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oksian1 [2.3K]
3 years ago
7

Help me do this question ​

Mathematics
1 answer:
pshichka [43]3 years ago
3 0

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The radius of a cone is decreasing at a constant rate of 7 inches per second, and the volume is decreasing at a rate of 948 cubi
inessss [21]

Answer:

The height of cone is decreasing at a rate of 0.085131 inch per second.        

Step-by-step explanation:

We are given the following information in the question:

The radius of a cone is decreasing at a constant rate.

\displaystyle\frac{dr}{dt} = -7\text{ inch per second}

The volume is decreasing at a constant rate.

\displaystyle\frac{dV}{dt} = -948\text{ cubic inch per second}

Instant radius = 99 inch

Instant Volume = 525 cubic inches

We have to find the rate of change of height with respect to time.

Volume of cone =

V = \displaystyle\frac{1}{3}\pi r^2 h

Instant volume =

525 = \displaystyle\frac{1}{3}\pi r^2h = \frac{1}{3}\pi (99)^2h\\\\\text{Instant heigth} = h = \frac{525\times 3}{\pi(99)^2}

Differentiating with respect to t,

\displaystyle\frac{dV}{dt} = \frac{1}{3}\pi \bigg(2r\frac{dr}{dt}h + r^2\frac{dh}{dt}\bigg)

Putting all the values, we get,

\displaystyle\frac{dV}{dt} = \frac{1}{3}\pi \bigg(2r\frac{dr}{dt}h + r^2\frac{dh}{dt}\bigg)\\\\-948 = \frac{1}{3}\pi\bigg(2(99)(-7)(\frac{525\times 3}{\pi(99)^2}) + (99)(99)\frac{dh}{dt}\bigg)\\\\\frac{-948\times 3}{\pi} + \frac{2\times 7\times 525\times 3}{99\times \pi} = (99)^2\frac{dh}{dt}\\\\\frac{1}{(99)^2}\bigg(\frac{-948\times 3}{\pi} + \frac{2\times 7\times 525\times 3}{99\times \pi}\bigg) = \frac{dh}{dt}\\\\\frac{dh}{dt} = -0.085131

Thus, the height of cone is decreasing at a rate of 0.085131 inch per second.

3 0
3 years ago
Write the equation of the line shown in the graph above in slope-intercept form
qwelly [4]
Y = mx + c
y= -2/3x + 1
1= c
4 0
3 years ago
Read 2 more answers
Help me on this plz I don't get it
kherson [118]
You must first attach the problems with your question.
3 0
4 years ago
"What is element a23 in matrix A <br><br> "
Zolol [24]
A matrix is an array of numbers and may be presented in 3x3, 4x4 and so on forms. The 3x3 corresponds to the coefficients of the given algebraic equation. It also corresponds to the placement of the given coefficients. In here, <span>element a23 in matrix A is 8. </span>
5 0
3 years ago
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Which statement describes how the graph of the given polynomial would change if the term -3x6 is adde
Lesechka [4]

Given:

Polynomial is 2x^6+9x^5-7x^3-1.

Term -3x^6 is added in the given polynomial.

To find:

The end behavior of new polynomial.

Solution:

Let, P(x)=2x^6+9x^5-7x^3-1.

New polynomial is

f(x)=2x^6+9x^5-7x^3-1+(-3x^6)

f(x)=(2x^6-3x^6)+9x^5-7x^3-1

f(x)=-x^6+9x^5-7x^3-1

Highest power of x is 6 which is even and leading coefficient is negative. So,

f(x)\to -\infty\text{ as }x\to -\infty

f(x)\to -\infty\text{ as }x\to \infty

Both ends of the graph will approach negative infinity.

Therefore, the correct option is A.

5 0
3 years ago
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