Suppose that the price p (in dollars) and the weekly sales x (in thousands of units) of a certain commodity satisfy the demand equation 8p cubedplusx squaredequals104 comma 000. Determine the rate at which sales are changing at a time when xequals200, pequals20, and the price is falling at the rate of $.50 per week.

dx/dt = 12 (in thousands of units /week)

Step-by-step explanation:

We have from problem statement that:

8*p³ + x² = 104    (1)

Where p is price in $, and "x" is the weekly sales in thousands of units

All variables  x  and  p change in relation to time then

Differentiating on both sides of the equation, we get:

24*p²*dp/dt +  2*x*dx/dt = 0      (1)

We need to find dx/dt and we know

p = 20

x = 200

And price is falling at the rate of 0,5 $/week

Then plugging these values in equation (1)

24*p²*dp/dt  = - 2*x*dx/dt

24*(20)²(-0,5) = -400*dx/dt

-4800  = -400*dx/dt

dx/dt = 4800/400

dx/dt = 12 (in thousands of units /week)

x > 1.3

step by step:

8.5−0.9x> 9.8−1.9x

step 1: simplify both sides of the inequality.

−0.9x+8.5> −1.9x+9.8

step 2: add 1.9x to both sides.

−0.9x+8.5+1.9x> −1.9x+9.8+1.9x

1x+8.5> 9.8

step 3: subtract 8.5 from both sides.

1x+8.5−8.5> 9.8−8.5

1x> 1.3

step 4: divide both sides by 1.

1x/1 > 1.3/1

12.5 feet

step-by-step explanation: