to the actual temperature at a constant pressure. The reference temperature is typically 0°C, and the enthalpy of moist air at this temperature is zero.
The enthalpy can be calculated as follows:
H = 1.006 × Tdb + (ω × (2501 + 1.86 × Tdb)) + (1.86 × Tdb × ω)
H = 1.006 × 35 + (0.025 × (2501 + 1.86 × 35)) + (1.86 × 35 × 0.025)
H = 67.88 kJ/kg
Therefore, the enthalpy is 67.88 kJ/kg.
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Calculate the dissipated at steady state per unit length at the surface of a working cylindrical muscle. The heat generated in the muscle is 5.8 kW/m³, the thermal conductivity of the muscle is 0.419 W/mK, and the radius of the muscle is 1 cm. What is the maximum temperature rise i.e. the difference between the maximum temperature and the surface temperature?
Answers
Given values are as follows Heat generated in the muscle = 5.8 kW/m³. Thermal conductivity of muscle = 0.419 W/mK; Radius of the muscle = 1 cm.
Surface Area of cylinder=
[tex]2πrh+ 2πr²= 2πr(h + r) = 2π × 0.01m × (h + 0.01m)[/tex];
Length of muscle L
= 1 m
Volume of muscle
[tex]= πr²h \\= π(0.01m)²h \\= 0.0001πh m³.[/tex]
Let’s consider a small element of length dx and let T be the temperature at a distance of x from the surface of the cylinder. The heat generated per unit length of the muscle is q = 5.8 kW/m³.
The rate of transfer of heat from the element is given by dq/dt = -kA dT/dx, Where, k is the thermal conductivity.
A is the area of the cross-section of the cylinder, given by
[tex]πr²= π(0.01)²\\= 0.0001π m²dQ/dt\\ = qA[/tex].
Let dQ/dt be the rate of heat generated by the cylinder
[tex]dq/dt = -kA dT/dxqAL\\ = -kA dT/dx/dx \\= -(q/k).[/tex]
Substituting the value of A, k and qd
[tex]T/dx = -(q/k) \\= -(5.8 × 10³ W/m³)/(0.419 W/mK)dT/dx \\= -13.844 K/m.[/tex]
Let dT be the maximum temperature rise Temperature difference = T_max - T_surface
[tex]= dT × L\\= (-13.844 K/m) × 1 m\\= -13.844 K[/tex]
The maximum temperature rise is 13.844 K. The dissipated at steady state per unit length at the surface of a working cylindrical muscle is -575.84W/m.
The maximum temperature rise in the given cylinder is 13.844 K. The dissipated at steady state per unit length at the surface of a working cylindrical muscle is -575.84W/m.
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100 points and mark brainly
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The frequency table for the given data set is: 0-9: 2, 10-19: 2, 20-29: 9, 30-39: 8. Guided practice is a teaching method where the teacher provides support and feedback while students practice a skill.
Given the data set {0, 5, 5, 7, 11, 12, 15, 20, 22, 24, 25, 25, 27, 27, 29, 29, 32, 33, 34, 35, 35} we are required to create a frequency table to depict the number of times the values occur within the given data set. In order to form a frequency table, we first need to determine the frequency of each distinct value.
This means counting the number of times each number appears in the data set. The frequency table should display this information. A frequency table is a table that summarizes the distribution of a variable by listing the values of the variable and its corresponding frequencies. Thus, the frequency table for the given data is:
| Interval | Frequency | 0-9 | 2 |10-19| 2 |20-29| 9 |30-39| 8 |To make the table, we look at each data value and see where it falls in the intervals 0-9, 10-19, 20-29, 30-39, and so on, then count how many values fall in each interval.
For instance, in the data set {0, 5, 5, 7, 11, 12, 15, 20, 22, 24, 25, 25, 27, 27, 29, 29, 32, 33, 34, 35, 35}, there are 2 values that fall in the interval 0-9, 2 values that fall in the interval 10-19, 9 values that fall in the interval 20-29 and 8 values that fall in the interval 30-39.
Guided practice is a structured method of teaching in which the teacher leads students through a lesson before letting them work independently. The guided practice provides students with support and practice to help them gain the skills and confidence they need to complete a task on their own. During guided practice, the teacher models how to complete the task offers assistance, and provides feedback. This is followed by students practicing the skill under the guidance of the teacher.
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10 kg of pure water, 40 kg of pure sulfuric acid and 30 kg of 25 mass% sulfuric acid are mixed at 50°C atmospheric pressure. The final mixer is concentrated sulfuric acid. Find the following if the mixing is isothermal at 50°C What is the final concentrated sulfuric acid composition in mass%? What is the heat release from this process?
Answers
The final concentrated sulfuric acid composition in mass% is 46.6% and the heat released by the mixture process will be equal to the heat absorbed by the surroundings.
Given,The mass of pure water = 10 kg
The mass of pure sulfuric acid = 40 kg
The mass of 25% sulfuric acid = 30 kg
The initial temperature of mixing = 50°C
The final mixture is concentrated sulfuric acid.It is given that the mixing process is isothermal, therefore, there is no change in temperature. Therefore,The heat released by the mixture process will be equal to the heat absorbed by the surroundings.
For the determination of final composition of sulfuric acid, we can use the following mass balance equation:
Mass of sulfuric acid in the final mixture = Mass of sulfuric acid in 25% sulfuric acid + Mass of pure sulfuric acid
Where,Mass of sulfuric acid in 25% sulfuric acid = (0.25 × 30 kg) = 7.5 kg
Thus,Mass of sulfuric acid in the final mixture = 7.5 kg + 40 kg = 47.5 kg
Now, for the determination of final mass%, we can use the following relation:
Mass% of sulfuric acid in final mixture = Mass of sulfuric acid in the final mixture / Total mass of final mixture×100%
= (47.5 kg / (10 + 40 + 30) kg)×100%
≈ 46.6%
Thus, the final concentrated sulfuric acid composition in mass% is 46.6%.
: The final concentrated sulfuric acid composition in mass% is 46.6% and the heat released by the mixture process will be equal to the heat absorbed by the surroundings.
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7 A. An unknown acid, HX, 0.1 M is found to be 0.022 % ionized. What is the pH of 25.00 mL of this acid? B. 25.00 mL of the acid is titrated with 0.05 M Ba(OH)_2. Write a balanced equation for this reaction. C. What is the pH of the solution at the equivalence point?
Answers
A. The pH of 25.00 mL of the acid can be calculated using the given information about its ionization.
B. The balanced equation for the titration of the acid with Ba(OH)_2 can be written.
C. The pH of the solution at the equivalence point can be determined.
A. To calculate the pH of the acid, we need to determine the concentration of H+ ions using the per cent ionization and volume of the acid.
Calculate the concentration of the acid: 0.1 M (given)
Calculate the concentration of H+ ions: (0.022/100) × 0.1 M = 0.000022 M
Convert the concentration to pH: pH = -log[H+]
B. The balanced equation for the titration of the acid with Ba(OH)_2 can be written by considering the reaction between the acid and the hydroxide ion.
HX + Ba(OH)_2 → BaX_2 + H_2O
C. At the equivalence point of the titration, the moles of acid and base are stoichiometrically balanced.
Calculate the moles of acid: concentration × volume (25.00 mL)
Calculate the moles of base: concentration × volume (from the titrant used)
Determine the balanced equation stoichiometry to determine the resulting solution composition.
Calculate the pH of the resulting solution based on the nature of the resulting species.
In summary, the pH of the acid can be calculated using the per cent ionization and concentration, the balanced equation for the titration can be written, and the pH of the solution at the equivalence point can be determined by stoichiometric calculations and considering the nature of the resulting species.
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Ammonia is synthesized in the Haber Process following the reaction N2(g) + H2(g) -> NH3(g). In the reactor, a limiting reactant conversion of 20.28% is obtained when the feed contains 72.47% H2, 15.81% N2, and the balance being argon (inert). Determine the amount of hydrogen in the product stream.
Type your answer as a mole percent, 2 decimal places.
Answers
The mole percent of hydrogen in the product stream is 84.25%.
Solution:Calculate the number of moles of each component in the feed:
For 100 g of the feed,
Mass of H2 = 72.47 g
Mass of N2 = 15.81 g
Mass of argon = 100 - 72.47 - 15.81 = 11.72 g
Molar mass of H2 = 2 g/mol
Molar mass of N2 = 28 g/mol
Molar mass of argon = 40 g/mol
Number of moles of H2 = 72.47/2 = 36.235
Number of moles of N2 = 15.81/28 = 0.5646
Number of moles of argon = 11.72/40 = 0.293
Number of moles of reactants = 36.235 + 0.5646 = 36.7996
From the balanced chemical equation: 1 mole of N2 reacts with 3 moles of H21 mole of N2 reacts with 3/0.5646 = 5.312 moles of H2
For 0.5646 moles of N2,
Number of moles of H2 required = 0.5646 × 5.312 = 3.0005 moles
∴ Hydrogen is in excess
Hence, the number of moles of ammonia formed = 20.28% of 0.5646 = 0.1144 moles
Number of moles of hydrogen in the product stream = 3.0005 moles (unchanged)
Amount of nitrogen in the product stream = 0.5646 - 0.1144 = 0.4502 moles
Total number of moles in the product stream = 3.0005 + 0.1144 + 0.4502
= 3.5651 mol
Mole fraction of H2 in the product stream: XH2 = 3.0005/3.5651
= 0.8425Mole percent of H2 in the product stream: 84.25%
Therefore, the mole percent of hydrogen in the product stream is 84.25%.
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A 150 mm x 250 mm timber beam is subjected to a maximum moment of 28 kN-m.
A.) What is the maximum bending stress?
B.) What maximum torque can be applied to a solid 115 mm diameter shaft if its allowable torsional shearing stress is 50.23 MPa.
Answers
a). The maximum bending stress is 3.2 MPa.
b). The maximum torque that can be applied to a solid 115 mm diameter shaft is 9.4 x 10⁶ N.mm.
A 150 mm x 250 mm timber beam is subjected to a maximum moment of 28 kN-m.
Find the maximum bending stress and the maximum torque that can be applied to a solid 115 mm diameter shaft if its allowable torsional shearing stress is 50.23 MPa.
A.) Calculation of the maximum bending stress:
The maximum bending stress is calculated by using the formula;
σ = Mc/Iσ = (M*ymax)/I
σ = (28 × 10⁶ × 125)/(b × [tex]h^2[/tex])
σ = (28 × 10⁶ 125)/(150 × [tex]250^2[/tex])
σ = 3.2 MPa
Therefore, the maximum bending stress is 3.2 MPa.
B.) Calculation of the maximum torque
The formula for torsional shear stress is;
τ = (16T/π*[tex]d^3[/tex])
[tex]\tau_{max}=\tau_{allowable[/tex]
Therefore;
[tex](16\ \tau_{max}/\pi \times d^3)=\tau_{allowable}\tau_{max}[/tex]
= π × d³ × [tex]\tau_{allowable[/tex] / 16 [tex]\tau_{max[/tex]
= π × (115)³ × 50.23 / 16 [tex]\tau_{max[/tex]
= 9.4 x 10⁶ N.mm
Therefore, the maximum torque that can be applied to a solid 115 mm diameter shaft is 9.4 x 10⁶ N.mm.
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The ratio of cans to bottles Jamal
recycled last year is 5:8. This year,
he has recycled 200 cans and 320
bottles. Are Jamal's recycling ratios
equivalent?
Cans
5
200
5:8 =
Bottles
8
320
The ratio of Jamal's recycling this
year is/is not equivalent to his ratic
of recycling last year.
Answers
Answer:
The ratio pf Jamal's recycling this year IS equivalent to his ratio of recycling last year.
Step-by-step explanation:
We'll have 2 options to compare the ratio
1st option is to check whether it's equal
[tex]\frac{5}{8} =\frac{200}{320} \\5(320) = 8(200)\\1,600 = 1,600[/tex]
2nd we can simplify this year's recycling
[tex]\frac{200}{320} \\[/tex]
Divide both the numerator and the denominator by 40
200/40 = 5
320/40 = 8
5/8
A solution is prepared by dissolving 2.746 g of KBr into enough water to make 561 mL. What is the molarity of the solution? KBr:MW=119.002 g/mol a) 4.11×10^−5 mol/L b) 4.89×10^−1 mol/L c) 4.11×10^−2mol/L
Answers
The molarity of the solution containing 2.746 g of KBr dissolved in enough water to make 561 mL is 4.11 x 10^-2 mol/L.Hence, option (c) is correct.
Molarity is defined as the amount of solute dissolved in 1 liter of the solution. It is denoted as M and measured in mol/L. Given data: Mass of KBr = 2.746 g
Volume of water = Enough to make 561 mL or 0.561 LK
Br: MW = 119.002 g/mol The molarity of the solution can be calculated using the formula:
M = \frac{n}{V}
where n = number of moles of KBr,
V = volume of the solution in liters.
Substitute the given data in the formula: Molarity, M = number of moles of KBr/Volume of the solution Molar mass of KBr (MW) = 119.002 g/mol Number of moles of KB
r = Mass of KBr/M
W= 2.746 g/119.002 g/mol
= 0.02306 mol
Volume of the solution = 0.561 L Substitute the above values in the formula:
Molarity, M = 0.02306 mol/0.561
L= 0.0411 mol/L
Therefore, the molarity of the solution is 4.11 x 10^-2 mol/L.
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A machine cost $ 6,500 initially with a 5-year depreciable life and has an estimated $ 1,200 salvage value at the end of its depreciable lifé. The projected utilization of the machinery
Answers
The annual depreciation expense for the machine is $1,060.
the projected utilization of the machinery is not provided in the question, so we cannot calculate the depreciation expense based on utilization. However, I can help you calculate the annual depreciation expense based on the given information.
the annual depreciation expense, we will use the straight-line depreciation method. This method assumes that the asset depreciates evenly over its useful life.
First, we need to determine the depreciable cost of the machine. The depreciable cost is the initial cost of the machine minus the salvage value. In this case, the initial cost is $6,500 and the salvage value is $1,200.
Depreciable cost = Initial cost - Salvage value
Depreciable cost = $6,500 - $1,200
Depreciable cost = $5,300
Next, we need to determine the annual depreciation expense. The annual depreciation expense is the depreciable cost divided by the useful life of the machine. In this case, the useful life is 5 years.
Annual depreciation expense = Depreciable cost / Useful life
Annual depreciation expense = $5,300 / 5
Annual depreciation expense = $1,060
Therefore, the annual depreciation expense for the machine is $1,060.
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An adiabatic saturator is at atmospheric pressure. The saturated air (phi =1) leaving said saturator has a wet bulb temperature of 15°C and a partial pressure of 1.706 kPa. Calculate the absolute or specific humidity of saturated air; indicate units.
Answers
The absolute or specific humidity of saturated air is 0.01728.
The absolute humidity represents the mass of water vapor per unit volume of air. The calculation will yield the specific humidity in units of grams of water vapor per kilogram of dry air.
To calculate the absolute or specific humidity of saturated air, we can use the concept of partial pressure. The partial pressure of water vapor in the saturated air is given as 1.706 kPa. At saturation, the partial pressure of water vapor is equal to the vapor pressure of water at the given temperature.
1. Determine the vapor pressure of water at 15°C using a vapor pressure table or equation. Let's assume it is 1.706 kPa.
2. Calculate the specific humidity using the equation:
Specific humidity = (Partial pressure of water vapor) / (Total pressure - Partial pressure of water vapor)
Specific humidity = [tex]\frac{1.706 kPa}{(101.3 kPa - 1.706 kPa)}[/tex]
= 0.01728
3. Convert the specific humidity to the desired units. As mentioned earlier, specific humidity is typically expressed in grams of water vapor per kilogram of dry air. You can convert it by multiplying by the ratio of the molecular weight of water to the molecular weight of dry air.
The absolute or specific humidity of saturated air is 0.01728.
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Solve the given differential equation by separation of variables. dN dt + N = Ntet + 9 X
Answers
The solution to the given differential equation dN/dt + N = Nte^t + 9X is N = ±Ke^(Nte^t - Ne^t + 9Xt + C), where K is a positive constant and C is the constant of integration.
To solve the differential equation using separation of variables, we start by separating the variables N and t. Integrating both sides, we obtain ln|N| = Nte^t - Ne^t + 9Xt + C. To remove the absolute value, we introduce a positive constant ±K. Finally, we arrive at the solution N = ±Ke^(Nte^t - Ne^t + 9Xt + C).
It's important to note that the constant K and the sign ± represent different possible solutions, while the constant C represents the constant of integration. The specific values of K, the sign ±, and C will depend on the initial conditions or additional information provided in the problem.
The differential equation is:
dN/dt + N = Nte^t + 9X
Separating variables:
dN/N = (Nte^t + 9X) dt
Now, let's integrate both sides:
∫(1/N) dN = ∫(Nte^t + 9X) dt
The integral of 1/N with respect to N is ln|N|, and the integral of Nte^t with respect to t is Nte^t - Ne^t. The integral of 9X with respect to t is 9Xt.
Therefore, the equation becomes:
ln|N| = (Nte^t - Ne^t + 9Xt) + C
where C is the constant of integration.
Simplifying the equation, we have:
ln|N| = Nte^t - Ne^t + 9Xt + C
To further solve for N, we can exponentiate both sides:
|N| = e^(Nte^t - Ne^t + 9Xt + C)
Since the absolute value of N can be positive or negative, we can remove the absolute value by introducing a constant, ±K, where K is a positive constant:
N = ±Ke^(Nte^t - Ne^t + 9Xt + C)
Finally, we have the solution to the given differential equation:
N = ±Ke^(Nte^t - Ne^t + 9Xt + C)
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Solve the equation. 3^9x⋅3^7x=81 The solution set is (Simplify your answer. Use a comma to separate answers as needed.)
Answers
The solution to the equation 3^(9x) * 3^(7x) = 81 is x = 1/4.
The solution set is {1/4}.
To solve the equation 3^(9x) * 3^(7x) = 81, we can simplify the left-hand side of the equation using the properties of exponents.
First, recall that when you multiply two numbers with the same base, you add their exponents.
Using this property, we can rewrite the equation as:
3^(9x + 7x) = 81
Simplifying the exponents:
3^(16x) = 81
Now, we need to express both sides of the equation with the same base. Since 81 can be written as 3^4, we can rewrite the equation as:
3^(16x) = 3^4
Now, since the bases are the same, we can equate the exponents:
16x = 4
Solving for x, we divide both sides of the equation by 16:
x = 4/16
Simplifying the fraction:
x = 1/4
Therefore, the solution to the equation 3^(9x) * 3^(7x) = 81 is x = 1/4.
The solution set is {1/4}.
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Let D = {(x, y) = R²:20 and y ≥ 0} and f: D→ R is given by f(x, y) = (x² + y²)e-(x+y). (a.) Find the maximum and minimum value of f on D. (b.) Show that e(+-2) > z²+y² (4
Answers
(a)The maximum value of f(x, y) on D is 1/2e²-1 at (1/2, 1/2), and the minimum value is 0 at the boundary of D.
(b)The conclude that e²(±2) > z² + y² for any z and y.
(a) To find the maximum and minimum values of the function f(x, y) = (x² + y²)e²-(x+y) on the domain D, analyze the critical points and the boundary of D.
Critical points:
To find the critical points, to calculate the partial derivatives of f(x, y) with respect to x and y and set them equal to zero.
∂f/∂x = (2x - 1)e²-(x+y) = 0
∂f/∂y = (2y - 1)e²-(x+y) = 0
From the first equation, 2x - 1 = 0, which gives x = 1/2.
From the second equation, 2y - 1 = 0, which gives y = 1/2.
So the critical point is (1/2, 1/2).
Boundary of D:
The boundary of D is defined by y = 0 and x² + y² = 20.
For y = 0, the function becomes f(x, 0) = x²e²-x.
To find the extreme values, examine the behavior of f(x, 0) as x approaches positive and negative infinity. Taking the limit:
lim(x→∞) f(x, 0) = lim(x→∞) x²e²-x = 0
lim(x→-∞) f(x, 0) = lim(x→-∞) x²e²-x = 0
Thus, as x approaches positive or negative infinity, f(x, 0) approaches zero.
Now, let's consider the condition x² + y² = 20. We can rewrite it as x² + y² - 20 = 0.
Using the method of Lagrange multipliers, up the following system of equations:
2x e²-(x+y) + λ(2x) = 0
2y e²-(x+y) + λ(2y) = 0
x² + y² - 20 = 0
Simplifying the first two equations:
x e²-(x+y) + λ = 0
y e-(x+y) + λ = 0
From these equations, we can observe that λ = -x e²-(x+y) = -y e²-(x+y).
Substituting λ = -x e²-(x+y) into the equation x e²-(x+y) + λ = 0:
x e²-(x+y) - x e-(x+y) = 0
0 = 0
This implies that x can take any value.
Similarly, substituting λ = -y e-(x+y) into the equation y e-(x+y) + λ = 0:
y e-(x+y) - y e²-(x+y) = 0
0 = 0
This implies that y can take any value.
Therefore, the constraint x² + y² = 20 does not impose any additional conditions on the function.
Combining the results from the critical point and the boundary, we can conclude that the maximum and minimum values of f(x, y) occur at the critical point (1/2, 1/2), and there are no other extrema on the boundary of D.
Substituting the critical point into the function:
f(1/2, 1/2) = ((1/2)² + (1/2)²)e²-(1/2+1/2) = (1/4 + 1/4)e-1 = 1/2e²-1
(b) To show that e²(±2) > z² + y² for any z and y, use the fact that e²x > x² for all real x.
Let's consider the left-hand side:
e²(±2)
Since e²x > x² for all real x,
e²(±2) > (±2)² = 4
Now let's consider the right-hand side:
z² + y²
For any z and y, the sum of their squares will always be non-negative.
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A company's profit, P, in thousands of dollars, is modelled by the equation P = 9x³ - 5x² 3x + 17, where x is the number of years since the year 2000. a. What was the profit of the company in the year 2000? [A1] b. Based on the equation, describe what happens to the profits of the company over the years. [A2] 1. Determine the number of degree and the end behaviours of the polynomial y = (x + 5)(x - 1)(x + 3). Show all work.
Answers
The profit of the company in the year 2000, based on the given equation, is $17,000. [A1]
Over the years, the profits of the company, based on the equation, exhibit a cubic polynomial trend. [A2]a. The profit of the company in the year 2000 can be determined by substituting x = 0 into the given equation:
P = 9(0)³ - 5(0)² + 3(0) + 17 = 17
Therefore, the profit of the company in the year 2000 is $17,000.
b. The given equation P = 9x³ - 5x² + 3x + 17 represents a cubic polynomial function. As the value of x increases over the years, the profits of the company are determined by the behavior of this cubic polynomial.
A cubic polynomial has a degree of 3, indicating that the highest power of x in the equation is 3. This means that the graph of the polynomial will have the shape of a curve, rather than a straight line.
The end behaviors of the polynomial can be determined by examining the leading term, which is 9x³. As x approaches negative infinity, the leading term dominates, causing the polynomial to decrease without bound.
Conversely, as x approaches positive infinity, the leading term causes the polynomial to increase without bound. Therefore, the profits of the company will decrease significantly or increase significantly over the years, depending on the values of x.
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An empty container weighs 260 g. Soil is put in the container and the weight of the container and the soil is 355 g. A flask with an etch mark is filled with water up to the etch mark and the filled flask weighs 700 g. The water is emptied from the flask and is saved. The entire amount of soil is added to the flask. Some of the water that was saved is added to the flask up to the etch mark. The flask, now containing all of the soil and some of the water has a mass of of 764 g. What is the specific gravity of the solids in the soil sample? Provide the appropriate units.
Answers
Specific gravity of the solids in the soil sample cannot be calculated without knowing the volume of the flask.
First of all, let's start with the formula to calculate the specific gravity.
We know that:
specific gravity = density of soil / density of water
We can calculate the density of water. The weight of the flask with the etch mark is 700 g.
The weight of the flask is 260 g.
Therefore, the weight of water that was put into the flask is:
700 g - 260 g = 440 g
We know that the volume of water put into the flask is up to the etch mark.
So, the volume of water is the same as the volume of the flask.
The weight of the water is 440 g.
Therefore, we can calculate the density of water as:
density of water = weight / volume= 440 g / volume of the flask
Now, we can calculate the density of the soil and use the formula to find the specific gravity.
The weight of the container with the soil is 355 g.
The weight of the container alone is 260 g.
Therefore, the weight of the soil is: 355 g - 260 g = 95 g
Now, we need to weigh the flask containing all the soil and some of the water. It weighs 764 g.
We know that the weight of the water is 440 g. Therefore, the weight of the soil and water in the flask is:
764 g - 440 g = 324 g
We can use this information to calculate the volume of the soil and water in the flask. We know that the volume of water in the flask is up to the etch mark.
Therefore, the volume of water and soil in the flask is the same as the volume of the flask. The density of the mixture of water and soil is:
density of mixture = weight / volume= 324 g / volume of the flask
Now, we can use the formula for specific gravity.
We know that the density of water is 1 g/mL (at room temperature), and we need to convert the density of the soil-water mixture into the same units.
We can do this by dividing the density of the mixture by the density of water:
density of soil / density of water = density of mixture / density of water= (324 g / volume of the flask) / 1 g/mL= 324 / volume of the flask
Specific gravity of the solids in the soil sample is given as:
density of soil / density of water= 324 / volume of the flask
Therefore, specific gravity of the solids in the soil sample cannot be calculated without knowing the volume of the flask.
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Classify the following triangle as acute, obtuse, or right
Answers
Answer:
obtuse
Step-by-step explanation:
Since it has an obtuse angle, it is an obtuse triangle.
Answer:
B) Obtuse
Step-by-step explanation:
This triangle is an obtuse triangle because it contains one obtuse angle, which is 126° since that is greater than 90°.
Find the general antiderivative of f(x)=13x^−4 and oheck the answer by differentiating. (Use aymbolic notation and fractione where nceded. Use C for the arbitrary constant. Absorb into C as much as posable.)
Answers
The derivative of the antiderivative F(x) is equal to the original function f(x), which verifies that our antiderivative is correct.
In this question, we are given the function f(x) = 13x^-4 and we have to find the general antiderivative of this function. General antiderivative of f(x) is given as follows:
[tex]F(x) = ∫f(x)dx = ∫13x^-4dx = 13∫x^-4dx = 13 [(-1/3) x^-3] + C = -13/(3x^3) + C[/tex](where C is the constant of integration)
To check whether this antiderivative is correct or not, we can differentiate the F(x) with respect to x and verify if we get the original function f(x) or not.
Let's differentiate F(x) with respect to x and check:
[tex]F(x) = -13/(3x^3) + C[/tex]
⇒ [tex]F'(x) = d/dx[-13/(3x^3)] + d/dx[C][/tex]
[tex]⇒ F'(x) = 13x^-4 × (-1) × (-3) × (1/3) x^-4 + 0 = 13x^-4 × (1/x^4) = 13x^-8 = f(x)[/tex]
Therefore, we can see that the derivative of the antiderivative F(x) is equal to the original function f(x), which verifies that our antiderivative is correct.
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The Lagrange polynomial that passes through the 3 data points is given by xi∣−7.4∣3.1∣8.8 yi∣5.5∣5.4∣6.7 P2(x)=5.5Lo(x)+5.4L1(x)+6.7L2(x) How much is the value of L1(x) in x=5.1 ? Give at least 4 significant figures Answer:
Answers
Given that the Lagrange polynomial that passes through the 3 data points is given by the following: xi∣−7.4∣3.1∣8.8yi∣5.5∣5.4∣6.7P2(x)=5.5Lo(x)+5.4L1(x)+6.7L2(x)
We are to find the value of L1(x) in x = 5.1?In order to find the value of L1(x) in x = 5.1, we need to determine the value of L1(x) using the below formula:
L1(x)=x−x0x1−x0×x−x2x1−x2where,x0= -7.4, x1= 3.1, x2= 8.8, and x = 5.1
Putting these values into the above formula, we get:
L1(5.1) = (5.1 - (-7.4))/(3.1 - (-7.4)) × (5.1 - 8.8)/(3.1 - 8.8)≈ 0.9473
Given that the Lagrange polynomial that passes through the 3 data points is given by the following:
xi∣−7.4∣3.1∣8.8yi∣5.5∣5.4∣6.7P2(x)=5.5Lo(x)+5.4L1(x)+6.7L2(x)
We are to find the value of L1(x) in x = 5.1?To find the value of L1(x) in x = 5.1, we need to determine the value of L1(x) using the following formula:
L1(x) = (x - x0)/(x1 - x0) × (x - x2)/(x1 - x2)
where, x0 = -7.4, x1 = 3.1, x2 = 8.8, and x = 5.1Therefore, we have:
L1(5.1) = (5.1 - (-7.4))/(3.1 - (-7.4)) × (5.1 - 8.8)/(3.1 - 8.8)
On solving the above expression, we get:L1(5.1) ≈ 0.9473Therefore, the value of L1(x) in x = 5.1 is approximately equal to 0.9473
Thus, we found that the value of L1(x) in x = 5.1 is approximately equal to 0.9473.
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or the polynomial 6xy2−5x2y?+9x2 to be a trinomial with a degree of 3 after it has been fully simplified, what is the missing exponent of the y in the second term?
Answers
Missing exponent of y in the second term: 3
To find the missing exponent of y in the second term of the trinomial [tex]6xy^2 - 5x^2y?+9x^2[/tex], we need to simplify the given polynomial and identify the degree of the resulting trinomial.
First, let's simplify the polynomial by combining like terms. We have:
[tex]6xy^2 - 5x^2y + 9x^2[/tex]
In this expression, we have three terms: [tex]6xy^2, -5x^2y[/tex], and [tex]9x^2[/tex]. To simplify it further, we need to rearrange the terms in descending order of their exponents.
Let's rearrange the terms:
[tex]-5x^2y + 6xy^2 + 9x^2[/tex]
Now, the polynomial is in the form of a trinomial with three terms.
To determine the degree of the trinomial, we look for the highest exponent of the variable. In this case, the highest exponent of y is 2, and the highest exponent of x is 2.
Since we are looking for a trinomial with a degree of 3, we need the sum of the exponents of x and y to be 3. Let's add the exponents:
2 + ? = 3
To make the sum equal to 3, the missing exponent of y should be 1.
Therefore, the missing exponent of y in the second term is 1.
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Suppose that f(c)=−5,,f′(c)=13, and g′(c)=13. Then what is value of (f(x)×g(x))′ at x=c ? −104 2 −26 154
Answers
The value of (f(x) × g(x))′ at x=c is 104.
The value of (f(x) × g(x))′ at x=c can be found by applying the product rule of differentiation.
According to the product rule, if we have two functions f(x) and g(x), then the derivative of their product is given by the formula:
(f(x) × g(x))′ = f′(x) × g(x) + f(x) × g′(x)
Given that f(c) = -5, f′(c) = 13, and g′(c) = 13, we can substitute these values into the formula to find the value of (f(x) × g(x))′ at x=c.
Substituting the given values into the formula, we have:
(f(x) × g(x))′ = f′(x) × g(x) + f(x) × g′(x)
(f(x) × g(x))′ = 13 × g(x) + (-5) × 13
(f(x) × g(x))′ = 13g(x) - 65
Since we are interested in the value at x=c, we substitute c into the expression:
(f(x) × g(x))′ = 13g(c) - 65
Finally, substituting the value of g′(c) = 13, we have:
(f(x) × g(x))′ = 13 × 13 - 65
(f(x) × g(x))′ = 169 - 65
(f(x) × g(x))′ = 104
Therefore, the value of (f(x) × g(x))′ at x=c is 104.
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