Shae makes $12.50 an hour. If she works 6.5 hours a day, after how many days will she have earned $500?
2 answers:
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Answer:
3π square units.
Step-by-step explanation:
We can use the disk method.
Since we are revolving around AB, we have a vertical axis of revolution.
So, our representative rectangle will be horizontal.
R₁ is bounded by y = 9x.
So, x = y/9.
Our radius since our axis is AB will be 1 - x or 1 - y/9.
And we are integrating from y = 0 to y = 9.
By the disk method (for a vertical axis of revolution):
So:
Simplify:
Integrate:
Evaluate (I ignored the 0):
The volume of the solid is 3π square units.
Note:
You can do this without calculus. Notice that R₁ revolved around AB is simply a right cone with radius 1 and height 9. Then by the volume for a cone formula:
We acquire the exact same answer.
In the figure, we can consider that the base is the side that mesures 12 in and that the height is the side that measures 15 in, since that sides are perpendicular. So, we just need to use the given formula:
Hence, the area of the triangle is 90 in² (B).