Question

1. Evaluate
(1^2 - 0^2) + (2^2- 1^2) + (3^2- 2^2)+ (4^2- 3^2)+.......+(10^2 - 9^2).
A) 110
B) 123
C) 100
D) 114
E) 125
2. A cylinder with radius 8 and height 17 is rolled long the floor so that it compltes 2 full revolutions. what is the area of the region of the floor that was touched by the cylinder during the roll?
A) 453 pi
B) 434 pi
C) 456 pi
D) 544 pi
E) 478 pi
(pi is 3.14) :)

Answer 1

100

Answer 2

1 is a "telescoping sum" meaning that you subtract off all the stuff that came before it. only term that survive is 10^2=100

Answer 3

for second one circumference of the circle is
\[2\pi r=2\pi \times 8=16\pi\]

Answer 4

rolls across twice so you have a rectangle with base
\[32\pi\] and height 17 for a total area of
\[17\times 32\pi=544\pi\]

Answer 5

thank you very much :) for your help