Answer:
![\large\boxed{\dfrac{dy}{dx}=2\sin(3x)+6\cos(3x)}](https://tex.z-dn.net/?f=%5Clarge%5Cboxed%7B%5Cdfrac%7Bdy%7D%7Bdx%7D%3D2%5Csin%283x%29%2B6%5Ccos%283x%29%7D)
Step-by-step explanation:
![\dfrac{dy}{dx}=(2x\sin(3x))'\\\\\text{use}\ \bigg(g(x)\cdot f(x)\bigg)'=g'(c)f(x)+g(x)f'(x)\\\\\text{and}\ \bigg(f(g(x))\bigg)'=f'(g(x))\cdot g'(x)\\\\\dfrac{dy}{dx}=(2x)'(\sin(3x))+(2x)(\sin(3x))'\\\\\dfrac{dy}{dx}=2\sin(3x)+(2x)(\cos(3x)\cdot(3x)')\\\\\dfrac{dy}{dx}=2\sin(3x)+2x\cos(3x)\cdot3\\\\\dfrac{dy}{dx}=2\sin(3x)+6\cos(3x)](https://tex.z-dn.net/?f=%5Cdfrac%7Bdy%7D%7Bdx%7D%3D%282x%5Csin%283x%29%29%27%5C%5C%5C%5C%5Ctext%7Buse%7D%5C%20%5Cbigg%28g%28x%29%5Ccdot%20f%28x%29%5Cbigg%29%27%3Dg%27%28c%29f%28x%29%2Bg%28x%29f%27%28x%29%5C%5C%5C%5C%5Ctext%7Band%7D%5C%20%5Cbigg%28f%28g%28x%29%29%5Cbigg%29%27%3Df%27%28g%28x%29%29%5Ccdot%20g%27%28x%29%5C%5C%5C%5C%5Cdfrac%7Bdy%7D%7Bdx%7D%3D%282x%29%27%28%5Csin%283x%29%29%2B%282x%29%28%5Csin%283x%29%29%27%5C%5C%5C%5C%5Cdfrac%7Bdy%7D%7Bdx%7D%3D2%5Csin%283x%29%2B%282x%29%28%5Ccos%283x%29%5Ccdot%283x%29%27%29%5C%5C%5C%5C%5Cdfrac%7Bdy%7D%7Bdx%7D%3D2%5Csin%283x%29%2B2x%5Ccos%283x%29%5Ccdot3%5C%5C%5C%5C%5Cdfrac%7Bdy%7D%7Bdx%7D%3D2%5Csin%283x%29%2B6%5Ccos%283x%29)
Answer:
The answer is x=9 so, its option 3.
Answer:
Total bill = $88.50
Step-by-step explanation:
Amount of bill = $75
Tip = 18%
Amount of tip = ![\frac{18}{100}*75](https://tex.z-dn.net/?f=%5Cfrac%7B18%7D%7B100%7D%2A75)
Amount of tip = ![0.18 * 75](https://tex.z-dn.net/?f=0.18%20%2A%2075)
Amount of tip = $13.50
Total bill = Bill + Tip
Total bill = 75 + 13.50
Total bill = $88.50
Answer:
(2, 7 )
Step-by-step explanation:
Given the 2 equations
y = 2x + 3 → (1)
y = 3x + 1 → (2)
Substitute y = 3x + 1 into (1)
3x + 1 = 2x + 3 ( subtract 2x from both sides )
x + 1 = 3 ( subtract 1 from both sides )
x = 2
Substitute x = 2 into either of the 2 equations for corresponding value of y
Substituting x = 2 into (1)
y = 2(2) + 3 = 4 + 3 = 7
Solution is (2, 7 )
It makes it alot easier to call out locations and plot them fast.