1 answer:
Answer:
2&17
Step-by-step explanation:
34 is a composite number. 34 = 1 x 34 or 2 x 17. Factors of 34: 1, 2, 17, 34. Prime factorization: 34 = 2 x 17.
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Answer: Age:25
Step-by-step explanation:
<h2>1)</h2>
![\\\\\ \textbf{a)}\\\\~~~\displaystyle \int (6x- \sin 3x) ~ dx\\\\=6\displaystyle \int x ~ dx - \displaystyle \int \sin 3x ~ dx\\\\=6 \cdot \dfrac{x^2}2 - \dfrac 13 (- \cos 3x) +C~~~~~~~~~~~;\left[\displaystyle \int x^n~ dx = \dfrac{x^{n+1}}{n+1}+C,~~~n \neq -1\right]\\\\ =3x^2 +\dfrac{\cos 3x}3 +C~~~~~~~~~~~~~~~~~~~~;\left[\displaystyle \int \sin (mx) ~dx = -\dfrac 1m ~ (\cos mx)+C \right]\\](https://tex.z-dn.net/?f=%5C%5C%5C%5C%5C%20%5Ctextbf%7Ba%29%7D%5C%5C%5C%5C~~~%5Cdisplaystyle%20%5Cint%20%286x-%20%5Csin%203x%29%20~%20dx%5C%5C%5C%5C%3D6%5Cdisplaystyle%20%5Cint%20x%20~%20dx%20-%20%5Cdisplaystyle%20%5Cint%20%5Csin%203x%20~%20dx%5C%5C%5C%5C%3D6%20%5Ccdot%20%5Cdfrac%7Bx%5E2%7D2%20-%20%5Cdfrac%2013%20%28-%20%5Ccos%203x%29%20%2BC~~~~~~~~~~~%3B%5Cleft%5B%5Cdisplaystyle%20%5Cint%20x%5En~%20dx%20%3D%20%5Cdfrac%7Bx%5E%7Bn%2B1%7D%7D%7Bn%2B1%7D%2BC%2C~~~n%20%5Cneq%20-1%5Cright%5D%5C%5C%5C%5C%20%3D3x%5E2%20%2B%5Cdfrac%7B%5Ccos%203x%7D3%20%2BC~~~~~~~~~~~~~~~~~~~~%3B%5Cleft%5B%5Cdisplaystyle%20%5Cint%20%5Csin%20%28mx%29%20~dx%20%3D%20-%5Cdfrac%201m%20~%20%28%5Ccos%20mx%29%2BC%20%5Cright%5D%5C%5C)
![\textbf{b)}\\\\~~~~\displaystyle \int(3e^{-2x} +\cos (0.5 x)) dx\\\\=3\displaystyle \int e^{-2x} ~dx+ \displaystyle \int \cos(0.5 x) ~dx\\\\\\=-\dfrac 32 e^{-2x} + \dfrac 1{0.5} \sin (0.5 x) +C~~~~~~~~~~~~~~;\left[\displaystyle \int e^{mx}~dx = \dfrac 1m e^{mx} +C \right]\\\\\\=-\dfrac 32 e^{-2x} + 2 \sin(0.5 x) +C~~~~~~~~~~~~~~~~~;\left[\displaystyle \int \cos(mx)~ dx = \dfrac 1m \sin(mx) +C\right]\\\\\\=-1.5e^{-2x} +2\sin(0.5x) +C](https://tex.z-dn.net/?f=%5Ctextbf%7Bb%29%7D%5C%5C%5C%5C~~~~%5Cdisplaystyle%20%5Cint%283e%5E%7B-2x%7D%20%2B%5Ccos%20%280.5%20x%29%29%20dx%5C%5C%5C%5C%3D3%5Cdisplaystyle%20%5Cint%20e%5E%7B-2x%7D%20~dx%2B%20%5Cdisplaystyle%20%5Cint%20%5Ccos%280.5%20x%29%20~dx%5C%5C%5C%5C%5C%5C%3D-%5Cdfrac%2032%20e%5E%7B-2x%7D%20%2B%20%5Cdfrac%201%7B0.5%7D%20%5Csin%20%280.5%20x%29%20%2BC~~~~~~~~~~~~~~%3B%5Cleft%5B%5Cdisplaystyle%20%5Cint%20e%5E%7Bmx%7D~dx%20%3D%20%5Cdfrac%201m%20e%5E%7Bmx%7D%20%2BC%20%5Cright%5D%5C%5C%5C%5C%5C%5C%3D-%5Cdfrac%2032%20e%5E%7B-2x%7D%20%2B%202%20%5Csin%280.5%20x%29%20%2BC~~~~~~~~~~~~~~~~~%3B%5Cleft%5B%5Cdisplaystyle%20%5Cint%20%5Ccos%28mx%29~%20dx%20%20%3D%20%5Cdfrac%201m%20%5Csin%28mx%29%20%2BC%5Cright%5D%5C%5C%5C%5C%5C%5C%3D-1.5e%5E%7B-2x%7D%20%2B2%5Csin%280.5x%29%20%2BC)
<h2>2)</h2>
![\textbf{a)}\\\\y = \displaystyle \int \cos(x+5) ~ dx\\\\\text{Let,}\\\\~~~~~~~u = x+5\\\\\implies \dfrac{du}{dx} = 1+0~~~~~~;[\text{Differentiate both sides.}]\\\\\implies \dfrac{du}{dx} = 1\\\\\implies du = dx\\\\\text{Now,}\\\\y= \displaystyle \int \cos u ~ du\\\\~~~= \sin u +C\\\\~~~=\sin(x+5) + C](https://tex.z-dn.net/?f=%5Ctextbf%7Ba%29%7D%5C%5C%5C%5Cy%20%3D%20%5Cdisplaystyle%20%5Cint%20%5Ccos%28x%2B5%29%20~%20dx%5C%5C%5C%5C%5Ctext%7BLet%2C%7D%5C%5C%5C%5C~~~~~~~u%20%3D%20x%2B5%5C%5C%5C%5C%5Cimplies%20%5Cdfrac%7Bdu%7D%7Bdx%7D%20%3D%201%2B0~~~~~~%3B%5B%5Ctext%7BDifferentiate%20both%20sides.%7D%5D%5C%5C%5C%5C%5Cimplies%20%5Cdfrac%7Bdu%7D%7Bdx%7D%20%3D%201%5C%5C%5C%5C%5Cimplies%20du%20%3D%20dx%5C%5C%5C%5C%5Ctext%7BNow%2C%7D%5C%5C%5C%5Cy%3D%20%5Cdisplaystyle%20%5Cint%20%5Ccos%20u%20~%20du%5C%5C%5C%5C~~~%3D%20%5Csin%20u%20%2BC%5C%5C%5C%5C~~~%3D%5Csin%28x%2B5%29%20%2B%20C)
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<h2>3)</h2>
![\textbf{a)}\\\\y = \displaystyle \int xe^{3x} dx\\\\\text{We know that,}\\\\ \displaystyle \int (uv) ~dx = u \displaystyle \int v ~ dx - \displaystyle \int \left[ \dfrac{du}{dx} \displaystyle \int ~ v ~ dx \right]~ dx\\\\\text{Let}, u =x~ \text{and}~ v=e^{3x} .\\\\y= \displaystyle \int xe^{3x} ~dx\\\\\\~~= x\displaystyle \int e^{3x} ~ dx - \displaystyle \int \left[\dfrac{d}{dx}(x) \displaystyle \int e^{3x}~ dx \right]~ dx\\\\\\](https://tex.z-dn.net/?f=%5Ctextbf%7Ba%29%7D%5C%5C%5C%5Cy%20%3D%20%20%5Cdisplaystyle%20%5Cint%20xe%5E%7B3x%7D%20dx%5C%5C%5C%5C%5Ctext%7BWe%20know%20that%2C%7D%5C%5C%5C%5C%20%5Cdisplaystyle%20%5Cint%20%20%28uv%29%20~dx%20%3D%20u%20%20%5Cdisplaystyle%20%5Cint%20%20v%20~%20dx%20-%20%20%5Cdisplaystyle%20%5Cint%20%5Cleft%5B%20%5Cdfrac%7Bdu%7D%7Bdx%7D%20%5Cdisplaystyle%20%5Cint%20~%20v%20~%20dx%20%5Cright%5D~%20dx%5C%5C%5C%5C%5Ctext%7BLet%7D%2C%20u%20%3Dx~%20%5Ctext%7Band%7D~%20v%3De%5E%7B3x%7D%20%20.%5C%5C%5C%5Cy%3D%20%20%5Cdisplaystyle%20%5Cint%20xe%5E%7B3x%7D%20~dx%5C%5C%5C%5C%5C%5C~~%3D%20%20x%5Cdisplaystyle%20%5Cint%20e%5E%7B3x%7D%20~%20dx%20-%20%20%5Cdisplaystyle%20%5Cint%20%20%5Cleft%5B%5Cdfrac%7Bd%7D%7Bdx%7D%28x%29%20%20%5Cdisplaystyle%20%5Cint%20%20e%5E%7B3x%7D~%20dx%20%5Cright%5D~%20dx%5C%5C%5C%5C%5C%5C)
<h2 />
I would say since thats $1500+ a month about 600 dollars, because she will have bills and then have to buy food drinks and alot more.
Drawn ray
Answer: drawn ray
