Solve the problem.The formula y = 
models the relationships needed to focus an image where y is the distance between the film and projector lens, x is the distance between the move screen and the projector lens, and f is the focal length. a) Sketch the graph of this rational function for f = 5 centimeters. 
b) Bob and Carol are showing home movies. Use the graph to describe the desired distance between the film and the projector lens as Carol moves the projector further from the screen.
What will be an ideal response?
a)
b) To remain focused, the desired distance between the film and the projector lens decreases and approaches 5 centimeters as the distance between the movie screen and the projector lens increases.
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Find fx, fy, and fz.f(x,y,z) = xe(x2 + y2 + z2)
A. fx = (1 + 2x2) e(x2 + y2 + z2); fy = 2xye(x2 + y2 + z2); fz = 2xze(x2 + y2 + z2) B. fx = (1 + 2x2) e(x2 + y2 + z2); fy = xe(x2 + y2 + z2); fz = xe(x2 + y2 + z2) C. fx = 2x2e(x2 + y2 + z2); fy = xye(x2 + y2 + z2); fz = 2xze(x2 + y2 + z2) D. fx = (1 + 2x2) e(x2 + y2 + z2); fy = xy2e(x2 + y2 + z2); fz = xz2e(x2 + y2 + z2)
Simplify. Write final answer in radical form when necessary.
A. x8
B. 
C. x12
D. 
Solve the problem.In one state's Multi-Million Lottery you choose 5 numbers between 1 and 56 plus a Mega number between 1 and 36. Suppose that a winning ticket pays $60 million (assume that the prize will not be split among several winners). Find the expected value of a $1 lottery ticket. Round your answer to the nearest penny.
A. $-0.56 B. $-0.44 C. $-1.00 D. $0.44 E. $0.56
Divide.
A. 
+ 
i
B. - 
+ 
i
C. - 
- 
i
D. 
+ 
i