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: C
Mathematics
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Solve the problem.Find the derivative of the function 
at the point 
in the direction in which the function decreases most rapidly.
A. -
B. -
C. -3
D. -
Mathematics
Write the expression in the standard form a + bi.If z = 7 - 9i and w = 6 + 7i, evaluate 
.
A. -13 + 2i B. 13 - 2i C. 1 + 16i D. 13 + 2i
Mathematics
Solve the system of equations using matrices. Use Gauss-Jordan elimination. x + y - z + w = -5 3x - y + 3z - 2w = 7-2x + 2y + z - w =16 -x - 2y - 3z + 3w = -22
A. {(-2, -3, 5, 
)}
B. {(2, -3, -4, -2)}
C. {(
, - 
, - 
, - 
)}
D. {(-2, 3, 4, -2)}
Mathematics
Determine the number of terms and identify the coefficient of each term of the expression.6n - 5c - x
A. 3; 6, -5, 1 B. 2; 6 and -5 C. 3; 6, 5, 1 D. 3; 6, -5, -1
Mathematics