Explain why the rate of change of the radius of the sphere is not constant even though dV/dt is constant. dr dt depends on r2, not simply r. The volume only appears constant; it is actually a rational relationship. The rate of change of the radius is a linear relationship whose slope is dV dt . The rate of change of the radius is a cubic relationship. dr dt as a function runs parallel to the volume function, which is not linear.

Answers

Answer 1

Answer:

Hello your question has some missing parts below is the missing part

A spherical balloon is inflated with gas at a rate of 600 cubic centimeters per minute  

answer :

dr/dt  depends on r^2  not simply r

Step-by-step explanation:

The rate of change of the radius of the sphere is not constant even though dv/dt is constant is because ;

dr/dt  depends on r^2  not simply r

and this is because  dr/dt is proportional to  1/r^2 therefore the rate of change of the radius cannot be constant even though dv/dt is constant


Related Questions

Molly shared a spool of ribbon with 12 people. Each person received 3 feet of ribbon. Which equation can she use to find
r, the number of feet of ribbon that her spool originally had?

Answers

Answer: R/12=3

             

Step-by-step explanation: This is because / = divide so since we need to divide then multiply its better you go with /

Answer:D

Step-by-step explanation:

Using the binomial theorem, expand the expression (4 + y) to the power of 4

Answers

Answer:

When raised to the power of 4, the binomial (4 + y) expands to:

[tex]y^4 + 16y^3 + 96y^2 + 256y + 256[/tex]

Step-by-step explanation:

[tex](4 + y)^4 \\= (y^2 + 8y + 16)^2\\= y^4 + 8y^3 + 16y^2 + 8y^3 + 64y^2 + 128y + 16y^2 + 128y + 256\\= y^4 + 16y^3 + 96y^2 + 256y + 256[/tex]

1. (a) Let A = 1, 3, 5, 7 and B = X : X is the first three multiple of 7 . Find (A−B).
(b) Find the remainder when f (x)=3x^3 −11x−48 is divided by x−1 .
(c) Let f (x)= x3 , g(x)= x+5. Find (f •g)(x)
(d) Find the derivative of y = 3+ x^2+ x^3y^3.

Answers

Answer:

a) A-B = { 1 , 3, 5 }

b) The remainder is 50

c) f + g)(x) = x⁴+ 5x³

d) [tex]\frac{dy}{dx} = \frac{2x- y^3(3x^2)) }{ 1- x^3 3y^2}[/tex]

Step-by-step explanation:

Step(I):-

1) a)

Let A = { 1, 3, 5, 7 } and B = { 7 , 14 , 21 }

A - B = {1,3,5,7} - { 7,14,21}

A - B  = { 1 , 3, 5}

b)

Given f (x)=3x³−11x−48

    x-1  ) 3 x³ - 11x -48 (- 3x²-3x -2

            -3x³ +3x²

                 3x²-11x-48

                -3x²+9x

                     2x -48

                    -2x +2  

                                       

                         50

The remainder is 50

   

c)  Given f(x) = x³ and g(x) = x + 5

(f. g)(x) = f(x) .g(x) = x³ . (x+5) = x³(x) + 5 x³ = x⁴+ 5x³

d)

 Given function   y = 3 + x²+x³y³  ...(I)

By using derivative formulas

            y = xⁿ

            [tex]\frac{dy}{dx} = n x^{n-1}[/tex]

Apply d/dx ( UV) = U V¹ + V U¹



Differentiating equation (I) with respective to 'x' , we get

                      [tex]\frac{dy}{dx} = 0 + 2x + ( x^3 3y^2(\frac{dy}{dx} )+ y^3(3x^2))[/tex]

                     [tex]\frac{dy}{dx} - ( x^3 3y^2(\frac{dy}{dx} )= 2x- y^3(3x^2))[/tex]

                   [tex]\frac{dy}{dx} = \frac{2x- y^3(3x^2)) }{ 1- x^3 3y^2}[/tex]



5
Mo spends of his pocket money on a present for his sister.
He gives of his pocket money to charity.
What fraction of his pocket money does he have left?
You may use the fraction strip to help you.

Answers

love shot

Step-by-step explanation:

1x24 minus 1 and that is good

hope it helps

The temperature on Sunday was 45 degrees. The next day the temperature dropped by 13 degrees. What is the temperature the next day" *

Answers

Answer:

The answer is 32 degrees

Step-by-step explanation:

45 minus 13 equals 32

de acuerdo con la siguiente figura calcula el ancho del río y la distancia del árbol a la lancha.

Answers

lo siento pero no hay nada ahí

is 1/3, 7/21 proportion ​

Answers

Answer:

1/3

Step-by-step explanation:

which one of these is a rational number
A. square root of 9/2
B. square root of 13/16
C. square root of 34
D. square root of 49

Answers

D is the ans. Square root of 49 equals to 7

I give 20! Find the surface area. And without explanation please, I don’t have enough time.

Answers

Answer:

816 cm²

Step-by-step explanation:

Surface area of the composite figure = (surface area of the larger rectangular prism + surface area of the smaller rectangular prism) - area of the side of the smaller rectangular prism that is joined to the bigger prism.

✔️Surface area of the larger rectangular prism:

Area = L*W*H = 20*5*6 = 600 cm²

✔️surface area of the smaller rectangular prism:

Area = L*W*H = 12*4*6 = 288 cm²

✔️area of the side of the smaller rectangular prism that is joined to the bigger prism.

Area = L*W = 12*6 = 72 cm²

Surface area of the composite = (600 + 288) - 72 = 888 - 72 = 816 cm².

Hayley and Tyra had lunch at
Ruby Tuesday. Their bill was
$22.40. If they leave a 15%
tip, how much is the tip?

Answers

22.40 * 0.15 = 3.36
The tip is $3.36
$3.36 hope this helps.
22.40*.15= 3.36

What is the value of StartFraction negative 3 (7 + 5) over 3 squared EndFraction + 9 (2)? –6 –2 14 22 Please help timed test??????

Answers

Answer:

your dad left to get the milk

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

i took the test on edge 2021

Use a matrix to solve the system:

Answers

Answer:

(2.83 , 1 , 4)

Step-by-step explanation:

[tex]2x+2y-z=4\\4x-2y-2z=2\\3x+3y-4z=-4\\[/tex]

Rewrite these equations in matrix form

[tex]\left[\begin{array}{ccc}2&2&-1\\4&-2&-2\\3&3&-4\end{array}\right] \left[\begin{array}{ccc}x\\y\\z\end{array}\right]=\left[\begin{array}{ccc}4\\2\\-4\end{array}\right] \\[/tex]

we can write it like this,

[tex]AX=B\\X=A^{-1}B[/tex]

so to solve it we need to take the inverse of the 3 x 3 matrix A then multiply it by B.

We get the inverse of matrix A,

[tex]A^{-1}=\left[\begin{array}{ccc}7/15&1/6&-1/5\\1/3&-1/6&0\\3/5&0&-2/5\end{array}\right] \\[/tex]

now multiply the matrix with B

[tex]X=A^{-1}B\\\\\left[\begin{array}{ccc}x\\y\\z\end{array}\right] =\left[\begin{array}{ccc}7/15&1/6&-1/5\\1/3&-1/6&0\\3/5&0&-2/5\end{array}\right]\left[\begin{array}{ccc}4\\2\\-4\end{array}\right] \\\\\\\left[\begin{array}{ccc}x\\y\\z\end{array}\right] =\left[\begin{array}{ccc}2.83\\1\\4\end{array}\right] \\[/tex]

Elena has 20 apples and 35 crackers for making snack bags. She wants to make as many snack bags as possible and wants each bag to have the same combination of apples and crackers. What is the largest number of snack bags she could make?
Which one is it? GCF(greatest common factor) LCM (least common multiple).

Answers

Answer:

GCF

Step-by-step explanation:

Answer: The largest number of snack bags she could make is 5

Step-by-step explanation:

20/5=4 apples

35/5=7 crackers

In each bag she will place 4 apples and 7 crackers

What is the slope of the line containing the ordered pairs (5,-3) and (-2,-3)

Answers

Answer:

0

Step-by-step explanation:

Use the slope formula: m = [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

m = [tex]\frac{-3+3}{-2-5}=\frac{0}{-7} =0[/tex]

The slope of the line is 0.

A motocross ramp is 16 feet tall and 24 feet long what is the slope of the ramp

Answers

384 step by step explanation:

55% means 55 out of 100. Write 55% as a fraction in simplest form. Is it 55/100 plz give me an explanation.

Answers

The answer is 11/20. You have to divide the numerator (55) and the denominator (100) by the greatest common factor (5) to get the simplest form of 55/100 (or 55%).

Complete the table by using your knowledge of the formula for simple interest.​

Answers

Answer:

that look hard

Step-by-step explanation:

You use a line of best fit for a set of data to make a prediction about an unknown value. The correlation coefficient for your data set is -0.015. Can you be confident that your predicted value will be reasonably close to the actual value?

a. Yes, because the correlation is close to zero, it is strong.
b. Yes, No, because the correlation is close to zero, it is strong.
c. No, because the correlation is close to zero, it is weak.
d. No, because the correlation is negative, it is weak.

Answers

Answer:

Following are the solution to this question:

Step-by-step explanation:

For this set, the correlation coefficient is = -0.015.

It shows that financial variables have trust issues. Once a price rises, the other one is decreasing the value of -0,015 shows, that there are several fewer associations in the set of data among x and y and between y values. This interaction also can range between -1 to 1, to 0 being completely unrelated. But you'd never be sure, in this situation, 0.015 is very similar to 0.

It means that your prediction is nothing better than just a wild choice. Its odds of an estimated value being relatively close to the actual result are therefore much smaller as the points are it's hardly the best match.

A supervisor records the repair cost for 17 randomly selected VCRs. A sample mean of $68.83 and standard deviation of $12.17 are subsequently computed. Determine the 80% confidence interval for the mean repair cost for the VCRs. Assume the population is approximately normal.

Step 1 of 2: Find the critical value that should be used in constructing the confidence interval. Round your answer to three decimal places.

Answers

Answer:

27

Step-by-step explanation:

im smart

When performing a Translation to a segment. What will be the change between the pre-image and the image? (HELP I need this done by 5 Minutes.)

Answers

different directions

if k(x)=x²-4 find k(2x)


1 -4
2-x²
3-2x²-4
4-4x²-4

Answers

Answer:

4. 4x² - 4

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to Right

Algebra I

Function NotationCombining Like Terms

Step-by-step explanation:

Step 1: Define

k(x) = x² - 4

k(2x) is x = 2x

Step 2: Evaluate

Substitute in x:                    k(2x) = (2x)² - 4Exponents:                          k(2x) = 4x² - 4

i need help with this please

Answers

Answer:

31/8

Step-by-step explanation:

For history class, Joe spent 2 hours writing a 4-page report on ancient Egypt. This weekend, he needs to write a 12-page report on the Roman Empire.
If he writes at the same rate, how long will it take Joe to write his report?

Answers

Answer:

2hours/4pages

2/4=1/2

1/2=x/12

cross multiply

12=2x

divide by 2 both sides

6=x

6 hours

Answer:

the answer is 6

Step-by-step explanation:

Help pleasseeeee!!!!!!

Answers

Answer:

i think C sorry if wrong

I believe that The solution of equation A is -1 and of equation B is -2 , so A will be greater that B

PLEASE HELP ME THIS IS URGENT!! THIS IS ACC MATHEMATICS!! Please I need to turn this in

Answers

?so yeah but I don’t get it soooooooooooooooo

if I have a 15 gallon tank what percentage is in tank if it only takes 12 gallons to fill it​

Answers

Step-by-step explanation:

12/15 * (100%)

= 4/5 * (100%)

= 4 * 20%

= 80%

Please gimme brainliest

The correct answer is that 12 is 80% of 15 gallons.

Sandra rode her bike 9 1/3 miles on Monday and 6 4/5 miles on Tuesday how many miles did Sandra walk in both days

Answers

There’s no calculations for walking.

She rode a total of 16 2/15 for the 2 days

Answer:

2 8/15

Step-by-step explanation:

Amy raises $58.75 to participate in a walk-a-thon. Jeremy raises $23.25 more than Amy. Oscar raises 3 times as much as Jeremy. How much does Oscar raise? Please show work and equation and this is 5th grade math.

1. 246.00
2. 245.00
3. 246.08

Answers

Answer:

246.00

Step-by-step explanation:

58.75+23.25=82 then 82*3

Answer:

246.000

Step-by-step explanation:

Well If you take it and Line it up like this,

(A)Amy; 58.75

(J)Jeremy; A+23.25

(O)Oscar; A+23.25= ?x3

This is an easy way to find out what it is you need to do, So A+23.25 is 58.75+23.2 which should give you the value of 82, which brings you to the next step of A+23.25= ?x3 which in this you only wanna focus on the ?x3, we now know ?= 82 so this brings it to 82 times 3 which gives you a value of 246. Thus giving you your answer.

  Hope this helps.

Type the correct answer In each box.
What are the values of x and y that make the equations true?
Equation A
(x + yi) + (4 – 7i) = 3 - 4i
Equation B (x + yi) - (-6 + 14i) = 18 + 2i
In equation A, x =
and y =
In equation B, r =
and y =

Answers

9514 1404 393

Answer:

  A: x = -1  and  y = 3

  B: x = 12  and  y = 16

Step-by-step explanation:

In each case, you can add the opposite of the constant to find the variable.

Equation A

  (x +yi) +(4 -7i) = (3 -4i)

  (x +yi) +(4 -7i) -(4 -7i) = (3 -4i) -(4 -7i) . . . . . add -(4-7i) to both sides

  x +yi = (3 -4) +(-4-(-7))i = -1 +3i

  x = -1  and  y = 3

__

Equation B

  (x +yi) -(-6 +14i) = (18 +2i)

  (x +yi) -(-6 +14i) +(-6 +14i) = (18 +2i) +(-6 +14i) . . . . . add (-6 +14i) to both sides

  x + yi = (18 -6) +(2 +14)i = 12 +16i

  x = 12  and  y = 16

Answer:

In equation A: x=-1 and y=3

In equation B: x=12 and y=16

Step-by-step explanation:

What investment/savings options has the greatest risk?

Answers

Stocks / Equity Investments include stocks and stock mutual funds. These investments are considered the riskiest of the three major asset classes, but they also offer the greatest potential for high returns.
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