Factor 5a^2-30a+45, and 2x^5+x^4-2x-1.
1 answer:
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Answer:
120
Step-by-step explanation:
Since we're dealing with a problem where the order matters and the first two letters are already chosen we need to subtract the number of letters and the number of available slots per group.
We use the permutation formula to find the answer, but before that let's check values.
n = 8
k = 5
Now since there are two letters already chosen we have to deduct two from both the value of n and k.
n = 6
k = 3
Now we can use the permutation formula:
The 3*2*1 cancels out and leaves us with:
So there are 120 possible ways to arrange eight letters into groups of five where order matters and the first two letters are already chosen.
Answer:
The correct answer B) The volumes are equal.
Step-by-step explanation:
The area of a disk of revolution at any x about the x- axis is πy² where y=2x. If we integrate this area on the given range of values of x from x=0 to x=1 , we will get the volume of revolution about the x-axis, which here equals,
which when evaluated gives 4pi/3.
Now we have to calculate the volume of revolution about the y-axis. For that we have to first see by drawing the diagram that the area of the CD like disk centered about the y-axis for any y, as we rotate the triangular area given in the question would be pi - pi*x². if we integrate this area over the range of value of y that is from y=0 to y=2 , we will obtain the volume of revolution about the y-axis, which is given by,
If we just evaluate the integral as usual we will get 4pi/3 again(In the second step i have just replaced x with y/2 as given by the equation of the line), which is the same answer we got for the volume of revolution about the x-axis. Which means that the answer B) is correct.