Solve the problem.A window is in the form of a rectangle surmounted by a semicircle. The rectangle is of clear glass, whereas the semicircle is of tinted glass that transmits only one-fifth as much light per unit area as clear glass does. The total perimeter is fixed. Find the proportions of the window that will admit the most light. Neglect the thickness of the frame.
A. 
= 
B. 
= 
C. 
= 
D. 
= 
Answer: B
Mathematics
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Calculate the derivative of the function. Then find the value of the derivative as specified.g(x) = x3 + 5x; g '(1)
A. g '(x) = 3x2 + 5x; g '(1) = 8 B. g '(x) = 3x2; g '(1) = 3 C. g '(x) = 3x2 + 5; g '(1) = 8 D. g '(x) = x2 + 5; g '(1) = 6
Mathematics
Solve the problem.Find f(-4) when f(x) = -x2 + 2x - 1.
A. 9 B. 23 C. - 25 D. 7
Mathematics
Find the standard form of the equation of the hyperbola.
A. 
- 
= 1
B. 
- 
= 1
C. 
- 
= 1
D. 
- 
= 1
Mathematics
Find the double integral over the rectangular region R with the given boundaries.
R0 ? x ? 4, -2 ? y ? 1
A. 76
B. 67
C. 112
D. 
Mathematics