Set up the integral that would give the volume v generated by rotating the region bounded by the given curves about the y-axis.
y = x^3, y = 0, x = 5
1 answer:
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Answer:
f(x) = |x|
g(x) = |x| - 2
h(x) = |x| + 3
Step-by-step explanation:
All the functions graphed represent the absolute value functions.
Since function g(x) passes through (0, 0) and (1, 1),
Let the equation of a line passing through these points is,
y = mx + b
Slope of the line passing through these points 'm' =
m = 1
y-intercept of the line 'b' = 0
Therefore, equation of the line will be,
y = x
And the function representing the two lines (both are the mirror images) joining at the origin will be,
f(x) = |x|
When the parent function is shifted 3 units up, the new function will be
h(x) = |x| + 3
When the parent function is shifted 2 units down,
g(x) = |x| - 2
Answer:
19.6 cubic centimeters
Step-by-step explanation:
The ratio of two similar 3D figures' volumes is equivalent to the ratio of their corresponding lengths (whether it's width, height, length, radius, etc) cubed.
Here, we know the cones are similar, and we know the smaller radius is 2 and the larger radius is 3. Then the ratio of the volume of the smaller one to the volume of the larger one is .
We also know the actual volume of the larger cone is 66. So, if x is the volume of the smaller cone, we have the proportion:
x / 66 = 8 / 27
Cross-multiply:
27x = 66 * 8 = 528
Divide by 27:
x = 528/27 ≈ 19.6
The answer is thus 19.6 cubic centimeters.
<em>~ an aesthetics lover</em>
Answer:
Step-by-step explanation:
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