An hourglass consists of two sets of congruent composite figures on either end. Each composite figure is made up of a cone and a
cylinder, as shown below: Hourglass with sand measuring 45 millimeters high © 2011 Jupiterimages Corporation Each cone of the hourglass has a height of 15 millimeters. The total height of the sand within the top portion of the hourglass is 45 millimeters. The radius of both cylinder and cone is 6 millimeters. Sand drips from the top of the hourglass to the bottom at a rate of 10π cubic millimeters per second. How many seconds will it take until all of the sand has dripped to the bottom of the hourglass? (4 points) Select one: a. 126 b. 108 c. 18 d. 29
1 answer:
Answer:
126
Step-by-step explanation:
Total volume of sand = pi/3*(6^2)*(15) + pi*(6)^2*(30) = 1260*pi mm^3
So it will therefore take 1260*pi/10*pi = 126 seconds for all of the sand from the top hourglass to drip down to the bottom hourglass.
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Answer:
a
Step-by-step explanation:
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a. Recall that
For 
, we have
By integrating both sides, we get
If 
, then
so that
We can shift the index to simplify the sum slightly.
b. The power series for 
can be obtained simply by multiplying both sides of the series above by 
.
c. We have
