Answer:
![{ \sf{ \int 4x \cos(2 - 3x) dx = {4x}^{2} \cos(2 - 3x) + c }}](https://tex.z-dn.net/?f=%7B%20%5Csf%7B%20%5Cint%204x%20%5Ccos%282%20-%203x%29%20dx%20%3D%20%20%7B4x%7D%5E%7B2%7D%20%5Ccos%282%20-%203x%29%20%20%2B%20c%20%7D%7D)
Step-by-step explanation:
<u>From integration by parts:</u>
![{ \boxed{ \bf{ \int u \: \frac{dv}{dx} = uv - \int v \: \frac{du}{dx} }}}](https://tex.z-dn.net/?f=%7B%20%5Cboxed%7B%20%5Cbf%7B%20%5Cint%20u%20%20%5C%3A%20%20%5Cfrac%7Bdv%7D%7Bdx%7D%20%20%3D%20uv%20-%20%20%5Cint%20v%20%5C%3A%20%5Cfrac%7Bdu%7D%7Bdx%7D%20%7D%7D%7D)
<u>let u be cos(2-3x) and let </u><u>dv</u><u>/</u><u>dx</u><u> be 4x:</u>
![{ \sf{ \frac{du}{dx} = 3 \sin(2 - 3x) }} \\ \\ { \sf{ v = \int 4x = 2 {x}^{2} }}](https://tex.z-dn.net/?f=%7B%20%20%5Csf%7B%20%5Cfrac%7Bdu%7D%7Bdx%7D%20%20%3D%20%203%20%5Csin%282%20-%203x%29%20%7D%7D%20%5C%5C%20%20%5C%5C%20%7B%20%5Csf%7B%20v%20%20%3D%20%20%5Cint%204x%20%3D%202%20%7Bx%7D%5E%7B2%7D%20%7D%7D)
Substitute in formular box:
![{ \sf{ = (2 {x}^{2} \times \cos(2 - 3x)) - \int 2 {x}^{2} .3 \sin(2 - 3x) dx}} \\ = { \sf{2 {x}^{2} ( \cos(2 - 3x) - 3 \int \sin(2 - 3x)dx }} \\ { \sf{ = 2 {x}^{2} ( \cos(2 - 3x) - 3( - \frac{1}{3} \cos(2 - 3x) ) + c}} \\ { \sf{ = {4x}^{2} \cos(2 - 3x) + c}}](https://tex.z-dn.net/?f=%7B%20%5Csf%7B%20%20%3D%20%282%20%7Bx%7D%5E%7B2%7D%20%20%5Ctimes%20%20%5Ccos%282%20-%203x%29%29%20-%20%20%5Cint%202%20%7Bx%7D%5E%7B2%7D%20.3%20%5Csin%282%20-%203x%29%20%20dx%7D%7D%20%5C%5C%20%20%3D%20%7B%20%5Csf%7B2%20%7Bx%7D%5E%7B2%7D%20%28%20%5Ccos%282%20-%203x%29%20%20-%203%20%5Cint%20%20%5Csin%282%20-%203x%29dx%20%7D%7D%20%5C%5C%20%7B%20%5Csf%7B%20%3D%202%20%7Bx%7D%5E%7B2%7D%20%28%20%5Ccos%282%20-%203x%29%20-%203%28%20-%20%20%5Cfrac%7B1%7D%7B3%7D%20%20%20%5Ccos%282%20-%203x%29%20%29%20%2B%20c%7D%7D%20%5C%5C%20%7B%20%5Csf%7B%20%3D%20%20%7B4x%7D%5E%7B2%7D%20%20%5Ccos%282%20-%203x%29%20%20%2B%20c%7D%7D)
Answer:
6
Step-by-step explanation:
So we have a number (let's call it x) and it was multiplied by 8 and added by 2. Therefore:
![8x+2](https://tex.z-dn.net/?f=8x%2B2)
And we are told that the sum is equal to the product of 2 and 25 (or 50). Thus:
![8x+2=50](https://tex.z-dn.net/?f=8x%2B2%3D50)
To find the number, we just need to find x. Thus, subtract 2 from both sides:
![8x=48](https://tex.z-dn.net/?f=8x%3D48)
Divide both sides by 8:
![x=6](https://tex.z-dn.net/?f=x%3D6)
And we're done!
So, our original number was 6.
Step-by-step explanation:
Watch all steps in picture
The answer is 10 hope it helps SORRY IF I’M WRONG