Hello, please consider the following.
![\displaystyle \begin{aligned} \int\limits^x {5sin(5t)sin(t)} \, dt &= -\int\limits^x {5sin(5t)} \, d(cos(t))\\ \\&=-[5sin(5t)cos(t)]+ \int\limits^x {25cos(5t)cos(t)} \, dt\\\\&=-5sin(5x)cos(x)+ \int\limits^x {25cos(5t)} \, d(sin(t))\\ \\&=-5sin(5x)cos(x)+[25cos(5t)sin(t)]+ \int\limits^x {25sin(5t)sin(t)} \, dt\\\\&=-5sin(5x)cos(x)+25cos(5x)sin(x)+ \int\limits^x {(25*5)sin(5t)sin(t)} \, dt\end{aligned}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cbegin%7Baligned%7D%20%5Cint%5Climits%5Ex%20%7B5sin%285t%29sin%28t%29%7D%20%5C%2C%20dt%20%26%3D%20-%5Cint%5Climits%5Ex%20%7B5sin%285t%29%7D%20%5C%2C%20d%28cos%28t%29%29%5C%5C%20%5C%5C%26%3D-%5B5sin%285t%29cos%28t%29%5D%2B%20%5Cint%5Climits%5Ex%20%7B25cos%285t%29cos%28t%29%7D%20%5C%2C%20dt%5C%5C%5C%5C%26%3D-5sin%285x%29cos%28x%29%2B%20%5Cint%5Climits%5Ex%20%7B25cos%285t%29%7D%20%5C%2C%20d%28sin%28t%29%29%5C%5C%20%5C%5C%26%3D-5sin%285x%29cos%28x%29%2B%5B25cos%285t%29sin%28t%29%5D%2B%20%5Cint%5Climits%5Ex%20%7B25sin%285t%29sin%28t%29%7D%20%5C%2C%20dt%5C%5C%5C%5C%26%3D-5sin%285x%29cos%28x%29%2B25cos%285x%29sin%28x%29%2B%20%5Cint%5Climits%5Ex%20%7B%2825%2A5%29sin%285t%29sin%28t%29%7D%20%5C%2C%20dt%5Cend%7Baligned%7D)
And we can recognise the same integral, so.

And then,

Thanks
Eay peasy
solve graphically
graph them and find the poitn that they intersect at
y=mx+b
m=slope
b= y intercept
y=7x-9
slope=7
yintercept=-9
y=3x-1
slope=3
yinercept=-1
I have attached graph below
easier way would be to simply sub them and solve
7x-9=y=3x-1
7x-9=3x-1
4x-9=-1
4x=8
x=2
y=3x-1
y=3*2-1
y=6-1
y=5
(2,5) is solution
Short Answer 5/216
Comment
The question really is, how many different types of throws with 4 dice will give 21? You can count them
Pattern 1
6663
Pattern 2
5556
Pattern 3 [ The hard one]
6654
Patterns 1 and 2 give 4 each.
6 6 6 3
6 6 3 6
6 3 6 6
3 6 6 6
5553 will do the same thing
Both can be found by (4/1) as a combination.
Now for 6654 That gives 12
6 6 5 4
6 6 4 5
6 5 4 6
6 5 6 4
6 4 5 6
6 4 6 5
5 6 4 6
5 6 6 4
5 4 6 6
4 5 6 6
4 6 5 6
4 6 6 5
That should total 12
The total number of ways of getting 21 with this pattern is 12
Total successes
12 + 4 + 4 = 30
What is the total number of ways you can throw 4 dice?
Total = 6 * 6 * 6 * 6 = 1296
What is the probability of success?
30 / 1296 = 5 / 216
Answer:
More money was spent on the fall dance, than the spring dance.
Answer:
2/-2
Step-by-step explanation:
2 is the numberator and -2 is the denominator.