Mathematics: Suppose that the price p, in dollars, and the number of sales, x, of a certain item follow the equation 6 p plus 3 x plus 2 pxequals69. Suppose also that p and x are both functions of time, measured in days. Find the rate at which x is changing when xequals3, pequals5, and StartFraction dp Over dt EndFraction equals1.5.

Suppose that the price p, in dollars, and the number

Ответ:

cassanovaanthony

30.01.2022

Mathematics

$\dfrac{dx}{dt}=-1.3846$ sales per day$

Step-by-step explanation:

The price p, in dollars, and the number of sales, x, of a certain item follow the equation: 6p+3x+2px=69

Taking the derivative of the equation with respect to time, we obtain:

$6\dfrac{dp}{dt} +3\dfrac{dx}{dt}+2p\dfrac{dx}{dt}+2x\dfrac{dp}{dt}=0\\$Rearranging$\\6\dfrac{dp}{dt}+2x\dfrac{dp}{dt}+3\dfrac{dx}{dt}+2p\dfrac{dx}{dt}=0\\\\(6+2x)\dfrac{dp}{dt}+(3+2p)\dfrac{dx}{dt}=0$

When x=3, p=5 and $\dfrac{dp}{dt}=1.5$

$(6+2(3))(1.5)+(3+2(5))\dfrac{dx}{dt}=0\\(6+6)(1.5)+(3+10)\dfrac{dx}{dt}=0\\18+13\dfrac{dx}{dt}=0\\13\dfrac{dx}{dt}=-18\\\dfrac{dx}{dt}=-\dfrac{18}{13}\\\\\dfrac{dx}{dt}=-1.3846$ sales per day$

The number of sales, x is decreasing at a rate of 1.3846 sales per day.

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Ответ:

samarkanduzbek

12.04.2022

Mathematics

0.81-3=0.27

Step-by-step explanation:

0.81-3=0.27 it

It is similar to 3.21÷3=1.07 this is division

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