Jeff and his family are driving to visit his grandmother.they have driven about 30 miles, which is about 2/3 of the way. ow much
1 answer:
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Here we have a system of equation like this:
from the first equation we get:
Substitute in the second equation we get:
Substitute i the first equation again we get:
We deduce that:
A is bigger than B.
from the first equation we get:
Substitute in the second equation we get:
Substitute i the first equation again we get:
We deduce that:
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.