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Charra [1.4K]
2 years ago
5

Help? question below

Mathematics
2 answers:
andre [41]2 years ago
8 0
First you set up your equations
Company 1–> 9.65x+43
Company 2–> 8.40x+58

Next you set them equal to each other
9.65x+43=8.40x+58
9.65x-8.40x=58-43
1.25x=15/1.25
x=12
When you plug 12 into both equations you’ll get that they both equal 158.8
Readme [11.4K]2 years ago
7 0

Answer:

12 shirts

Step-by-step explanation:

First, let x = # of shirts and y = total cost in $. Then create an equation with x and y representing each company. The first company is y = 9.65x + 43 and the second company is y = 8.40x + 58. Since we need to find the # of shirts that would result in the equal total cost, we need to find x when y is equal to the other. Thus here is the setup: 9.65x + 43 = 8.40x + 58, and we would get 1.25x = 15, so x = 12.

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Find the dimensions of the rectangle with area 256 square inches that has minimum perimeter, and then find the minimum perimeter
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Answer:

Dimensions: A=a\cdot b=256

Perimiter: P=2a+2b

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Step-by-step explanation:

This is a problem of optimization with constraints.

We can define the rectangle with two sides of size "a" and two sides of size "b".

The area of the rectangle can be defined then as:

A=a\cdot b=256

This is the constraint.

To simplify and as we have only one constraint and two variables, we can express a in function of b as:

b=\frac{256}{a}

The function we want to optimize is the diameter.

We can express the diameter as:

P=2a+2b=2a+2*\frac{256}{a}

To optimize we can derive the function and equal to zero.

dP/da=2+2\cdot (-1)\cdot\frac{256}{a^2}=0\\\\\frac{512}{a^2}=2\\\\a=\sqrt{512/2}= \sqrt {256} =16\\\\b=256/a=256/16=16

The minimum perimiter happens when both sides are of size 16 (a square).

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