215 ÷ 2 = 107.50
He needs to save $107.50 each month
2 goes into 2 = 1
2 goes into 1 = 0
Now 2 goes into 15 = 7 with 1 left over
107 & 1/2
OR $107.50
Answer:
Step-by-step explanation:
There are
.. floor(200/6) = 33 multiples of 6
in the range 1 .. 200.
There are
.. floor(200/15) = 13 multiples of 15
in the range 1 .. 200, half of which are also multiples of 6.
So, there are 33 +13 -6 = 40 numbers in the range 1 .. 200 that are multiples of either 6 or 15 or both.
The remaining 200 -40 = 160 numbers are not multiples of either.
Algebraically, that will be expressed as:
Cross sections of the volume are washers or annuli with outer radii <em>x(y)</em> + 1, where
<em>y</em> = <em>x(y) </em>² - 1 ==> <em>x(y)</em> = √(<em>y</em> + 1)
and inner radii 1. The distance between the outermost edge of each shell to the axis of revolution is then 1 + √(<em>y</em> + 1), and the distance between the innermost edge of <em>R</em> on the <em>y</em>-axis to the axis of revolution is 1.
For each value of <em>y</em> in the interval [-1, 3], the corresponding cross section has an area of
<em>π</em> (1 + √(<em>y</em> + 1))² - <em>π</em> (1)² = <em>π</em> (2√(<em>y</em> + 1) + <em>y</em> + 1)
Then the volume of the solid is the integral of this area over [-1, 3]: