Verify the identity.csc 4 x - cot 4 x = csc 2 x + cot 2 x
What will be an ideal response?
csc 4 x - cot 4 x = (csc 2 x + cot 2 x)(csc 2 x - cot 2 x) = (csc 2 x + cot 2 x)(1) = csc 2 x + cot 2 x.
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Solve the problem.How close does the curve y = 
come to the point 
? (Hint: If you minimize the square of the distance, you can avoid square roots.)
A. The distance is minimized when x = 
; the minimum distance is 
units.
B. The distance is minimized when x = 
; the minimum distance is 
units.
C. The distance is minimized when x = - 
; the minimum distance is 
units.
D. The distance is minimized when x = 
; the minimum distance is 
units.
Find the indicated probability. Round your answer to 6 decimal places when necessary.What is the probability that a family with three children does not have three children of the same gender? Assume boys and girls are equally likely.
A. 
B. 
C. 
D. 
Use integration by parts to establish a reduction formula for the integral.
A. 
= xn ex - n 
B. 
= xn ex - n 
C. 
= xn ex + n 
D. 
= xn ex - 
Solve. If necessary, round answers to the nearest hundredth.The following test scores were recorded for a student: 84, 53, 73, 53, 54. Find the mean, median, and mode.
A.
| mean: 66 | median: 73 | mode: 84 |
B.
| mean: 63.4 | median: 54 | mode: 84 |
C.
| mean: 79.3 | median: 63.5 | mode: 53 |
D.
| mean: 63.4 | median: 54 | mode: 53 |