3 years ago

Which expression is equivalent to

Mathematics

1 answer:

Finger [1]3 years ago

7 0

The answer would be A. because two negatives equal a positive

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ANSWER 20%

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(X^-3)^-5x^6<br> A. X^21<br> B. X^-21<br> C. X^48<br> D. X^-48

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3 years ago

The surface area of a sphere is increasing at a rate of 14\pi14π14, pi square meters per hour. At a certain instant, the surface

Sauron [17]

Answer:

$21\pi$ cubic meters per hour

Step-by-step explanation:

We know that the surface area of a sphere is,

$A=4\pi r^2$ ...........(1),

Where,

r = radius of the sphere,

We have, A = $36\pi$ square meters,

$36\pi = 4\pi r^2$

$9 = r^2$

$\implies r = 3\text{ meters}$

Now, differentiating equation (1) with respect to t ( time ),

$\frac{dA}{dt} = 8\pi r\frac{dr}{dt}$

We have,

$\frac{dA}{dt}=14\pi\text{ square meters per hour}, r = 3\text{ meters}$

$14\pi = 8\pi (3) \frac{dr}{dt}$

$\frac{14}{24}=\frac{dr}{dt}$

$\frac{7}{12} = \frac{dr}{dt}$

Also, the volume of a sphere is,

$V = \frac{4}{3}\pi r^3$

Differentiating with respect to t(time)

$\frac{dV}{dt}=4\pi r^2\frac{dr}{dt}$

By substituting the values,

$\frac{dV}{dt}=4\pi (3)^2 (\frac{7}{12})=36\pi \frac{7}{12}=21\pi\text{ cube meters per hour}$

Hence, the rate of change of the volume of the sphere at that instant would be $21\pi$ cubic meters per hour

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3 years ago