Pls help me with this last question

A circle is growing so that the radius is increasing at the rate of 3 cm/min. How fast is the area of the circle changing at the

Naya [18.7K]

Answer:

The area is growing at a rate of $\frac{dA}{dt} =226.2 \,\frac{cm^2}{min}$

Step-by-step explanation:

<em>Notice that this problem requires the use of implicit differentiation in related rates (some some calculus concepts to be understood), and not all middle school students cover such.</em>

We identify that the info given on the increasing rate of the circle's radius is 3 $\frac{cm}{min}$ and we identify such as the following differential rate:

$\frac{dr}{dt} = 3\,\frac{cm}{min}$

Our unknown is the rate at which the area (A) of the circle is growing under these circumstances,that is, we need to find $\frac{dA}{dt}$ .

So we look into a formula for the area (A) of a circle in terms of its radius (r), so as to have a way of connecting both quantities (A and r):

$A=\pi\,r^2$

We now apply the derivative operator with respect to time ( $\frac{d}{dt}$ ) to this equation, and use chain rule as we find the quadratic form of the radius:

$\frac{d}{dt} [A=\pi\,r^2]\\\frac{dA}{dt} =\pi\,*2*r*\frac{dr}{dt}$

Now we replace the known values of the rate at which the radius is growing ( $\frac{dr}{dt} = 3\,\frac{cm}{min}$ ), and also the value of the radius (r = 12 cm) at which we need to find he specific rate of change for the area :

$\frac{dA}{dt} =\pi\,*2*r*\frac{dr}{dt}\\\frac{dA}{dt} =\pi\,*2*(12\,cm)*(3\,\frac{cm}{min}) \\\frac{dA}{dt} =226.19467 \,\frac{cm^2}{min}\\$

which we can round to one decimal place as:

$\frac{dA}{dt} =226.2 \,\frac{cm^2}{min}$

4 0

4 years ago

Willy and Bill kept track of the distance each rode on his bike last week. Willy rode a total of 121.3 kilometers. Bill rode a t

balandron [24]

C. Because you don't need the 0,0 is nothing so it is 121.3

7 0

3 years ago

To divide 343 by 9, would you use partial quotients or the division algorithm? Explain the reasoning.

Katarina [22]

To divide 343 by 9, you will use the division algorithm.

The reason is because 343 is not divisible evenly by nine.

You know this because the sum of the digits, 3+4+3 or 10, is not evenly divisible by 9.

Therefore, 343 is not evenly divisible by 9.

7 0

4 years ago

63,756 • 60 / 70 • 5,280

iVinArrow [24]

Step-by-step explanation:

10.35 according to chemistry . product

8 0

4 years ago

Which expression correctly simplifies (312415)56?

Andreyy89

Answer:

$\sf C)\quad \large\text{$\dfrac{3^{\frac{5}{12}}}{4^{\frac{1}{6}}}$}$