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Vinil7 [7]
3 years ago
6

Suppose customers in a hardware store are willing to buy N(p) boxes of nails at p dollars per box, as given by the following fun

ction. N(p) = 80-5p2; Find the average rate of change of demand for a change in price from $2 to $3. The average rate of change of demand for a change in price from $2 to $3 is -25 boxes per dollar. (Type an integer or a decimal.) Find the instantaneous rate of change of demand when the price is $2. The instantaneous rate of change of demand when the price is $2 is - 20 boxes per dollar. (Type an integer or a decimal.) Find the instantaneous rate of change of demand when the price is $3. The instantaneous rate of change of demand when the price is $3 is boxes per dollar. (Type an integer or a decimal.)
Mathematics
1 answer:
Viktor [21]3 years ago
7 0

Answer:

(a) - 25 boxes per dollar

(b) - 20 boxes per dollar

Step-by-step explanation:

Given that,

Consumer's willing to buy boxes of nails at p dollars per box:

N(p) = 80 - 5p^{2}

(a) Change in price from $2 to $3.

N(2) = 80 - 5(2)^{2}

       = 80 - 20

       = 60

N(3) = 80 - 5(3)^{2}

       = 80 - 45

       = 35

Therefore, the average rate of change of demand is

= [N(3) - N(2)] ÷ (3 - 2)

= 35 - 60

= - 25 boxes per dollar.

(b) N(p) = 80 - 5p^{2}

Now, differentiating the above function with respect to p,

N'(p) = -10p

Therefore, the instantaneous rate of change of demand when the price is $2 is calculated as follows:

N'(p) = -10p

N'(2) = -10 × 2

        = -20 boxes per dollar

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Step-by-step explanation:

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kondaur [170]

Linear equation are the equation which has the highest power of the unknown variable is 1.The expressions given in the  option 1, 2, and 3 are equivalent to 7x - 14.

The equations given in the problem are the linear equations.

<h3>Linear equation</h3>

Linear equation are the equation which has the highest power of the unknown variable is 1.

Given-

1) The given expression in the problem is,

f(x)=7x-14

Rewrite the equation as,

f(x)=(7x-14)

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Rewrite the equation with positive terms first.

f(x)=-(14-7x)

Hence the given equation is equivalent to the option 1.

2) The given equation,

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On solving further take out the 7 common from the bracket,

f(x)=7(x-2)

Thus the given equation is equivalent to the option 2.

3) The given equation,

f(x)=7x-14

Split the term of <em>x,</em>

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Rewrite the equation,

f(x)=3x-14+4x

Hence the given equation is equivalent to the option 3.

4) The given equation,

f(x)=7x-14

Split the term of <em>x </em>and constant term,

<em />f(x)=5x+2x-10-4<em />

Rewrite the equation,

f(x)=2x-10+5x-4

Hence the given equation is not equivalent to the option 4.

Thus the expressions given in the  option 1, 2, and 3 are equivalent to 7x - 14.

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Graph each side of the equation. The solution is the x-value of the point of intersection.

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