3 years ago

How does writing an equation help you solve a problem.

Mathematics

2 answers:

nekit [7.7K]3 years ago

5 0

It helps the teacher know you understand the subject, helps you remember the process

Murrr4er [49]3 years ago

4 0

Cause you when you right the equation you study it

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If a snowball melts so that its surface area decreases at a rate of 3 cm2/min, find the rate (in cm/min) at which the diameter d

grin007 [14]

Answer:

The diameter decreases at a rate of 0.053 cm/min.

Step-by-step explanation:

Surface area of an snowball

The surface area of an snowball has the following equation:

$S_{a} = \pi d^2$

In which d is the diameter.

Implicit differentiation:

To solve this question, we differentiate the equation for the surface area implictly, in function of t. So

$\frac{dS_{a}}{dt} = 2d\pi\frac{dd}{dt}$

Surface area decreases at a rate of 3 cm2/min

This means that $\frac{dS_{a}}{dt} = -3$

Tind the rate (in cm/min) at which the diameter decreases when the diameter is 9 cm.

This is $\frac{dd}{dt}$ when $d = 9$ . So

$\frac{dS_{a}}{dt} = 2d\pi\frac{dd}{dt}$

$-3 = 2*9\pi\frac{dd}{dt}$

$\frac{dd}{dt} = -\frac{3}{18\pi}$

$\frac{dd}{dt} = -0.053$

The diameter decreases at a rate of 0.053 cm/min.

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