(a) To determine the complexity in terms of g(n) for the expression √(8n^2 + 2n) - 16, we need to simplify it and find the dominant term.
√(8n^2 + 2n) - 16 can be rewritten as √(8n^2) * √(1 + 1/(4n)) - 16.
Ignoring the constant terms and lower-order terms, we are left with √(8n^2) = 2n.
Therefore, the complexity of expression (a) can be represented as g(n) = O(n).
Now let's discuss the complexities of the other expressions without giving formal proofs:
(b) log(n³) + log(n²):
The logarithm of a product is the sum of the logarithms. So, this expression simplifies to log(n³ * n²) = log(n^5).
The complexity of this expression is g(n) = O(log n).
(c) 20 - 2^n + 3^n:
The exponential terms dominate in this expression. Therefore, the complexity is g(n) = O(3^n).
(d) 7n log n + 3n^15:
The dominant term here is 3n^15, as it grows much faster than 7n log n. So, the complexity is g(n) = O(n^15).
(e) (n+1)! + 2^n:
The factorial term (n+1)! grows faster than the exponential term 2^n. Therefore, the complexity is g(n) = O((n+1)!).
To summarize:
(a) g(n) = O(n)
(b) g(n) = O(log n)
(c) g(n) = O(3^n)
(d) g(n) = O(n^15)
(e) g(n) = O((n+1)!)
Please note that these are simplified complexity representations without formal proofs.
Learn more about logarithm here:
https://brainly.com/question/30226560
#SPJ11
Solve the following compound inequality: x greater-than-or-equal-to negative 1 or x less-than 2. a. Negative 1 less-than-or-equal-to x less-than 2 c. x greater-than-or-equal-to negative 1 b. no solution d. all real numbers Please select the best answer from the choices provided A B C D
Combining the two sets of values, we find that the overlapping solution is: -1 ≤ x < 2. Option A is the correct answer.
The compound inequality given is: x ≥ -1 or x < 2.
To solve this compound inequality, we can break it down into two separate inequalities and then find the overlapping solution.
First inequality: x ≥ -1
This inequality represents all the values of x that are greater than or equal to -1.
Second inequality: x < 2
This inequality represents all the values of x that are less than 2.
To find the overlapping solution, we need to determine the values that satisfy both inequalities.
From the first inequality, x ≥ -1, we know that x can take any value that is greater than or equal to -1.
From the second inequality, x < 2, we know that x can take any value that is strictly less than 2.
Combining these two sets of values, we find that the overlapping solution is:
-1 ≤ x < 2
For such more question on overlapping:
https://brainly.com/question/10711016
#SPJ8
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?
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.
For more such questions on exponent, click on:
https://brainly.com/question/11975096
#SPJ8
The Hayflick limit is the limit telomeres can be shorten. Please explain and provide detail on how/why telomeres get shorten? Are telomeres able to be recreated? If so how and where would we find this?
Telomeres, which protect chromosome ends, shorten with each cell division due to the limitations of DNA replication, but can be partially replenished by telomerase in certain cell types, while their length and telomerase activity have implications for aging and disease.
The Hayflick limit refers to the maximum number of times a normal human cell can divide before reaching a state of replicative senescence or cell death. It was discovered by Leonard Hayflick in the 1960s and is associated with the shortening of telomeres.
Telomeres are repetitive DNA sequences located at the ends of chromosomes. Their primary function is to protect the genetic material of the chromosome from degradation and prevent the loss of essential genes during DNA replication. However, with each cell division, the telomeres progressively shorten.
Telomere shortening occurs due to the inherent limitations of DNA replication. The DNA replication machinery is unable to fully replicate the very ends of linear chromosomes, leading to the loss of a small portion of telomeric DNA with each round of cell division. This process is known as the "end replication problem."
To know more about Telomeres,
https://brainly.com/question/14131705
#SPJ11
When the following equation is balanced properly under acidic conditions, what are the coefficients of the species shown? _____Cr^3+ + _______Br^-_______Cr^2+ + _______BrO_3- .Water appears in the balanced equation as a __________(reactant, product, neither) with a coefficient of ___________ (Enter 0 for neither.)Which element is oxidized? _________
Water appears as a product with a coefficient of 2.
The balanced equation for the given reaction under acidic conditions is as follows:
4H^+ + 3Cr^3+ + 3Br^- -> 3Cr^2+ + BrO_3^- + 2H_2O
In this balanced equation, the coefficients of the species are:
- 3 for Cr^3+
- 3 for Br^-
- 3 for Cr^2+
- 1 for BrO_3^-
Water appears in the balanced equation as a product with a coefficient of 2.
To determine which element is oxidized, we need to look at the change in oxidation states. In this equation, Cr goes from an oxidation state of +3 to +2, which means it has gained electrons and is being reduced. Therefore, the element that is oxidized in this reaction is Br.
In summary, the coefficients of the species in the balanced equation are:
- Cr^3+: 3
- Br^-: 3
- Cr^2+: 3
- BrO_3^-: 1
Water appears as a product with a coefficient of 2.
The element that is oxidized in this reaction is Br.
learn more about coefficient on :
https://brainly.com/question/1038771
#SPJ11
A city has a sewage treatment plant with a capacity of 100 MGD. The rate of input to the plant is 200 gallons per day per person. The present population of the city is 400,000 and is 5Y,000 more than its population 10 years ago. Assuming a linear growth, the existing plant would be adequate for how many more years (to the nearest year). Adequate for _______ more years
Hence, the plant will be adequate for 10 more years (to the nearest year).
Given, Rate of input to the plant = 200 gallons per day per person
Population of the city = 400,000
Let the population of the city 10 years ago be x gallons per day per person
Then, population of the city 5 years ago = x+ (400000-5000)
= x+ 395000
Thus, rate of input to the plant 10 years ago = 200x gallons per day
After 10 years, population will increase by 5000 and become 405000 people.
Therefore, rate of input to the plant after 10 years = 405000 × 200
= 81,000,000 gallons per day
Now, the plant with capacity of 100 MGD = 100×1000×365×24 gallons per year
= 876,000,000 gallons per year
Thus, the present plant would be adequate for = 876,000,000 ÷ 81,000,000
= 10.81 years
To know more about gallons visit:
https://brainly.com/question/31702678
#SPJ11
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.
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.
To know more about bending stress, visit:
https://brainly.com/question/30328948
#SPJ11
Use the References to access important values if needed for this question. Identify the species oxidized, the species reduced, the oxidizing agent and the reducing agent in the following electron-transfer reaction. 3Hg^2+(aq)+2Al(s)⟶3Hg(5)+2Al^3+ (aq) species oxidized species reduced oxidizing agent reducing agent As the reaction proceeds, electrons are transferred from
Species oxidized: Al(s), Species reduced: Hg^2+(aq), Oxidizing agent: Hg^2+(aq), Reducing agent: Al(s)
In the given electron-transfer reaction:
3Hg^2+(aq) + 2Al(s) ⟶ 3Hg^0 + 2Al^3+(aq)
Species oxidized: Al(s) (Aluminum)
Species reduced: Hg^2+(aq) (Mercury ion)
Oxidizing agent: Hg^2+(aq) (Mercury ion)
Reducing agent: Al(s) (Aluminum)
As the reaction proceeds, electrons are transferred from the reducing agent, Aluminum (Al), to the oxidizing agent, Mercury ion (Hg^2+). Aluminum is oxidized as it loses electrons and forms Al^3+ ions, while Mercury ions (Hg^2+) are reduced as they gain electrons and form elemental Mercury (Hg^0).
To learn more about Oxidizing agent vusut:
https://brainly.com/question/14041413
#SPJ11
A vertical curve below has a lower point (A) which exists at station (53+50) with elevation (1271.2 m). the back grade of (-4%) meet the forward grade of (+3.8%) at (PVI) station (52+00) with elevation (1261.5 m). determine the length of the curve with the stations of (PVC) and (PVT)?
A vertical curve is a road with changing elevation over a distance. A crest curve has an increasing slope, while a sag curve has a decreasing slope. Calculating the elevation of PVC and PVT stations using the formula, we get a length of 275.70 m. The equations for PVC and PVT give us the desired length.
A vertical curve is a curve on a road where the elevation is changing over a certain distance. A curve with an increasing slope is referred to as a crest curve, while a curve with a decreasing slope is referred to as a sag curve. The problem has given us the following details:
Lets' calculate the Elevation of PVC:
PVC station lies before the PVI, and it is a point of intersection between the back grade and the vertical curve. Let's assume that the length of the vertical curve is (L).The elevation of PVC can be calculated as follows:
Elevation of PVC = Elevation of Lower Point + Vertical Distance of PVC from Lower Point
Elevation of PVC = 1271.2 m - [(-4/100)(53.5 m - 52.0 m)]
Elevation of PVC = 1271.2 m - (-0.54 m)
Elevation of PVC = 1271.74 m
Let's calculate the Elevation of PVT:PVT station lies after the PVI, and it is a point of intersection between the forward grade and the vertical curve. The elevation of PVT can be calculated as follows:
Elevation of PVT = Elevation of PVI + Vertical Distance of PVT from PVI
Here, the vertical distance between the PVI and PVT is unknown, but it can be calculated using the following formula: Vertical Distance between PVI and
PVT = L/2 * [(BG + FG)/(BG * FG)]
Vertical Distance between PVI and
PVT = L/2 * [(-4 + 3.8)/(-4 * 3.8)]
Vertical Distance between PVI and
PVT = L/2 * [-0.0658]
Vertical Distance between PVI and PVT = -0.0329 * L
Substitute the above value of the vertical distance between PVI and PVT in the formula for calculating the elevation of PVT:
Elevation of PVT = 1261.5 m + [-0.0329 * L]
Let's equate the elevations of PVC and PVT:
Elevation of PVC = Elevation of PVT1271.74 m
= 1261.5 m + [-0.0329 * L]
Solve for L to determine the length of the vertical curve:L = 275.70 m
Therefore, the length of the curve with the stations of (PVC) and (PVT) is 275.70 m.
To know more about Elevation of PVC Visit:
https://brainly.com/question/32891538
#SPJ11
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
(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.
To know more about value here
https://brainly.com/question/1578158
#SPJ4
(i) List and describe one (1) physical and one (1) biological waste water quality parameter each, of concern during waste water treatment. What are their sources and impacts on the environment? [2+2+3+3 marks] 15000
Turbidity is a physical wastewater quality parameter and refers to the turbidity of water caused by suspended solids. It is generated from sources such as soil erosion, industrial waste, and wastewater itself.
When turbidity increases, it affects the environment by reducing the amount of solar radiation, impairing the growth of aquatic plants, and impairing the respiratory and feeding mechanisms of aquatic organisms. affects In addition, reduced heat dissipation can lead to higher water temperatures, further impacting aquatic life.
Biological oxygen demand (BOD), a water quality parameter for biological wastewater, measures the amount of dissolved oxygen consumed by microorganisms when breaking down organic matter. Elevated BOD levels cause oxygen starvation, harming fish and other aquatic organisms and unbalancing aquatic ecosystems.
To learn more about Turbidity:
https://brainly.com/question/31558188
#SPJ4
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:
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.
To learn more about Lagrange polynomial visit:
brainly.com/question/31473778
#SPJ11
Classify the following triangle as acute, obtuse, or right
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°.
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?
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.
To learn more about the balanced equations
https://brainly.com/question/31242898
#SPJ11
h. W solve y′=2xyy2−x2
The solution to the differential equation is given by y = ±√[(4x^2 + 4C)/(y^2 - 2x^2)], where C is a constant.To solve the differential equation y′=2xyy2−x2, we can use the method of separation of variables.
1. Rewrite the equation in a more convenient form:
y′ = 2xy(y^2 - x^2)
2. Separate the variables by moving all the terms involving y to one side and all the terms involving x to the other side:
y(y^2 - x^2)dy = 2x dx
3. Integrate both sides with respect to their respective variables:
∫y(y^2 - x^2)dy = ∫2x dx
4. Evaluate the integrals:
∫y(y^2 - x^2)dy = y^4/4 - x^2y^2/2 + C1
∫2x dx = x^2 + C2
5. Set the two resulting expressions equal to each other:
y^4/4 - x^2y^2/2 + C1 = x^2 + C2
6. Rearrange the equation to isolate y:
y^4/4 - x^2y^2/2 = x^2 + C2 - C1
7. Combine the constants:
C = C2 - C1
8. Multiply through by 4 to eliminate fractions:
y^4 - 2x^2y^2 = 4x^2 + 4C
9. Factor out y^2:
y^2(y^2 - 2x^2) = 4x^2 + 4C
10. Solve for y^2:
y^2 = (4x^2 + 4C)/(y^2 - 2x^2)
11. Take the square root of both sides:
y = ±√[(4x^2 + 4C)/(y^2 - 2x^2)]
Learn more about differential equation from the link https://brainly.com/question/1164377
#SPJ11
Armed with the knowledge that full compaction of a segregated concrete mix is impossible, outline the importance of maintaining a heterogeneous mixture with uniform distribution of the mixture constituents.
It is essential to maintain a heterogeneous mixture with uniform distribution of the mixture constituents since full compaction of a segregated concrete mix is impossible. The concrete mix is created by mixing cement, sand, water, and aggregates.
The constituents of concrete mix have different sizes, shapes, densities, and water absorption properties.As a result, they segregate due to gravity during the mixing and transportation process. The denser materials such as coarse aggregate sink to the bottom while the lighter ones such as cement tend to float to the top. This segregation leads to an uneven distribution of materials in the mixture.
As a result, during the pouring of the concrete, there is a probability of unevenness in the density of the final product.This will lead to various problems, for instance, the creation of cracks in the concrete, or weakening the structure and ultimately resulting in an unsafe and unusable product.
Therefore, it is vital to maintain a uniform distribution of the mixture constituents in the concrete mix. This is achievable by controlling the mixing process and ensuring that the concrete mix remains in a plastic state during transportation, placement, and compaction.
The homogeneous mixture provides a uniform consistency and density throughout the mixture. It results in a high-quality product that has consistent strength, durability, and resistance to cracking.
In conclusion, a heterogeneous mixture with a uniform distribution of mixture constituents is essential in ensuring the quality of the final product. In the construction industry, the quality of concrete is of utmost importance since it affects the strength and durability of the structure. It is important to achieve a homogeneous mixture to ensure the quality and strength of the final product.
To know more about uniform distribution visit:
brainly.com/question/30639872
#SPJ11
By what number should 6 2/9 be divided to obtain 4 2/3
Answer:
Step-by-step explanation:ns:
ANS: 4/3.
A 1.8 m concrete pipe 125 mm thick carries water at a velocity of 2.75 m/s. The pipe line is 1250 m long and a valve is used to close the discharge end. Use E_B =2.2GPa and E_c =21GPa. What will be the maximum rise in pressure at the valve due to water hammer? A)2273kPa B)2575kPa C)1328kPa D)1987kPa
The maximum rise in pressure at the valve due to water hammer is 2273 kPa. Therefore, option A) 2273k Pa is the correct option.
Water hammer is a phenomenon that occurs in pipelines when the valve is suddenly closed, causing the pressure to rise and the flow to decelerate.
To calculate the maximum pressure rise at the valve due to water hammer, we can use the following formula:
ΔP = (ρ * v * L)/2 * [(E_B/E_c) * (t_o/t_i)^2 - 1]
where:
ΔP = maximum pressure rise
ρ = density of water = 1000 kg/m³
v = velocity of water = 2.75 m/s
L = length of pipeline = 1250 mt_
o = outer radius of pipe = 1.8 m/2 = 0.9 mt_
i = inner radius of pipe = 0.9 m - 0.125 m
= 0.775 m (assuming 125 mm thick pipe)
t_o/t_
i = (1.8/2)/(0.9 - 0.125) = 2.286
E_B = modulus of elasticity of concrete = 2.2 G
Pae_c = modulus of elasticity of water = 21 G
Plug in the values and simplify:
ΔP = (1000 * 2.75 * 1250)/2 * [(2.2/21) * (0.9/0.775)^2 - 1]
ΔP ≈ 2273 kPa
Therefore, the maximum rise in pressure at the valve due to water hammer is 2273 kPa. Therefore, option A) 2273k Pa is the correct option.
To know more about pressure visit:
https://brainly.com/question/30673967
#SPJ11
4. Solve the difference equation using Z-transforms Yn+3 - 3yn+12yn = 3", yo = 2, ₁ = 1, y2 = 6.
We have to solve this equation using the Z-transform, we follow the following steps:
Step 1: Apply the Z-transform to the given difference equation, resulting in:
[tex]Z{Yn+2} - Z{yn} = 3/(1 - 3Z⁻¹ + 12Z⁻²)[/tex]
Step 2: Multiply the Z-transform of Yn by Z³ and subtract it from the Z-transform of Yn+3, resulting in:
[tex]Z³{Yn+3} - Z³{yn} = 3Z³{Yn+2}[/tex]
Step 3: Multiply the Z-transform of Yn+1 by Z and subtract it from the Z-transform of Yn+2, resulting in:
[tex]Z²{Yn+2} - Z{Yn+1} = Z²{Yn+1}[/tex]
Step 4: Simplify the equation to obtain:
[tex]Z²{Yn+2} = Z²{Yn+1} + Z{Yn+1} + 3Z⁻¹{Yn} - 12Z⁻²{Yn-1}[/tex]
Step 5: Substitute the values of Yo, Y1, and Y2 in the equation to find [tex]Z²{Y3}[/tex], which results in:
[tex]Z²{Y3} = 7 + 6Z⁻¹ - 12Z⁻²[/tex]
Step 6: Using the equation[tex]Z²{Yn+2} = Z²{Yn+1} + Z{Yn+1} + 3Z⁻¹{Yn} - 12Z⁻²{Yn-1}[/tex], substitute Z²{Y3} and simplify to find Z²{Y4}, which results in:
[tex]Z²{Y4} = 13 + 6Z⁻¹ - 6Z⁻²[/tex]
Step 7: Apply the inverse Z-transform to Z²{Y4} to obtain the final solution, which is:
Y4 = 13δn - 6n + 6(1/2)ⁿ
Therefore, the solution of the difference equation using Z-transforms is Y4 = 13δn - 6n + 6(1/2)ⁿ.
To know more about Z-transform visit:
https://brainly.com/question/11709244
#SPJ11
Categorise the following emissions to their respective scopes
under NGER:
Wastewater treatment
On-site fuel combustion for a bus company
Methane is produced from anaerobic digestion processes
Waste d
On the other hand, waste disposal emissions are typically classified as Scope 3, which encompasses indirect emissions occurring in the value chain, including waste disposal activities outside the reporting organization's direct control.
What are the categorizations of the following emissions under NGER?Under the National Greenhouse and Energy Reporting (NGER) framework, emissions are categorized into three scopes based on the source and control of emissions.
Scope 1 includes direct emissions from sources owned or controlled by the reporting organization, such as on-site fuel combustion for a bus company and methane produced from anaerobic digestion processes.
Wastewater treatment emissions can also fall under Scope 1 if the treatment facility has on-site fuel combustion or anaerobic digestion processes.
Learn more about encompasses indirect
brainly.com/question/13753880
#SPJ11
Analia is a school district manager. Here are some details about two schools in her district. Analia wants to know which school has higher athletic achievement relative to the budget per student. Determine which school has higher athletic achievement relative to the budget per student, according to the two definitions. Did you get the same result for both definitions?
Answer:
The given information does not provide numerical data to compare the two schools' budget per student and athletic achievement. Therefore, it is not possible to determine which school has a higher athletic achievement relative to the budget per student
Step-by-step explanation:
100 points and mark brainly
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.
For more questions on frequency
https://brainly.com/question/27820465
#SPJ8
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.
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%.
Know more about hydrogen here:
https://brainly.com/question/24433860
#SPJ11
Find the annual percentage yield (APY) in the following situation. A bank offers an APR of 3.3% compounded monthly. The annual percentage yield is___%.
Calculating this expression will give you the Annual Percentage Yield. The calculation, the APY in this situation is approximately 3.357%.
To find the Annual Percentage Yield (APY) when given the Annual Percentage Rate (APR) compounded monthly, we can use the following formula:
[tex]APY = (1 + (APR / n))^{n - 1[/tex]
Where:
APY is the Annual Percentage Yield
APR is the Annual Percentage Rate
n is the number of compounding periods per year
In this case, the APR is 3.3% and it is compounded monthly,
so n = 12 (since there are 12 months in a year).
Substituting the values into the formula:
[tex]APY = (1 + (0.033 / 12))^{12} - 1[/tex]
Calculating this expression will give you the Annual Percentage Yield.
By performing the calculation, the APY in this situation is approximately 3.357%.
To know more about Annual Percentage Yield visit:
https://brainly.com/question/30774234
#SPJ11
A bank offers an APR of 3.3% compounded monthly. The annual percentage yield is 3.46%.
The annual percentage yield (APY) represents the total amount you will earn on your investment, taking into account compounding. To find the APY when the bank offers an APR of 3.3% compounded monthly, we need to use the following formula:
APY = (1 + (APR / n))^n - 1
where APR is the annual percentage rate and n is the number of compounding periods in a year. In this case, the APR is 3.3% and it is compounded monthly, so n = 12 (since there are 12 months in a year).
Plugging the values into the formula:
APY = (1 + (0.033 / 12))^12 - 1
Calculating the values within the parentheses first:
APY = (1 + 0.00275)^12 - 1
Evaluating the exponential term:
APY = (1.00275)^12 - 1
Calculating the result:
APY = 1.0346 - 1
APY = 0.0346
Therefore, the annual percentage yield (APY) in this situation is 3.46%.
In summary, the APY when a bank offers an APR of 3.3% compounded monthly is 3.46%.
Learn more about percentage
https://brainly.com/question/32197511
#SPJ11
A. A plant treats an ore containing Pyrite (FeS2), Arsenopyrite (FeAss) and chalcopyrite (CuFeS2). After ore upgrading and analysis, the Arsenic (As), Copper (Cu) and Iron (Fe) concentration in the concentrate were 9.6%, 13.5% and 63.3% respectively. What is the concentration of pyrite, arsenopyrite, chalcopyrite in the concentrate? (Molar masses of As, Cu, Fe and Sare 74.92 g/mol, 63.55 g/mol, 55.85 g/mol and 32.07 g/mol respectively). (15 marks) B. 150 tph of material is subjected screening to separate the oversize from the undersize materials. If the cut-point size for the feed, oversize and undersize are 0.3, 0.85 and 0.15 respectively, calculate the recovery of oversize and undersize materials. Also determine the overall screen efficiency. (15 marks) C. Calculate how many kg of magnetite must be added to 1L of water to make a slurry with a pulp density of 1.9 g/cm3. Assume density of magnetite is 5.2g/cm3
A. The concentration of pyrite, arsenopyrite, and chalcopyrite in the concentrate is:
- Pyrite (FeS2): 2.268 mol
- Arsenopyrite (FeAsS): 0.128 mol
- Chalcopyrite (CuFeS2): 0.212 mol
B. The recovery of oversize materials is 80%, the recovery of undersize materials is 20%, and the overall screen efficiency is 100%.
C. Approximately 0.9 grams of magnetite must be added to 1 L of water to make a slurry with a pulp density of 1.9 g/cm3.
A. To find the concentration of pyrite, arsenopyrite, and chalcopyrite in the concentrate, we need to calculate the amount of each mineral present based on their respective concentrations of arsenic (As), copper (Cu), and iron (Fe).
First, let's assume we have 100 grams of the concentrate. From the given concentrations, we can calculate the weight of each element in the concentrate as follows:
- Arsenic (As): 9.6% of 100 g = 9.6 g
- Copper (Cu): 13.5% of 100 g = 13.5 g
- Iron (Fe): 63.3% of 100 g = 63.3 g
Now, we need to convert the weight of each element to moles by dividing it by its molar mass:
- Arsenic (As): 9.6 g / 74.92 g/mol = 0.128 mol
- Copper (Cu): 13.5 g / 63.55 g/mol = 0.212 mol
- Iron (Fe): 63.3 g / 55.85 g/mol = 1.134 mol
Since pyrite (FeS2) contains 2 moles of iron (Fe) for every 1 mole of sulfur (S), the concentration of pyrite can be calculated as:
- Pyrite (FeS2): 2 * 1.134 mol = 2.268 mol
Similarly, arsenopyrite (FeAsS) contains 1 mole of arsenic (As), 1 mole of iron (Fe), and 1 mole of sulfur (S), so the concentration of arsenopyrite can be calculated as:
- Arsenopyrite (FeAsS): 0.128 mol
Chalcopyrite (CuFeS2) contains 1 mole of copper (Cu), 1 mole of iron (Fe), and 2 moles of sulfur (S), so the concentration of chalcopyrite can be calculated as:
- Chalcopyrite (CuFeS2): 0.212 mol
Therefore, the concentration of pyrite, arsenopyrite, and chalcopyrite in the concentrate is:
- Pyrite (FeS2): 2.268 mol
- Arsenopyrite (FeAsS): 0.128 mol
- Chalcopyrite (CuFeS2): 0.212 mol
B. To calculate the recovery of oversize and undersize materials, as well as the overall screen efficiency, we need to consider the feed, oversize, and undersize materials' cut-point sizes.
The recovery of oversize materials is the percentage of material larger than the cut-point size that passes through the screen. In this case, the cut-point size for oversize is 0.85. If the oversize material passing through the screen is 120 tph, we can calculate the recovery as:
- Recovery of oversize = (120 tph / 150 tph) * 100 = 80%
The recovery of undersize materials is the percentage of material smaller than the cut-point size that passes through the screen. In this case, the cut-point size for undersize is 0.15. If the undersize material passing through the screen is 30 tph, we can calculate the recovery as:
- Recovery of undersize = (30 tph / 150 tph) * 100 = 20%
The overall screen efficiency is the percentage of material passing through the screen compared to the total feed. If the total feed is 150 tph and the material passing through the screen is 150 tph, we can calculate the overall screen efficiency as:
- Overall screen efficiency = (150 tph / 150 tph) * 100 = 100%
C. To calculate the amount of magnetite required to make a slurry with a pulp density of 1.9 g/cm3, we need to use the density of magnetite and the volume of water.
Given:
- Density of magnetite = 5.2 g/cm3
- Pulp density = 1.9 g/cm3
- Volume of water = 1 L
First, we need to determine the mass of water by multiplying the volume by its density:
- Mass of water = Volume of water * Density of water = 1 L * 1 g/cm3 = 1000 g
Now, let's assume we need x grams of magnetite. The total mass of the slurry will be the sum of the mass of water and the mass of magnetite:
- Total mass of slurry = Mass of water + Mass of magnetite = 1000 g + x g
Since the pulp density is given as 1.9 g/cm3, the volume of the slurry can be calculated as the total mass of the slurry divided by the pulp density:
- Volume of slurry = Total mass of slurry / Pulp density = (1000 g + x g) / 1.9 g/cm3
Since the volume of slurry is given as 1 L, we can equate the volume equation to 1 L and solve for x:
- (1000 g + x g) / 1.9 g/cm3 = 1 L
- 1000 g + x g = 1.9 g/cm3 * 1 L
- x g = 1.9 g/cm3 * 1 L - 1000 g
- x g = 1.9 g - 1000 g
- x g = 0.9 g
Therefore, approximately 0.9 grams of magnetite must be added to 1 L of water to make a slurry with a pulp density of 1.9 g/cm3.
In summary:
A. The concentration of pyrite, arsenopyrite, and chalcopyrite in the concentrate is:
- Pyrite (FeS2): 2.268 mol
- Arsenopyrite (FeAsS): 0.128 mol
- Chalcopyrite (CuFeS2): 0.212 mol
B. The recovery of oversize materials is 80%, the recovery of undersize materials is 20%, and the overall screen efficiency is 100%.
C. Approximately 0.9 grams of magnetite must be added to 1 L of water to make a slurry with a pulp density of 1.9 g/cm3.
Learn more about efficiency from given link: https://brainly.com/question/13222283
#SPJ11
Zara and H&M Through channel differentiati ntiation differentiate on channel's coverage, expertise, performance, e Through people differentiation - differentiate on firm's people or employees (friendly, helpful, better trained, etc...) Through image differentiation - differentiate on company's brand image (including reputation and history
Zara and H&M differentiate themselves through their channel coverage, expertise, employee quality, and brand image. Zara stands out with its extensive global presence, supply chain efficiency, friendly staff, and reputation for fast fashion. H&M, on the other hand, emphasizes affordability, sustainability, well-trained employees, and a commitment to ethical fashion. These differentiating factors contribute to their unique positions in the fashion industry.
Zara and H&M differentiate themselves through various aspects of their channels, people, and brand image. In terms of channel differentiation, Zara and H&M differ in their coverage and expertise. Zara has a wide global presence with numerous stores in prime locations, offering a convenient shopping experience for customers. They also excel in their supply chain management, allowing them to quickly respond to fashion trends and deliver new products to stores. On the other hand, H&M has an extensive network of stores as well but focuses on a broader customer base with more affordable fashion options.
Through people differentiation, both Zara and H&M strive to provide excellent customer service. Zara's employees are known for their friendly and helpful attitude, creating a positive shopping experience. H&M also invests in employee training to ensure their staff is knowledgeable and can assist customers effectively.
Regarding image differentiation, Zara and H&M have distinct brand images. Zara is known for its fast-fashion concept, offering trendy and up-to-date designs. They have built a reputation for innovation and quick turnaround times. H&M, on the other hand, focuses on sustainability and ethical practices, emphasizing their commitment to responsible fashion.
Learn more about brand image
https://brainly.com/question/12495783
#SPJ11
Use the standard electrochemical series given in your e-text to identify whether the following reactions would take place or not. If it takes place, please write the complete balanced reaction (starting with half reactions) and explain the reaction in your own words. a. Can Cd metal dissolve in HCl ? b. Can O_2 oxidize Fe^2⋅ to Fe^3+? c. Can Ni reduce Sn^2+? Will it reduce Co^2+ ? d. Is Cl_2gas a stronger oxidizing agent than O_2 gas? e. Can F_2 gas oxidize water?
a. Cd metal will not dissolve in HCl.
b. O₂ can oxidize Fe²⁺ to Fe³⁺.
c. Ni can reduce Sn²⁺ but cannot reduce Co²⁺.
d. Cl₂ gas is a stronger oxidizing agent than O₂ gas.
e. F₂ gas can oxidize water
To determine whether the given reactions would take place, we can use the standard electrochemical series. The electrochemical series ranks the elements and ions based on their tendency to undergo reduction or oxidation reactions. In general, a reaction will occur if the species being oxidized is higher in the series than the species being reduced.
a. Looking at the electrochemical series, we find that Cd is below hydrogen (H+) in the series. This means that Cd has a lower tendency to undergo oxidation compared to hydrogen. Therefore, Cd metal will not dissolve in HCl.
b. In the electrochemical series, O₂ is above Fe²⁺. This indicates that O₂ has a higher tendency to undergo reduction compared to Fe²⁺. Therefore, O₂ can oxidize Fe²⁺ to Fe³⁺. The balanced half-reactions and the overall reaction can be written as follows:
Half-reaction at the cathode (reduction): O₂ + 4H⁺ + 4e⁻ → 2H₂O
Half-reaction at the anode (oxidation): Fe²⁺ → Fe³⁺ + e⁻
Overall reaction: 2Fe²⁺ + O₂ + 4H⁺ → 2Fe³⁺ + 2H₂O
c. Referring to the electrochemical series, Ni is above Sn²⁺ but below Co²⁺. This means that Ni has a higher tendency to undergo reduction compared to Sn²⁺ but a lower tendency compared to Co²⁺. Therefore, Ni can reduce Sn²⁺ but cannot reduce Co²⁺.
d. Comparing Cl₂ and O₂ in the electrochemical series, we find that Cl₂ is higher than O₂. This indicates that Cl₂ has a higher tendency to undergo reduction compared to O₂. Therefore, Cl₂ gas is a stronger oxidizing agent than O₂ gas.
e. Looking at the electrochemical series, we see that F₂ is above O₂. This indicates that F₂ has a higher tendency to undergo reduction compared to O₂. Therefore, F₂ gas can oxidize water. The balanced half-reactions and the overall reaction can be written as follows:
Half-reaction at the cathode (reduction): F₂ + 2e⁻ → 2F⁻
Half-reaction at the anode (oxidation): 2H₂O → O₂ + 4H⁺ + 4e⁻
Overall reaction: F₂ + 2H₂O → 2F⁻ + O₂ + 4H⁺
Learn more about oxidation at https://brainly.com/question/31967581
#SPJ11
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?
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.
To know more about sulfuric acid visit:
brainly.com/question/12125396
#SPJ11
Question 3 A bored and snowbound chemist fills a balloon with 321 g water vapor, temperature 102 °C. She takes it the snowy outdoors and lets it pop, releasing the vapor, which drops in temperature to the match the outdoor temperature of -12.0 °C. What is the total energy change for the water? Give your answer with unit kJ and 3 sig figs. Heat Capacity of H₂0 as: Solid 2.05 J/(g K) Liquid 4.18 J/(g K). Vapor 2.08 J/(g K) Molar Heat of Fusion for H₂O: 6.02 kJ/mol Molar Heat of Vaporization for H₂0: 40.7 kJ/mol Tbp = 100.0 °C Tfp = 0.00 °C 0 / 2 pts 977 kJ
The total energy change for the water when the balloon pops and the vapor drops in temperature to match the outdoor temperature is -977 kJ.
To find the total energy change, we need to consider the energy changes during the phase transitions and temperature change.
First, we need to calculate the energy change when the water vapor condenses into liquid water. We use the molar heat of vaporization (40.7 kJ/mol) to calculate the energy change per mole of water vapor. Since we have 321 g of water vapor, we need to convert it to moles by dividing by the molar mass of water (18.015 g/mol). Then, we multiply the number of moles by the molar heat of vaporization to get the energy change during condensation.
Next, we need to consider the energy change when the liquid water freezes into ice. We use the molar heat of fusion (6.02 kJ/mol) to calculate the energy change per mole of water. Again, we convert the mass of water (321 g) to moles and multiply by the molar heat of fusion.
Finally, we consider the energy change due to the temperature change from 102 °C to -12.0 °C. We calculate the heat capacity of water in the vapor phase and the liquid phase using the given values (2.08 J/(g K) and 4.18 J/(g K) respectively). Then, we multiply the heat capacity by the mass of water (321 g) and the temperature change (-12.0 °C - 102 °C) to get the energy change due to temperature change.
Adding all these energy changes together, we get a total energy change of -977 kJ. The negative sign indicates that the system has lost energy during these processes.
Know more about heat of vaporization here:
https://brainly.com/question/31804446
#SPJ11
Select the correct answer.
Which statement is false?
A. The inequality sign always opens up to the larger number.
The greater number in an inequality is always above the other number on the vertical number line.
The smaller number in an inequality is always located to the left of the other number on the horizontal number line.
OD. The inequality sign always opens up to the smaller number.
B.
C.
Reset
Next
What is the density of a certain liquid whose specific weight is 99.6 lb/ft3? Express your answer in g/cm³. 2. A moving plate is 15mm from a fixed plate. If the moving plate requires a force per unit area of 15 Pa to maintain a speed of 0.70 m/s, determine the viscosity of the substance between the two plates.
Density of a certain liquid:Specific weight is also called the weight density of a liquid and it's given as .Therefore, the viscosity of the substance between the two plates is 0.32 Pa.s.
w = ρgwhere
w = weight density,
ρ = density of the liquid,
g = acceleration due to gravity.
Now, we can express the density of the liquid as;
ρ = w/g = 99.6 lb/ft³ / 32.2 ft/s²
= 3.1 kg/m³
Now, we can convert the density from kg/m³ to g/cm³ as follows;
ρ = 3.1 kg/m³ x 1000 g/kg / (100 cm/m)³
= 0.0031 g/cm³
Therefore, the density of the certain liquid is 0.0031 g/cm³2. Viscosity of the substance between two plates:We can find the viscosity of the substance between the two plates by using the formula;
F/A = μv/dwhere F/A is the shear stress,
μ is the viscosity of the substance,
v is the velocity of the moving plate,
d is the distance between the plates. Substituting the values given into the formula, we have;
15 Pa = μ(0.70 m/s) / 0.015 mμ
= 15 Pa x 0.015 m / 0.70 m/sμ
= 0.32 Pa.s
To know more about weight visit:
https://brainly.com/question/28532216
#SPJ11