Solve the problem.The strength S of a wooden beam with rectangular cross section is given by the formula S = kd3 sin2 ? cos ?where d is the diagonal length, ? the angle illustrated, and k is a constant that varies with the type of wood used. 
Let d = 1 and express the strength S in terms of the constant k for ? = 45°, 50°, 55°, 
and 65°. Does the strength always increase as ? gets larger?
What will be an ideal response?
0.354k; 0.377k; 0.385k; 0.375k and 0.347k; No, it reaches a maximum near 55°.
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What value of x gives the minimum value of the quadratic function 
? Round your answer to two decimal places.
?
A. 2.66 B. 2.44 C. 1.27 D. 0.38
Evaluate the integral by first performing long division on the integrand and then writing the proper fraction as a sum of partial fractions.
A. 
+ 16x + 32 ln 
- 32 ln 
+ C
B. 
+ 8 ln 
- 8 ln 
+ C
C. 
+ 16x + 32 ln 
- 32 ln 
+ C
D. 
+ 16x - 32 ln 
+ 32 ln 
+ C
Use the Gauss-Jordan method to solve the system of equations. If the system has infinitely many solutions, give the solution with y arbitrary. 6x + 4y = -4 5x + 7y = 4
A. ? B. {(2, -2)} C. {(-2, -2)} D. {(-2, 2)}
Find the equation that the given graph represents.
A. f(x) = x3 + x2 + x + 5 B. f(x) = x3 + 4x2 - x - 5 C. f(x) = -x3 + 4x2 + x - 5 D. f(x) = x2 + 4x - 5