Solve for the value of k. (k+8) 400
1 answer:
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(1/3) × the cone's volume = The cylinder's volume.
Step-by-step explanation:
Step 1:
The volume of any cone is obtained by multiplying with π, the square of the radius (
) and the height (
).
So the volume of the cone, .
Step 2:
The cylinder's volume is nearly the same as the cone but instead by multiplying we multiply with 1.
So the cylinder's volume is determined by multiplying π with the square of the radius of the cylinder () and the height of the cylinder (
).
So the the cone's volume, .
Step 3:
Now we equate both the volumes to each other.
The cone's volume : The cylinder's volume = =
.
So if we multiply the cone's volume with we will get the cylinder's volume with the same dimensions.
Answer: Any real number x as long as and
In other words, anything but 0 or -2/3 is valid.
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Explanation:
Set the denominator equal to zero and solve for x
2(3x^2 + 2x) = 0
3x^2 + 2x = 0
x(3x + 2) = 0
x = 0 or 3x+2 = 0 .... zero product property
x = 0 or 3x = -2
x = 0 or x = -2/3
If either x = 0 or x = -2/3, then the denominator 2(3x^2 + 2x) will be zero. But recall that we cannot have zero in the denominator. Dividing by zero is not allowed. The expression is undefined when we divide by zero.
Therefore, we must exclude x = 0 and x = -2/3 from the domain. Any other real number is valid as an x input.