Answer:
The volume is:
Step-by-step explanation:
See the sketch of the region in the attached graph.
We set the integral using washer method:
Notice here the radius of the washer is the difference of the given curves:
So the integral becomes:
We solve it:
Factor 
out and distribute the exponent (you can use FOIL):
Notice: 
So the integral becomes:
Then using the basic rule to evaluate the integral:
Simplifying a bit:
Then plugging the limits of the integral:
![\displaystyle\pi\left[\frac{4^3}{3}-\frac{4(4)^{5/2}}{5}+\frac{4^2}{2}-\left(\frac{1}{3}-\frac{4}{5}+\frac{1}{2}\right)\right]](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Cpi%5Cleft%5B%5Cfrac%7B4%5E3%7D%7B3%7D-%5Cfrac%7B4%284%29%5E%7B5%2F2%7D%7D%7B5%7D%2B%5Cfrac%7B4%5E2%7D%7B2%7D-%5Cleft%28%5Cfrac%7B1%7D%7B3%7D-%5Cfrac%7B4%7D%7B5%7D%2B%5Cfrac%7B1%7D%7B2%7D%5Cright%29%5Cright%5D)
Taking the root (rational exponents):
![\displaystyle\pi\left[\frac{4^3}{3}-\frac{4(2)^{5}}{5}+\frac{4^2}{2}-\left(\frac{1}{3}-\frac{4}{5}+\frac{1}{2}\right)\right]](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Cpi%5Cleft%5B%5Cfrac%7B4%5E3%7D%7B3%7D-%5Cfrac%7B4%282%29%5E%7B5%7D%7D%7B5%7D%2B%5Cfrac%7B4%5E2%7D%7B2%7D-%5Cleft%28%5Cfrac%7B1%7D%7B3%7D-%5Cfrac%7B4%7D%7B5%7D%2B%5Cfrac%7B1%7D%7B2%7D%5Cright%29%5Cright%5D)
Then doing those arithmetic computations we get:
It's irrational, number and intiger
Answer:
5
Step-by-step explanation:
In order to solve this problem, we need to use Pythagorem Theorem (a^2+b^2=c^2)
When using the pythagorem theorem the hypoteneuse would be the c^2 and the two other sides would be a and b (the order doesn't matter).
So, our formula would be:
4^2+3^2=c^2
Simplifies into:
25=c^2
In order to remove the exponent 2, we would have to square root both sides by 2. After doing so, you get the answer 5.
Hope this helps! :)
Answer:
P(4≤x≤7) = 2/3
Step-by-step explanation:
We'll begin by obtaining the sample space (S) i.e possible outcome of rolling both dice at the same time. This is illustrated below:
1,1 1,2 1,3 1,4 1,5 1,6
2,1 2,2 2,3 2,4 2,5 2,6
3,1 3,2 3,3 3,4 3,5 3,6
4,1 4,2 4,3 4,4 4,5 4,6
5,1 5,2 5,3 5,4 5,5 5,6
6,1 6,2 6,3 6,4 6,5 6,6
Adding the outcome together, the sample space (S) becomes:
2 3 4 5 6 7
3 4 5 6 7 8
4 5 6 7 8 9
5 6 7 8 9 10
6 7 8 9 10 11
7 8 9 10 11 12
Next, we shall obtain the event of 4≤x≤7. This is illustrated below:
4 5 6 7
4 5 6 7
4 5 6 7
4 5 6 7
4 5 6 7
4 5 6 7
Finally, we shall determine P(4≤x≤7). This can be obtained as follow:
Element in the sample space, n(S) = 36
Element in 4≤x≤7, n(4≤x≤7) = 24
Probability of 4≤x≤7, P(4≤x≤7) = ?
P(4≤x≤7) = n(4≤x≤7) / nS
P(4≤x≤7) = 24/36
P(4≤x≤7) = 2/3
Initial balance, I = $2376.10 .
Total amount of purchase made, A = $( 875.22+65.75+45.22+21.23 ) = $1007.42 .
Total amount credit, c = $875.22 .
Fine, f = $45.30 .
Another purchase, 
.
So, balance left is :
B = I - A - f - a + c
B = 2376.10 - 1007.42 - 45.30 - 59.4025 + 875.22
B = $2139.1975
Hence, this is the required solution.
