Answer:
<h2>a) length x = 45ft</h2><h2>b) maximum area = 4050 ft²</h2>
Step-by-step explanation:
Given the quadratic equation A=−2x2+180x that gives the area A of the yard for the length x, to maximize the area of the yard then dA/dx must be equal to zero i.e dA/dx = 0
If A=−2x²+180x
dA/dx = -4x + 180 = 0
-4x + 180 = 0
Add 4x to both sides
-4x + 180 + 4x = 0 + 4x
180 = 4x
x = 180/4
x = 45
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<em>Hence the length of the building that should border the yard to maximize the area is 45 ft</em>
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To find the maximum area, we will substitute x = 45 into the modelled equation of the area i.e A=−2x²+180x
A = -2(45)²+180(45)
A = -2(2025)+8100
A = -4050 + 8100
A = 4050 ft²
<em>Hence the maximum area of the yard is equal to 4050 ft²</em>
Answer:
(a + 1)²(a + 7).
Step-by-step explanation:
The original expression:
Factor each denominator:
Factor out
Multiply each term by the opposite denominator and add:
Remove brackets:
The least common denominator is (a + 1)²(a + 7).
I think it’s 82 because 78+4=82
Answer:
4 :-)))))))) have a wonderful day!