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
The maximum side would be at
This gives us 20.8569
Read more on areas and dimensions here:
brainly.com/question/19819849
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Answer:
j² - 5j²k - 2
Step-by-step explanation:
3j² - j²k - 6 - 4j²k - 2j² + 4
To simplify this polynomial, we can collect like terms. A term is number(s) or variable(s) that are grouped together by multiplication. <u>Like terms have the same variable and exponent</u>.
We have three groups of like terms:
The j-squares (j²), the j-squared k (j²k) and the constants (no variable).
Remember to include the negatives!
The j-squares are: 3j² ; -2j²
The j-squares k are: - j²k ; - 4j²k
The constants are: - 6 ; 4
Simplify:
3j² - j²k - 6 - 4j²k - 2j² + 4
Rearrange the polynomial by like terms
= (- j²k - 4j²k) + (3j² - 2j²) + (- 6 + 4)
Add or subtract the like terms
= (-5j²k) + (j²) + (-2)
Remove brackets and rearrange so the negative is not first
= j² + - 5j²k + - 2
Simplify where two signs are together. Adding a negative is subtraction.
= j² - 5j²k - 2 Simplified
The answer is x = 0, -13/2
Answer:
11
Step-by-step explanation:
By this logic, if you are simply placing the numbers side by side to make a new number, it would be 11.
25/100 is 1/4 in similest form
