Use mathematical induction to prove the following.
. . . 
= 
What will be an ideal response?
Answers may vary. One possibility:
Sn: 
. . . 
= 
S1: 
= 
Sk: 
. . . 
= 
Sk+1: 
. . . 
= 
1. Basis step: Since 
= 
= 1 - 
, S1 is true.
2. Induction step: Let k be any natural number. Assume Sk. Deduce Sk+1.
. . . 
= 
. . . 
= 
= 
= 
= 
= 
.
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Graph the function.y = csc 
A. 
B. 
C. 
D. 
Determine whether the relation represents a function. If it is a function, state the domain and range.{(4.22, 11.42), (4.222, -11.4), (
, 0), (0.71, -4)}
A. function
domain: {4.22, 4.222, 
, 0.71}
range: {11.42, -11.4, 0, -4}
B. function
domain: {11.42, -11.4, 0, -4}
range: {4.22, 4.222, 
, 0.71}
C. not a function
Solve.A projectile moves so that its position at any time t is given by the equations x = 24t and 
for t in [0, 12]. Graph the path of the projectile and find the equivalent rectangular equation. Use the window [0, 700] by [0, 800]. 
A. 
y = 3x - 
x2
B. 
y = 3x - 
x2
C. 
y = 8x - 
x2
D. 
y = 8x - 
x2
Identify the exercise as either a permutation (order matters) or combination (order does not matter) counting problem. Do not actually solve the exercise.Five of a sample of 100 computers will be selected and tested. How many ways are there to make this selection?
A. Permutation B. Combination