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SashulF [63]
2 years ago
7

The function f (x) = .85x+3.99 models the total cost of purchasing x key chains from an internet company that charges shipping t

he function g (x) = 1.10x models the total purchasing of x number of the same key chains from an company that does not charge shipping. Rounding to the nearest whole number what is the best approximation of the number of key chains for which the two companies charge the same amount?
Mathematics
1 answer:
lina2011 [118]2 years ago
4 0

Answer:

16 key chains

Step-by-step explanation:

Given

f(x) = 0.85x + 3.99 ---company A

g(x) = 1.10x --- company B

Required

Value of x when f(x) = g(x)

We have:

f(x) = g(x)

0.85x + 3.99 = 1.10x

Collect like terms

0.85x - 1.10x = -3.99

-0.25x = -3.99

Solve for x

x = \frac{-3.99}{-0.25}

x = 15.96

x= 16 --- approximated

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Step-by-step explanation:

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jenna's rectangular garden borders a wall. she buys 80 ft of fencing. what are the dimensions of the garden that will maximize i
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Answer:

The  dimensions are x =20 and y=20 of the garden that will maximize its area is 400

Step-by-step explanation:

Step 1:-

let 'x' be the length  and the 'y' be the width of the rectangle

given Jenna's buys 80ft of fencing of rectangle so the perimeter of the rectangle is    2(x +y) = 80

                         x + y =40

                               y = 40 -x

now the area of the rectangle A = length X width

                                                  A = x y

substitute 'y' value in above A = x (40 - x)

                                              A = 40 x - x^2 .....(1)

<u>Step :2</u>

now differentiating equation (1) with respective to 'x'

                                      \frac{dA}{dx} = 40 -2x     ........(2)

<u>Find the dimensions</u>

<u></u>\frac{dA}{dx} = 0<u></u>

40 - 2x =0

40 = 2x

x = 20

and y = 40 - x = 40 -20 =20

The dimensions are x =20 and y=20

length = 20 and breadth = 20

<u>Step 3</u>:-

we have to find maximum area

Again differentiating equation (2) with respective to 'x' we get

\frac{d^2A}{dx^2} = -2

Now the maximum area A =  x y at x =20 and y=20

                                        A = 20 X 20 = 400

                                         

<u>Conclusion</u>:-

The  dimensions are x =20 and y=20 of the garden that will maximize its area is 400

<u>verification</u>:-

The perimeter = 2(x +y) =80

                           2(20 +20) =80

                              2(40) =80

                              80 =80

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