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ic838847
08.07.2019 •
Mathematics
Which number line represents the solution set for the inequality 3(8-4x)< 6(x-5)?
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Ответ:
The dimensions of the rectangular part that allows as much light as possible are: 2.154 ft x 2.154 ft
Step-by-step explanation:
The dimensions of the Norman window are:
2x + 2y + pi x / 2 = 12 ft You should divide through by 2
x + y + (1/4)pi x = 6 ft X is cleared from multiplication
(1 + (1/4)pi ) x + y = 6 ft We clear Y
y = 6 - (1 + 0.25pi)x
So the total Area , A, to ensure the greatest amount of light is:
A = ( x * y + pi [(1/2)x]^2 ) / 2 Substituting y, we have
A = ( x * [ 6 - (1 + 0.25pi)x] + 0.25pix^2 ) / 2 Simplify
A = 6x - (1 + 0.25pi)*x^2 + 0.125pix^2
A = 6x - x^2 - 0.25pix^2 + 0.125pix^2
A = 6x - x^2 - 0.125pix^2
A= 6x - ( 1 + 0.125pi)x^2
The value of x that maximizes the area ≈ 2.154 ft
And y = [6 - (1 + 0.25pi)(2.154) ] ≈ 2.154 ft
So the rectangular part should be = 2.154 ft x 2.154 ft