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10 March, 05:07

Suppose that the price p, in dollars, and the number of sales, x, of a certain item follow the equation 4 p plus 4 x plus 2 pxequals56. Suppose also that p and x are both functions of time, measured in days. Find the rate at which x is changing when xequals2 , pequals6 , and StartFraction dp Over dt EndFraction equals1.5.

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  1. 10 March, 08:51
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    There is a decrease of 0.75 sales per day

    Step-by-step explanation:

    Given:-

    - The price of item = p

    - The number of sales = x

    - The relationship between "p" and "x" is given below:

    4p+4x+2px=56

    Find the rate at which x is changing when x=2, p=6, and dp/dt=1.5 The rate at which x is changing is [ ] sales per day

    Take the time derivative (d/dt) of the entire given expression and apply chain rule on d/dt (2px). Since both "p" and "x" are only functions of time "t":

    d/dt

    4p+4x+2px=56

    4*dp/dt + 4*dx/dt + 2 * (x*dp/dt + p*dx/dt) = 0

    Use the given values x=2, p=6, and dp/dt=1.5 to determine dx/dt

    4*1.5 + 4*dx/dt + 2 * (2*1.5+6*dx/dt) = 0

    6+4dx/dt + 2 * (3+6dx/dt) = 0

    6+4dx/dt + 6+12dx/dt=0

    12+16dx/dt=0

    12=-16dx/dt

    dx/dt = 12/-16

    = - 0.75
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