<h3>This cylinder is 8 inches tall and has a volume of 200 π in³. Find the area of the cross section.</h3>
Answer: cross section = 25π in²
Step-by-step explanation:
Cylinder volume is the product of the cross section by height.
Then cross section = cylinder volume/height = 200 π in³/8in = 25π in²
Answer: 25π in²
Answer:
B) -3
Step-by-step explanation:
The zeros of the function are found easily from the factors. They are 6 and -12. The x-coordinate is halfway between them, at (6 + (-12))/2 = -6/2 = -3.
If you want a formula, consider a quadratic with roots (zeros) p and q. Then it factors as
... y = (x -p)(x -q)
The line of symmetry through the vertex is also the line of symmetry between the roots, so has x-coordinate:
... x = (p+q)/2
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In your problem, you have p=6, q=-12, so x = (p+q)/2 = -6/2 = -3 is the line of symmetry and the x-coordinate of the vertex.
First, notice that, by the Pythagorean Theorem,
meaning that:
Also, since the volume of a cone with radius r and height h is we know that the volume of the cone is:
Therefore, we want to maximize the function subject to the constraint .
To find the critical points, we differentiate:
Therefore, when
meaning that or . Only is in the interval so that’s the only critical point we need to concern ourselves with.
Now we evaluate at the critical point and the endpoints:
Therefore, the volume of the largest cone that can be inscribed in a sphere of radius 3 is
Answer:
Step-by-step explanation:
b and c are the speeds of the boat in stool water, and current, respectively.
Going with the current, the boat travels b+c=16 km/h.
Going against the current, the boat travels b-c=6 km/h
add the equations together
b+c = 16
b-c = 6
—————
2b = 22
b = 11
c = 16-b = 5