Suppose that the price p (in dollars) and the weekly sales x (in thousands of units) of a certain commodity satisfy the demand equation 6p cubedplusx squaredequals850. Determine the rate at which sales are changing at a time when xequals10, pequals5, and the price is falling at the rate of $.40 per week.

9514 1404 393

  increasing 9000 units per week

Step-by-step explanation:

The price and sales relation is given as ...

  6p³ +x² = 850

Differentiating with respect to time gives ...

  18p²·p' +2x·x' = 0

Filling in the given values, we have ...

  18(5)²(-0.40) +2(10)x' = 0

  20x' = 180 . . . . . . add 180

  x' = 9 . . . . . . . . . . divide by 20

Sales are increasing at the rate of 9,000 units per week.

47

step-by-step explanation:

perimeter = 10 +  √10  units

explanation:

first, we will need to get the length of each line using the distance formula which is as follows:

distance = 

1- length of ab:

ab =   = 5 units

2- length of ac

length of ac is the same as ab = 5 units

3- length of bc:

bc =   =  √10  units

now, we can get the perimeter by adding the side lengths as follows:

perimeter = 5 + 5 +  √10

perimeter = 10 +  √10  units

hope this : )

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