Do you notice anything strange about those points ?
(0, 1),
(1, 2),
(2, 4),
(3, 8).
The y-coordinate of each point is (2) raised to the power of the x-coordinate.
First point: x=0, y=2⁰ = 1
Second point: x=1, y=2¹ = 2
Third point: x=2, y=2² = 4
Fourth point: x=3, y=2³ = 8
The equation of the curve appears to be
y = 2 ^ x .
So, after 10 hours, x=10, and y = 2¹⁰ = 1,024 .
Answer:
The volume of the ball with the drilled hole is:

Step-by-step explanation:
See attached a sketch of the region that is revolved about the y-axis to produce the upper half of the ball. Notice the function y is the equation of a circle centered at the origin with radius 15:

Then we set the integral for the volume by using shell method:

That can be solved by substitution:

The limits of integration also change:
For x=5: 
For x=15: 
So the integral becomes:

If we flip the limits we also get rid of the minus in front, and writing the root as an exponent we get:

Then applying the basic rule we get:

Since that is just half of the solid, we multiply by 2 to get the complete volume:


Answer:
68
Step-by-step explanation:
Step 1: Convert fraction to improper
4 1/4 = 16/4 + 1/4 = 17/4
Step 2: Multiply 16 and 17/4
16(17/4) = 272/4 = 68
Emily’s weekly allowance would be $7.
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