How to find the rate of change of the volume of cone?

1 answer:

8 0

You can use calculus ( related rates). Given the rate os change of the radius for example you can find the rate of change of volume using differential calculus.

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Which function has the greatest rate of change on the interval from x = 3 pi over 2 to x = 2π?

vodka [1.7K]

The average rate of change for the function f(x) can be calculated from the following equation
$\frac{f( x_{2})-f( x_{1} )}{ x_{2} - x_{1} }$

By applying the last formula on the given equations
(1) the first function f
from the table f(3π/2) = -2 and f(2π) = 0
∴ The average rate of f = $\frac{f(2 \pi)-f( \frac{3 \pi}{2} )}{2 \pi - \frac{3 \pi}{2} } = \frac{0-(-2)}{ \frac{\pi}{2} }= \frac{2}{ \frac{\pi}{2} } = \frac{4}{\pi}$

(2) the second function g(x)
from the graph g(3π/2) = -2 and g(2π) = 0
∴ The average rate of g = $\frac{g(2 \pi)-g( \frac{3 \pi}{2} )}{2 
\pi - \frac{3 \pi}{2} } = \frac{0-(-2)}{ \frac{\pi}{2} }= \frac{2}{ 
\frac{\pi}{2} } = \frac{4}{\pi}$

(3) the third function h(x) = 6 sin x +1
∴ h(3π/2) = 6 sin (3π/2) + 1 = 6 *(-1) + 1 = -5
 h(2π) = 6 sin (2π) + 1 = 6 * 0 + 1 = 1
∴ The average rate of h = $\frac{f(2 \pi)-f( \frac{3 \pi}{2} )}{2 
\pi - \frac{3 \pi}{2} } = \frac{1-(-5)}{ \frac{\pi}{2} }= \frac{6}{ 
\frac{\pi}{2} } = \frac{12}{\pi}$

By comparing the results, The function which has the greatest rate of change is h(x)


So, the correct answer is option C) h(x)

4 0

3 years ago

Find the difference of 5 2/3 -4 5/9 A 3/4 B 1 1/9 C 1 1/2 D 8/9

sergey [27]

Answer: B- 1 1/9
Work:
5 2/3 - 4 5/9
1 2/3 - 5/9
1 6/9 - 5/9
= 1 1/9

5 0

3 years ago

The English Alphabet has 20 letters more than one-fourth the number of letters in the Greek Alphabet. The English Alphabet has 2

melomori [17]

20+1/4g=26 is your answer

7 0

3 years ago

Write an algebraic expression for this situation . Steve made a down payment of $300 on a new tv. He paid $37 per month for x mo

Temka [501]

300+37x
300+37(9)
300+333
633

5 0

3 years ago

The average of six tests is 82. What is the total of the six tests?

ira [324]

Since the average of 6 tests is 6, and we know that the average is found by dividing the total score by the number of tests, we can just multiply the average by the number of tests to find the total score. Doing this, we get 82 * 6 which simplifies to 492.

8 0

3 years ago