Mathematics: Suppose the price p, in dollars, and number of sales, x, of an item is related by 5 8 6 50 p x px + + = . If p and x are functions of time, measured in days, find the rate at which x is changing when x = 15, p = 2.90 and dp/dt = -1.15

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Suppose the price p, in dollars, and number of

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23.01.2022

According to the information of the problem x = 15 , p=2.90 and dp/dt = -1.15

then $\frac{dx}{dt} = -3.357\\$

Step-by-step explanation:

Since everything is changing with respect to time and p,x are related according to the following equation

5p+5x+3px = 71

We need to find the implicit derivative with respect to the time. And we get the following.

$5\frac{dp}{dt}+5\frac{dx}{dt}+3x\frac{dp}{dt}+3p\frac{dx}{dt} = 0$

$\frac{dx}{dt}$ is what we don't know, so we solve for it and get

$\frac{dx}{dt} = - (5\frac{dp}{dt}-3x\frac{dp}{dt})/ (5+3p)$

Now. According to the information of the problem x = 15 , p=2.90 and dp/dt = -1.15

then $\frac{dx}{dt} = -3.357\\$

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