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# Math calculus derrivative question

The number x of printer cartridges that a store will sell per week and their price p (in dollars) are related by the equation
x^2 = 1680 − 5p^2
If the price is falling at the rate of \$1 per week, find how the sales will change if the current price is \$16.

### 2 Answers by Expert Tutors

Mark M. | Math Tutor--High School/College levelsMath Tutor--High School/College levels
4.9 4.9 (821 lesson ratings) (821)
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x2 = 1680 - 5p2

2x(dx/dt) = -10p(dp/dt)

Since dp/dt = -1, we have 2x(dx/dt) = 10p

When p = 16, x2 = 1680 - 5(16)2

x2 = 1680 - 1280

x2 = 400   x = 20

So, 40(dx/dt) = 10(16)

dx/dt = 160/40 = 4 printer cartridges per week

When p = \$16, the number of cartridges sold is increasing at the rate of 4 cartridges per week.

Thank you very much Mark! extremely helpful!!
Michael J. | Effective High School STEM Tutor & CUNY Math Peer LeaderEffective High School STEM Tutor & CUNY ...
5.0 5.0 (5 lesson ratings) (5)
0
Take the derivative of both sides of the equation.

2x = -10pp'

Solve for p'.

-x / (5p) = p'

Set p' equal to -1 because the rate is falling.

-x / (5p) = -1

Solve for x when p=16.  That is all you have to do.