Multiply: 4x ^3sqrt 4x^2 (2 ^3sqrt 32x^2 * x ^3sqrt 2x)
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Answer:
To find the exact vale of atan(-sqrt(3)) we're going to need the help of a calculator
atan(-sqrt(3)) = -1.04719755 rads.
If you take a look at the important angles, you will notice that the arc is minus 60 degrees which equals -1.04716755 radians.
The standard deviation is 19.91.
To find the standard deviation is a binomial distribution, you have to take the square root of the total number multiplied by the percent and its compliment.
Our expression will be:
This will evaluate to about 19.91.
To find the standard deviation is a binomial distribution, you have to take the square root of the total number multiplied by the percent and its compliment.
Our expression will be:
This will evaluate to about 19.91.
Explanation:
Let and
. The differential volume dV of the cylindrical shells is given by
Integrating this expression, we get
To determine the limits of integration, we equate the two functions to find their solutions and thus the limits:
We can clearly see that x = 0 is one of the solutions. For the other solution/limit, let's solve for x by first taking the square of the equation above:
or
Since we are rotating the functions around the y-axis, we are going to use the x = 25 solution as one of the limits. So the expression for the volume of revolution around the y-axis is