Mathematics, 12.07.2019 07:10 Bra1nPowers

The cost in dollars to manufacture x pairs of shoes is given by 12,000 + 19x. this month, the manufacturer produced 1000 more pairs of shoes than last month. the average cost per pair dropped by $0.43.
a) write an expression for the average cost per pair of shoes. use this expression to write an equation to represent there situation.
b) solve your equation
c) are there any mathematical restrictions on the domain? explain.
d) determine reasonable domain in the context of the problem. use your answers to parts i and ii to answer the question.

Answers: 1

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Answers

(a) The expression for the average cost per pair of shoes is $A(x)=\frac{12000}{x}+19$ and equation for the situation is $\frac{12000}{x}+19-(\frac{12000}{x+1000}+19)=0.43$ .

(b) x= $x\approx 4806$

(d) The reasonable domain is all natural numbers.

Step-by-step explanation:

The cost in dollars to manufacture x pairs of shoes is given by

C(x)=12000+19x

where, x is the pairs of shoes.

(a)

The expression for the average cost per pair of shoes.

$A(x)=\frac{C(x)}{x}$

$A(x)=\frac{12000+19x}{x}$

$A(x)=\frac{12000}{x}+19$

This month, the manufacturer produced 1000 more pairs of shoes than last month. The average cost per pair dropped by $0.43.

A(x)-A(x+1000)=0.43

$\frac{12000}{x}+19-(\frac{12000}{x+1000}+19)=0.43$

Therefore the expression for the average cost per pair of shoes is $A(x)=\frac{12000}{x}+19$ and equation for the situation is $\frac{12000}{x}+19-(\frac{12000}{x+1000}+19)=0.43$ .

(b)

On solving the above equation we get

$\frac{12000}{x}-\frac{12000}{x+1000}=0.43$

$\frac{12000000}{x^2 + 1000 x} = 0.43$

12000000=0.43(x^2 + 1000 x)

12000000=0.43x^2 + 430x

0=0.43x^2 + 430x-12000000

Using graphing calculator we get

$x\approx -5806.31,4806.31$

The pair of shoe can not be native and decimal value.

$x\approx 4806$

Therefore the solution is $x\approx 4806$ .

(c)

The average cost function is

$A(x)=\frac{12000}{x}+19$

The function is not defined if the denominator is 0.

The above function is not defined for x=0, so the domain of the function is all real numbers except 0.

(d)

In the average function x represents the number of pair of shoe.

It means the value of x must be a positive integer.

Since the average function is not defined for x=0, So the reasonable domain of average function is

Domain={x : x∈Z⁺, x≠0}

Domain=N

Therefore the reasonable domain is all natural numbers.

Answer from: Quest

there are lots of ways. pick's theorem tells us if the vertices are lattice points the area a is

a = b/2 + i - 1

where b is the number of boundary lattice points and i is the number of interior lattice points.

in the figure i count b=16, i=50 so

a = 8 + 50 - 1 = 57

let's try the shoelace formula. the area is half the sum of the cross products of the sides.

a(-2,6) -2(2)-6(-5) = 26

b(-5,2) -5(-3) - 2(-2) = 19

c(-2,-3) -2(-3) - (-3)(4) = 18

d(4,-3) 4(3) - (-3)(5) = 27

e(5,3) 5(3) - 3(1) = 12

f(1,3) 1(6) - 3(-2) = 12

a(-2,6)

each of the cross products is twice the area of the triangle with the associated side and one vertex the origin. so the area of abo=26/2=13.

area = (1/2) (26 + 19 + 18 + 27 + 12 + 12) = 57

that checks!

Find the area of the following shape. you must show all work to receive credit. need asap timed tes

Answer from: Quest

The answer is that the rate of change is $50 per 1 monthhope this ; )

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The cost in dollars to manufacture x pairs of shoes is given by 12,000 + 19x. this month, the manufa...