(6 points) Janet bakes a cake in the shape of a cube with side length z (in inch

Question

(6 points) Janet bakes a cake in the shape of a cube with side length z (in inches). She makes a vertical cut parallel to one of the sides, resulting in a slice with width y where r is 5 times as large as y. a) Define a function h that determines the volume of the cake before Janet makes the first cut in terms of the original width of the cake, z. b) Define a function g that determines the width of the slice of cake in terms of the original width of the cake, r. c) Define a function f that determines the volume of the slice of cake in terms of the original width of the cake, z. d. Using the functions you defined in part (a) and (c), represent the volume of the cake that remains after Janet eats this slice in terms of the original width of the cake, x. OA. f(h(z) B. h(f(x)) c. f(z)+h() D. h()-f(x) E. f()- h(x) O F. None of the above e) Define a function k that determines the remaining volume of cake in terms of the original width of the cake, z. f) Use the function you defined in part (e) to determine the remaining volume of cake if the original width of the cake was 10 inches.

Explanation / Answer

a)

h(x) =x3

b)

x =5y

=>y=(1/5)x

g(x) = (1/5)x

g(x) = 0.2x

c)

f(x)=x*x*(1/5)x

=>f(x)=(1/5)x3

=>f(x)=0.2x3

d)

h(x) - f(x)

e)

k(x) =x3 -(1/5)x3

=>k(x) =(4/5)x3

=>k(x) =0.8x3

f)

k(10) =(4/5)*103

k(10) =800

remaining volume of cake is 800 cubic inches

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