Solve the problem.Find the sum of the series by expressing as a geometric series, differentiating both sides of the resulting equation with respect to x, multiplying both sides by x, differentiating again, and replacing x by .

A.
B.
C.
D.


Answer: D

Mathematics

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Solve the problem.A man on a dock is pulling in a rope attached to a rowboat at a rate of 4 feet per second. If the man's hands are 3 feet higher than the point where the rope is attached to the boat, how fast is the angle of depression changing when there are still d feet of rope out? Give your answer in radians per second in terms of d.

A.   rads/sec
B.  rads/sec
C.  rads/sec
D.  rads/sec

Mathematics

Solve the problem.Emma's rubik cube has 216 cm2 of area. Each side of Sophie's cube is twice as wide as Emma's. Find the area of Sophie's cube.

A. 144 cm2 B. 72 cm2 C. 432 cm2  D. 864 cm2

Mathematics

Provide an appropriate response.Give five examples of the use of percent in sports or games.

What will be an ideal response?

Mathematics

Solve.A rectangular carpet has a perimeter of 270 inches. The length of the carpet is 89 inches more than the width. Find the dimensions of the carpet.

A. 79 in. by 102 in. B. 112 in. by 23 in. C. 112 in. by 135 in. D. 123.5 in. by 135 in.

Mathematics