Answer:
Suppose that you have a square of side length x, the area of this square will be:
A = x^2.
Now, by dynamics, we know that the position of an object that is falling down from a height H, can be written as:
H(t) = (-g/2)*t^2 + H.
We can see a pattern, x^2 is used in both.
Now, profit can be also modeled with quadratic equations, where our objective is to find the maximum of the quadratic (so we can have the maximum profit)
Then the parent function that is useful for gravity, calculating area and profit is the quadratic function:
f(x) = x^2
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
<em></em>
<em>Hence the length of the building that should border the yard to maximize the area is 45 ft</em>
<em></em>
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>
Rowan raised 640 last year
this year he raised 15% more
percent means parts out of 100
15%=15/100=3/20
15% of 640
'of' can be translated as multiply
15%=3/20
3/20 times 640=1920/20=192/2=96
this is 15%
he raised 15% MORE SO
640+96=this year=736
he raised 736 dollars this year
Answer:
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Step-by-step explanation: