Mary and Frank have two bags in front of them. Mary’s bag has 4 marbles; blue, yellow, red and green. Frank’s bag has 3 marbles;
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Answer:
Step-by-step explanation:
We know that the transformations of a cosine equation can be shown as:
y=±a(b(x-h))+k
Where 'a' is the amplitude
'b' is the horizontal change (Do 2π/b to find the period)
'h' is the horizontal shift
and 'k' is the vertical shift or midline.
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If the amplitude is 4, we can assume a=4.
Since the period is 4/7, we can solve for the 'b' value by:
Next, since the midline is 2, we know that a vertical shift of 2 occurred. Thus, the 'k' value is 2.
Writing this equation gives us:
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]: