Answer:
Numbers are 28 and -15
Step-by-step explanation:
Mark first number X, and second number Y, then:
x-y=43
and
x+y=13
We get system of two equations. Solve it by add both them together:
x-y+x+y=43+13
2x=56
x=28 we get first number
x+y=13
28+y=13
y=13-28
y=-15
The dimension that would give the maximum area is 20.8569
<h3>How to solve for the maximum area</h3>
Let the shorter side be = x
Perimeter of the semi-circle is πx
Twice the Length of the longer side
![[70-(\pi )x -x]](https://tex.z-dn.net/?f=%5B70-%28%5Cpi%20%29x%20-x%5D)
Length = ![[70-(1+\pi )x]/2](https://tex.z-dn.net/?f=%5B70-%281%2B%5Cpi%20%29x%5D%2F2)
Total area =
area of rectangle + area of the semi-circle.
Total area =
![x[[70-(1+\pi )x]/2] + [(\pi )(x/2)^2]/2](https://tex.z-dn.net/?f=x%5B%5B70-%281%2B%5Cpi%20%29x%5D%2F2%5D%20%2B%20%5B%28%5Cpi%20%29%28x%2F2%29%5E2%5D%2F2)
When we square it we would have
![70x +[(\pi /4)-(1+\pi)]x^2](https://tex.z-dn.net/?f=70x%20%2B%5B%28%5Cpi%20%2F4%29-%281%2B%5Cpi%29%5Dx%5E2)
This gives
![70x - [3.3562]x^2](https://tex.z-dn.net/?f=70x%20-%20%5B3.3562%5Dx%5E2)
From here we divide by 2
![35x - 1.6781x^2](https://tex.z-dn.net/?f=35x%20-%201.6781x%5E2)
The maximum side would be at
![x = 35/2*1.6781](https://tex.z-dn.net/?f=x%20%3D%2035%2F2%2A1.6781)
This gives us 20.8569
Read more on areas and dimensions here:
brainly.com/question/19819849
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Answer:
4. 2 2/3 yd
Step-by-step explanation:
96" = (96 ÷ 36) = 2.6666666666666 yd or 2 2/3
8 and 1/2 as an improper fraction is 17/2
To convert an improper fraction to a mixed fraction, follow these steps:
Divide the numerator by the denominator.
Write down the whole number answer.
Then write down any remainder above the denominator.