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Lostsunrise [7]
3 years ago
13

A local middle school recently reported that enrollment increased to 108% percent of last year. If enrollment last year was at 1

7,113, about how many students enrolled this year? Round to the nearest whole number.
Mathematics
1 answer:
Grace [21]3 years ago
5 0

Answer:

18961

Step-by-step explanation:

108% is the same as 0.108. If you multiply 17113 with 0.108 you will get 1848.204. Then round it. 1848. Add this to 17113 and you'll get 18961

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For the region bounded by y=2x​, the​ x-axis, and x=1​, determine which of the following is​ greater: the volume of the solid ge
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Answer:

The correct answer B) The volumes are equal.

Step-by-step explanation:

The area of a disk of revolution at any x about the x- axis is πy² where y=2x. If we integrate this area on the given range of values of x from x=0 to x=1 , we will get the volume of revolution about the x-axis, which here equals,

\int\limits^1_0 {(pi)y^{2} } \, dx

which when evaluated gives 4pi/3.

Now we have to calculate the volume of revolution about the y-axis. For that we have to first see by drawing the diagram that the area of the CD like disk centered about the y-axis for any y, as we rotate the triangular area given in the question would be pi - pi*x². if we integrate this area over the range of value of y that is from y=0 to y=2 , we will obtain the volume of revolution about the y-axis, which is given by,

\int\limits^2_0 {pi - pix^{2} } \, dy = \int\limits^2_0 {1 - y^{2}/4 } \, dy

If we just evaluate the integral as usual we will get 4pi/3 again(In the second step i have just replaced x with y/2 as given by the equation of the line), which is the same answer we got for the volume of revolution about the x-axis. Which means that the answer B) is correct.

7 0
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