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Mathematics

1 answer:

Kruka [31]3 years ago

3 0

Answer:

The answer is C!

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A company designs T-shirts. They charge $40 for set-up cost plus $12 per shirt. write the slope intercept form.

Dovator [93]

Answer: y= 12x +40

Step-by-step explanation:

7 0

4 years ago

A balloon is blowing up at a constant rate of 9 cubic centimeters per second. When the volume of the balloon is 2048/3 pi cubic

jekas [21]

Answer:

$\displaystyle \frac{dr}{dt}\approx 0,0112\ cm/sec$

Step-by-step explanation:

Rates of Change as Derivatives

If some variable V is a function of another variable r, we can compute the rate of change of one with respect to the other as the first derivative of V, or

$\displaystyle V'=\frac{dV}{dr}$

The volume of a sphere of radius r is

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

The volume of the balloon is growing at a rate of $9\ cm^3/sec$ . This can be written as

$\displaystyle \frac{dV}{dt}=9$

We need to compute the rate of change of the radius. Note that both the volume and the radius are functions of time, so we need to use the chain rule. Differentiating the volume with respect to t, we get

$\displaystyle \frac{dV}{dt}=\displaystyle \frac{dV}{dr}\displaystyle \frac{dr}{dt}$