Answer:
7/23
Step-by-step explanation:
Each answer is 1.5/23 less than the previous
17/46 - 1.5/23 = 17/46 - 3/46 = 14/46 = 7/23
The radius of a spherical balloon a is increasing at a constant rate of 0.1 cm/s. another balloon, b, is being continuously deflated in such a way that the total volume of a and b remains constant. suppose that at the beginning the radius of a is 10 cm and that of b is 9 cm. find the rate of change of the radius of b when the radius of a is 12 cm
Let [tex]r_A[/tex] and [tex]r_B[/tex] be the respective radii of balloons A and B. If the fixed total volume is V, then
[tex]V = \dfrac{4\pi}3\left({r_A}^3 + {r_B}^3\right)[/tex]
and knowing [tex]r_A=10\,\rm cm[/tex] and [tex]r_B=9\,\rm cm[/tex] at the start, we have V = 6916π/3 cm³. Then when [tex]r_A=12\,\rm cm[/tex], the radius of the other sphere is [tex]r_B=1\,\rm cm[/tex].
Differentiating both sides with respect to time t gives a relation between the rates of change of the radii:
[tex]0 = 4\pi \left({r_A}^2 \dfrac{dr_A}{dt} + {r_B}^2 \dfrac{dr_B}{dt}\right) \implies \dfrac{dr_B}{dt} = -\left(\dfrac{r_A}{r_B}\right)^2 \dfrac{dr_A}{dt}[/tex]
We're given [tex]\frac{dr_A}{dt} = 0.1\frac{\rm cm}{\rm s}[/tex] the whole time. At the moment [tex]r_A=12\,\rm cm[/tex], the radius of balloon B is changing at a rate of
[tex]\dfrac{dr_B}{dt} = -\left(\dfrac{12\,\rm cm}{1\,\rm cm}\right)^2 \left(0.1\dfrac{\rm cm}{\rm s}\right) = \boxed{-14.4 \dfrac{\rm cm}{\rm s}}[/tex]
Melissa wants to make a table representing the area of her vegetable
garden for a variety of different lengths of the tomato patch. she uses
her area expression to create the table.
complete the table by typing the correct answer in each box. use
numerals instead of words. do not round your decimal answers.
The correct numerical values that should be used in completing Melissa's table are:
13√2 or 18.384776 feet.42.25 square feet.12.13466 feet.49 square feet.Note: From the information provided in the table shown in the image attached below, we can deduce that Melissa's vegetable garden has a square shape.
How to calculate the area of a square?Mathematically, the area of a square can be calculated by using this formula;
A = x²
Where:
A is the area of a square.x is the side length of a square.Substituting the given parameters into the formula, we have;
338 = x²
x = √338
x = √2 × √169
x = 13√2 or 18.384776 feet.
For row 2, we have:
A = 6.5²
A = 42.25 square feet.
For row 3, we have:
147.25 = x²
x = √147.25
x = 12.13466 feet.
For row 4, we have:
A = 7²
A = 49 square feet.
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Let (-3, 5) be a point on the terminal side of 0.
Find the exact values of cos0, csc 0, and tan 0.
Answer:
[tex]\displaystyle \large{\cos \theta = \dfrac{-3}{\sqrt{34}} = -\dfrac{3\sqrt{34}}{34}}\\\\\displaystyle \large{\csc \theta = \dfrac{\sqrt{34}}{5}}\\\\\displaystyle \large{\tan \theta = -\dfrac{5}{3}}[/tex]
Step-by-step explanation:
Accorded to trigonometric formula, we know that:
[tex]\displaystyle \large{\cos \theta = \dfrac{x}{r}}\\\\\displaystyle \large{\csc \theta = \dfrac{1}{\sin \theta} = \dfrac{1}{\frac{y}{r}} = \dfrac{r}{y}}\\\\\displaystyle \large{\tan \theta = \dfrac{\sin \theta}{\cos \theta} = \dfrac{y}{x}}[/tex]
We know what x and y are but not yet knowing what r is. We can find r (radius) using the formula:
[tex]\displaystyle \large{r=\sqrt{x^2+y^2}}[/tex]
Input x = -3 and y = 5 in.
[tex]\displaystyle \large{r=\sqrt{(-3)^2+(5)^2}}\\\\\displaystyle \large{r=\sqrt{9+25}}\\\\\displaystyle \large{r=\sqrt{34}}[/tex]
Hence, radius is √34 and we know all we need now. Substitute x = -3, y = 5 and r = √34 in respective areas.
[tex]\displaystyle \large{\cos \theta = \dfrac{-3}{\sqrt{34}} = -\dfrac{3\sqrt{34}}{34}}\\\\\displaystyle \large{\csc \theta = \dfrac{\sqrt{34}}{5}}\\\\\displaystyle \large{\tan \theta = -\dfrac{5}{3}}[/tex]
These are the answers to your question. Please let me know if you have any questions regarding my answer or explanation!
Find the equation
of the line
that goes through (2,4) and has
a slope of -3.
The equation of the line that goes through (2,4) and has a slope of -3 y = -3x + 10
How to find the equation of a line with slope?The equation of a line can be represented as follows;
y = mx + b
where
m = slopeb = y-interceptTherefore,
y = -3x + b
Let's find b
hence,
4 = -3(2) + b
4 = -6 + b
b = 4 + 6
b = 10
Therefore,
y = -3x + 10
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In triangle RTS △RTS shown below, point U is on
ST, and point V is on RT so that angle RST UVT∠RST≅∠UVT. If ST=13 VT=5, and RV=13.2, find the length of TU. Figures are not necessarily drawn to scale.
Answer: 7
Step-by-step explanation:
As [tex]\angle T \cong \angle T[/tex] by the reflexive property, we know that [tex]\triangle RST \sim \triangle UVT[/tex] by AA.
Since corresponding sides of similar triangles are proportional,
[tex]\frac{UT}{5}=\frac{13.2+5}{13}\\UT=(5)\left(\frac{13.2+5}{13} \right)=\boxed{7}[/tex]
What is the median of this data set? 15, 14, 6, 10, 7, 15, 7, 8
The median of this set is:
9
A median is:In statistics and probability theory, the median is the value separating the higher half from the lower half of a data sample, a population, or a probability distribution. For a data set, it may be thought of as "the middle" value. The basic feature of the median in describing data compared to the mean is that it is not skewed by a small proportion of extremely large or small values, and therefore provides a better representation of a "typical" value. Median income, for example, may be a better way to suggest what a "typical" income is, because income distribution can be very skewed. The median is of central importance in robust statistics, as it is the most resistant statistic, having a breakdown point of 50%: so long as no more than half the data are contaminated, the median is not an arbitrarily large or small result.
HAVE A NICE DAY!
Answer:
Step-by-step explanation:
Remark
You always have to put the data in order to answer a question like this one.
6 7 7 8 10 14 15
The median is the middle number. In this case it is 8. There are 3 numbers below 8 and 3 numbers above 8, so 8 is the median.
Answer: 8
A bakery sold a total of 300 cupcakes in a day, and 57 of them were mocha flavored. What percentage of cupcakes sold that day were mocha flavored?
What numbers between 61 and 107 that is multiple of 5, 8, and 10?
========================================================
Explanation:
We'll need to find the LCM of 5, 8 and 10.
List out the prime factorization of the three numbers.
5 = 1*58 = 2^310 = 2*5The unique prime factors are 2 and 5. The '1' isn't a prime number, so we can ignore it.
The '2' has an exponent of 3 as the largest exponent, meaning 2^3 is part of the LCM. The '5' has the largest exponent of 1. So 5^1 = 5 is also part of the LCM
LCM = 2^3*5 = 8*5 = 40
List out the multiples of 40
40, 80, 120, 160, ...
The number 80 is the only multiple between 61 and 107
What is 1 2/3 multiple 2/3
Answer:
[tex]1\frac{1}{9}[/tex]
Step-by-step explanation:
Given the following question:
[tex]1\frac{2}{3} \times\frac{2}{3}[/tex]
In order to multiply the two, we have to convert the mixed number into a improper fraction and then multiply the numerator by the numerator, the denominator by the denominator.
[tex]1\frac{2}{3} =3\times1=3+2=\frac{5}{3}[/tex]
[tex]\frac{5}{3} \times\frac{2}{3}[/tex]
[tex]5\times2=10[/tex]
[tex]3\times3=9[/tex]
[tex]=\frac{10}{9}[/tex]
Convert the improper fraction into a mixed number:
[tex]\frac{10}{9}[/tex]
[tex]\frac{10}{9} =10\div9=1\frac{1}{9}[/tex]
[tex]=1\frac{1}{9}[/tex]
Your answer is "1 1/9."
Hope this helps.
If g (x) = one-third x and 3 x (StartFraction x Over 3 EndFraction), which expression could be used to verify that (one-third x) (3 x) is the inverse of One-third (3 x)?
The expression that can be used to verify that (one-third x) (3 x) is the inverse of One-third (3 x) is 1/3(3x).
What is an expression?It should be noted that an expression is a collection of symbols that can be used to jointly express a quantity.
From the information given, g(x) = 1/3x + 3x. Here, the expression that can be used to verify that (one-third x) (3 x) is the inverse of One-third (3 x) is 1/3(3x). The inverse in this case is the opposite of the function expressed.
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Answer:
c
Step-by-step explanation:
edge 2022
Question 3 of 5
Drag the tiles to the boxes to form correct pairs. Not all tiles will be used.
Match each person to the contribution they made to the field of geometry.
Leonhard Euler
Maryam Mirzakhani
Rene Descartes
illustrated geometry of iterations
proof of complex functions
developed geometry of curved surfaces
Benoit Mandelbrot
The Correct match up is:
Leonhard Euler - developed geometry of curved surfacesWho made proof of complex functions?The first proof of complex numbers was done by an Italian mathematicians known to be Girolamo Cardano and Raphael Bombelli.
The person who illustrated geometry of iterations is Gaston Maurice Julia.
Benoit Mandelbrot is known to have discover fractal geometry. Rene Descartes is known to be famous for making a connection between geometry and algebra.
Therefore, from the above, you can see that the only correct matchup is Leonhard Euler - developed geometry of curved surfaces
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Answer :
proof of complex functions --- > Maryam Mirzakhani
illustrated geometry of iterations --- > Benoit Mandelbrot
developed geometry of curved surfaces --- > Leonhard Euler
In the 15th century, Rene Descartes developed the field of analytical geometry by using functions to describe lines and curves in a coordinate plane. In the 18th century, Leonhard Euler extended geometric analysis to curved surfaces. in the late 20th century, Benoit Mandelbrot used computers to illustrate the geometry of iterations (fractals). In 2014, Maryam Mirzakhani received the Fields Medal for her work on geometric proofs involving complex functions.
A jewelry store has 88 rings to display they arrange the rings in a even rose how many rings are in each row
Answer:
2,4,8,11,22, or 44
Step-by-step explanation:
To figure out how many rings would be in each full row with no leftovers, we need to find all the factors of 88 (outside of 1 and 8) which are 2,4,8,11,22, and 44. Since the question does not give any more information on how big the rows need to be, I can't narrow this down any further, however if I had to choose I would say rows of 8 by 11 would be the best.
Hope this helps! :)
The cylinder in a sphere have the same radius for the height of the cylinder is equal to the diameter of the spear select the expression that describes the volume of the cylinder that is not occupied by the sphere
The volume of the cylinder that is not occupied by the sphere is 2πr³/3
Since the object is a sphere in a cylinder, we need to know the volume of sphere and cylinder.
What is volume of a cylinder?The volume of a cylinder is given by V '= πr²h where
r = radius of cylinder and h = height of cylinder.Since the height of the cylinder equals the diameter of the sphere, h = 2r
So, V' = πr²h
V' = πr² × 2r
V' = 2πr³
What is volume of sphere?
The volume of a sphere of radius r is given by V = 4πr³/3
Volume of cylinder not occupied by sphere
The volume of the cylinder not occupied by the sphere is V" = V' - V
= 2πr³ - 4πr³/3
= (6πr³ - 4πr³)/3
= 2πr³/3
So, the volume of the cylinder that is not occupied by the sphere is 2πr³/3
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There are two containers out of which one can hold 31/2 litres of oil while the other can hold 22/3 litres of oil. Suppose there are 4 containers of the first type and 9 containers of the second type. The volume of oil required to fill both the containers is litres.
please help in 5 mins sssssssss
The volume of the oil required to fill both containers will be 128 liters.
What is volume?
Volume is defined as the space occupied by any object in the three-Dimensions. All three parameters are required for the volume like length, width, and height of cube or cubied.
Given that:-
There are two containers out of which one can hold 31/2 liters of oil while the other can hold 22/3 liters of oil. Suppose there are 4 containers of the first type and 9 containers of the second type.The volume of oil in the first container is [tex]\dfrac{31}{2}[/tex] liters so for four containers the volume will be:-
V = 4 x [tex]\dfrac{31}{2}[/tex]
V = 2 x 31 = 62 liters
The volume of oil in the second container is [tex]\dfrac{22}{3}[/tex] liters.
V = 9 x [tex]\dfrac{22}{3}[/tex]
V = 3 x 22 = 66 liters
So total volume of oil will be calculated as:-
Total volume = 66 + 62 = 128 liters
Therefore the volume of the oil required to fill both containers will be 128 liters.
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Consider a circle whose equation is x2 + y2 – 2x – 8 = 0. Which statements are true? Select three options. The radius of the circle is 3 units. The center of the circle lies on the x-axis. The center of the circle lies on the y-axis. The standard form of the equation is (x – 1)² + y² = 3. The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.
Completing the squares, the correct statements regarding the equation of the circle are given by:
The radius of the circle is 3 unitsThe center of the circle lies on the x-axis.The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.What is the equation of a circle?The equation of a circle of center [tex](x_0, y_0)[/tex] and radius r is given by:
[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]
In this problem, the equation is given by:
x² + y² - 2x - 8 = 0.
Completing the squares:
(x - 1)² + y² = 8 + 1²
(x - 1)² + y² = 9.
Hence the center is (1,0), the radius is 3, and the correct statements are:
The radius of the circle is 3 unitsThe center of the circle lies on the x-axis.The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.More can be learned about the equation of a circle at https://brainly.com/question/24307696
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graph the zeros of the polynomial function p(x)=(x-1)^2(x+3)(x-2)
Answer:
69
Step-by-step explanation:
420
$560 is divided into two parts in the ratio 3:4. What is the larger amount?
Answer:
$320
Step-by-step explanation:
1. 3x + 4x = 560 (since they are ratios, x would be the same amount)
2. 7x = 560
3. x = 80
This means that 3 and 4 should be multiplied by 80 to get the $ amount. The amounts are $240 (3*80) and $320 (4*80).
So, the larger amount if $320.
12e < -96
Solving one step inequalities
(Please help! I need an actual answer not if it’s true or false / unidentified)
HELP ASAPP 10 POINTSSSSS
Answer:
209 cubic mm.
Step-by-step explanation:
Formula for volume of cone:
[tex]V=\frac{1}{3} \pi r^2 h[/tex]
Now let's plug in the values.
[tex]V=\frac{1}{3} \pi 5^2 8[/tex]
[tex]V=\frac{1}{3} \pi 200[/tex]
[tex]V=\frac{200}{3} \pi[/tex]
[tex]V=209.4395...[/tex]
Round to the nearest cubic mm and the volume is 209 cubic mm.
Answer:
209.333
Step-by-step explanation:
→ State the area for the volume for a cone
1/3 × π × r² × h
→ Substitute in the numbers
1/3 × 3.14 × 5² × 8
→ Evaluate
209.333
Please provide a step by step.
Answer:
5. m<STP = 134
6. m<PTS = 158
Step-by-step explanation:
5. Since ray TR bisects <PTS, angles PTR and STR are congruent.
m<PTR = m<STR
3x - 8 = 2x + 17
Subtract 2x from both sides.
x - 8 = 17
Add 8 to both sides.
x = 25
m<STP = 2m<PTR
m<STP = 2(3x - 8)
m<STP = 2(3 × 25 - 8)
m<STP = 2(67)
m<STP = 134
6.
2m<PTR = m<PTS
2(x - 23) = x + 56
2x - 46 = x + 56
x = 102
m<PTS = x + 56
m<PTS = 102 + 56
m<PTS = 158
•function notation•
does anyone know how to do this. please help.
f(3) = 16
Step-by-step explanation:Function notation is used to express a rule in terms of x and f(x), where x is independent and f(x) is dependent.
Pronunciation of Function Notation
To use function notation it is important to know how to express the function in words.
The function "f(x) = 3x + 7" would be pronounced "F of X equals three X plus 7."
So, the function is "F of" whatever variable or value is within the parentheses.
Use of Function Notation
The function y=x is similar to the function f(x)=x. As a matter of fact, when graphed they both work the same way, but the function notation seen in the question allows us to see the value of x.
This is because the value in the parentheses is the value of x. So, in this situation, the question asks what is the value of the function when x equals 3.
Solving for f(3)
To solve this function, all we have to do is plug 3 in for x and evaluate.
f(3) = 3(3) + 7First, multiple 3*3
f(3) = 9 + 7Next, add 7
f(3) = 16Grade 11 Math:
Application
3. When Jennifer turned 12 years old, her grandmother gave her $100. Jennifer deposited
the money into a savings account that paid 3.5%/a compounded annually. Since then,
Jennifer’s grandmother has made an automatic deposit of $100 into her account every
year.
a) What is the total amount of the annuity on Jennifer’s 18th birthday? [3 marks]
b) How much of the annuity is interest earned? [1 mark]
The future value of the annuity on Jennifer’s 18th birthday is $655.02
The interest earned is $55.02.
What is the future value of the annuity?An annuity is a fixed payment of money over a specified period of time.
The formula for determining the future value of the annuity is: yearly deposit x annuity factor
Annuity factor = {[(1+r)^n] - 1} / r
Where:
r = interest rate = 3.5%n = number of years = 18 - 12 = 6Future value of the annuity: $100 x [{(1.035^6) - 1} / 0.035} = $655.02
Interest earned = future value - total amount deposited
655.02 - (100 x 6)= $55.02
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area of number sense relates to the quantity of ingredients in recipes?
Measurement is the area of the number sense that has a relationship with the quantity of ingredients used in recipes.
How do you determine the measurements of recipes?The measures of recipes are determined by:
Weighing themCalculating their amount in volume etc.So measure recipes, one can either measure them using artefacts such as cups, spoons, or other kind of containers.
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please helppppp i really need this.
please help i’ll give brainliest
Answer:
3. 16.67
4. 25
Step-by-step explanation:
3. x+2÷8=14/6 (similar triangles have corresponding proportional sides)
x+2=(7×8)/3
x=56/3-6/3 (LCM)
x= 50/3
4. 27/72= (-4+4x)/64
3/2= (-1+x)/16
-1+x=24
x=24+1
what is the difference between squaring and taking the square root ?
Answer:
Squares are the numbers, generated after multiplying a value by itself. Whereas square root of a number is value which on getting multiplied by itself gives the original value.
Step-by-step explanation:
Hence, both are vice-versa methods. For example, the square of 2 is 4 and the square root of 4 is 2.
Drag the tiles to the correct boxes to complete the pairs. Match each system of inequalities to the graph representing its solution set. y − x > 1 and 2x + y ≤ 2 x + y ≥ -3 and 5x – y ≤ -3 2x – y ≤ -1 and x + 2y < 4 4x – 3y < 12 and x + 3y ≥ 6
The solutions to the systems of inequalities are (0.3, 1.3), (-1, -2), (0.4, 1.8) and (3.6, 0.8)
How to determine the solution to the systems?The graph of the systems of inequalities is not given.
So, I would plot a new graph to answer this question.
The systems of inequalities are given as:
y − x > 1 and 2x + y ≤ 2
x + y ≥ -3 and 5x – y ≤ -3
2x – y ≤ -1 and x + 2y < 4
4x – 3y < 12 and x + 3y ≥ 6
Next, we plot these inequalities on a graph and write out the points of intersection.
From the attached graph, we have:
y − x > 1 and 2x + y ≤ 2 ⇒ (0.3, 1.3)
x + y ≥ -3 and 5x – y ≤ -3 ⇒ (-1, -2)
2x – y ≤ -1 and x + 2y < 4 ⇒ (0.4, 1.8)
4x – 3y < 12 and x + 3y ≥ 6 ⇒ (3.6, 0.8)
Hence, the solutions to the systems of inequalities are (0.3, 1.3), (-1, -2), (0.4, 1.8) and (3.6, 0.8)
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What percent is 15 out of 500?
Answer:
3%
Step-by-step explanation:
P% = 15/500
P = 0.03
P% = 0.03 * 100 = 3%
Answer:
15% out of 100 is 15, multiply by 5 and you get 75
At Giant you can get 3 cases of water for $12.99. At Shoprite you can get 4 cases of water for $12.00. Which store is the best place to shop for water?
Answer:
Shoprite
Step-by-step explanation:
At giant each case of water is 4.33 You can figure this out by dividing the overall cost of 12.99 by 3 and that gives you the cost of one case of water. At Shoprite you get 4 cases for 12.00 again you divide the overall cost of 12.00 by 4 and that gives you 3.00 so you get a better deal at shoprite there fore shoprite is the better place to shop for water
Two airplanes leave Chicago at the same time and fly in opposite directions. If one travels at 450 miles per hour and the other at 550 miles per hour, how long will it take for them to be 4000 miles apart
450t+550t=4,000
1000t=4000
t=4000/1000
t=4 hours they will be 4,000 apart.
------------------------------------------
20t+12(4.5-t)=70
20t+54-12t=70
8t=70-54
8t=16
t=16/8
t=2 hours at 20 mph.
proof
20*2+12(4.5-2)=70
40+12(2.5)=70
40+30=70
70=70