Answer:
Side lengths = 1.68 ft and width = 3.36 ft.
Step-by-step explanation:
Let the side lengths of the window be L and the width = 2r ( r is also the radius of the semi-circle).
So we have
Perimeter = 2L + 2r + πr = 12
Area = 2rL + 0.5πr^2
From the first equation
2L = 12 - 2r - πr
Substitute for 2L in the equation for the area:
A = r(12 - 2r - πr) + 0.5πr^2
A = 12r - 2r^2 - πr^2 + 0.5πr^2
A = 12r - 2r^2 - 0.5πr^2
We need to find r for the maximum area:
Finding the derivative and equating to zero:
A' = 12 - 4r - πr = 0=
4r + πr = 12
r = 12 / ( 4 + π)
r = 1.68 ft.
So the width of the window = 2 * 1.68 = 3.36 ft.
Now 2L = 12 - 2r - πr
= 12 - 2*1.68 - 1.68π
= 3.36
L = 1.68.
5x - 3y = 10
x + y = 7......multiply by -5
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5x - 3y = 10
-5x - 5y = -35 (result of multiplying by -5)
------------------add
-8y = -25
y = 25/8
x + y = 7
x + 25/8 = 7
x = 7 - 25/8
x = 56/8 - 25/8
x = 31/8
solution is (31/8 , 25/8)
They are supplementary angles. Aka equal to 180 degrees.
The larger number is 6 and the smaller one is 2.
Answer:
It would b A
Step-by-step explanation:
