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.
My answer: $2000 were invested at 5%
Let x amount of money was invested at 5% and (6000-x) amount was invested as 3%
Answer:
option B is the correct answer of this question.
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Answer:
y = 14x
Step-by-step explanation:
Use the direct variation equation, y = kx
Plug in 7 as y and 0.5 as x, and solve for k:
y = kx
7 = k(0.5)
14 = k
Plug this into the equation:
y = kx
y = 14x
So, the equation of variation is y = 14x