Answer:
y-intercept: (0,-3)
Step-by-step explanation:
- Y-intercepts mean that the x-value has to be equal to 0. When plugging in 0 for the x-value, we receive:
- Therefore, the point is (0,-3).
Answer:
The slope is 1.
Step-by-step explanation: when you graph them you do the rise/run you get 1 which is the slope.
Answer:
![\boxed{\pink{\tt I = \dfrac{1}{3}sin(3x) - 3cos(x) + C}}](https://tex.z-dn.net/?f=%5Cboxed%7B%5Cpink%7B%5Ctt%20I%20%3D%20%20%5Cdfrac%7B1%7D%7B3%7Dsin%283x%29%20%20-%203cos%28x%29%20%2B%20C%7D%7D)
Step-by-step explanation:
We need to integrate the given expression. Let I be the answer .
- Let u = 3x , then du = 3dx . Henceforth 1/3 du = dx .
- Now , Rewrite using du and u .
![\implies\displaystyle\sf I = \int cos\ u \dfrac{1}{3}du + \int 3sin \ x \ dx \\\\\implies\displaystyle \sf I = \int \dfrac{cos\ u}{3} du + \int 3sin\ x \ dx \\\\\implies\displaystyle\sf I = \dfrac{1}{3}\int \dfrac{cos(u)}{3} + \int 3sin(x) dx \\\\\implies\displaystyle\sf I = \dfrac{1}{3} sin(u) + C +\int 3sin(x) dx \\\\\implies\displaystyle \sf I = \dfrac{1}{3}sin(u) + C + 3\int sin(x) \ dx \\\\\implies\displaystyle\sf I = \dfrac{1}{3}sin(u) + C + 3(-cos(x)+C) \\\\\implies \underset{\blue{\sf Required\ Answer }}{\underbrace{\boxed{\boxed{\displaystyle\red{\sf I = \dfrac{1}{3}sin(3x) - 3cos(x) + C }}}}}](https://tex.z-dn.net/?f=%5Cimplies%5Cdisplaystyle%5Csf%20I%20%3D%20%5Cint%20cos%5C%20u%20%5Cdfrac%7B1%7D%7B3%7Ddu%20%2B%20%5Cint%203sin%20%5C%20x%20%5C%20dx%20%5C%5C%5C%5C%5Cimplies%5Cdisplaystyle%20%5Csf%20I%20%3D%20%5Cint%20%5Cdfrac%7Bcos%5C%20u%7D%7B3%7D%20du%20%2B%20%5Cint%203sin%5C%20x%20%5C%20dx%20%5C%5C%5C%5C%5Cimplies%5Cdisplaystyle%5Csf%20I%20%3D%20%5Cdfrac%7B1%7D%7B3%7D%5Cint%20%5Cdfrac%7Bcos%28u%29%7D%7B3%7D%20%2B%20%5Cint%203sin%28x%29%20dx%20%5C%5C%5C%5C%5Cimplies%5Cdisplaystyle%5Csf%20I%20%3D%20%5Cdfrac%7B1%7D%7B3%7D%20sin%28u%29%20%2B%20C%20%2B%5Cint%203sin%28x%29%20dx%20%5C%5C%5C%5C%5Cimplies%5Cdisplaystyle%20%5Csf%20I%20%3D%20%5Cdfrac%7B1%7D%7B3%7Dsin%28u%29%20%2B%20C%20%2B%203%5Cint%20sin%28x%29%20%5C%20dx%20%5C%5C%5C%5C%5Cimplies%5Cdisplaystyle%5Csf%20I%20%3D%20%20%5Cdfrac%7B1%7D%7B3%7Dsin%28u%29%20%2B%20C%20%2B%203%28-cos%28x%29%2BC%29%20%5C%5C%5C%5C%5Cimplies%20%5Cunderset%7B%5Cblue%7B%5Csf%20Required%5C%20Answer%20%7D%7D%7B%5Cunderbrace%7B%5Cboxed%7B%5Cboxed%7B%5Cdisplaystyle%5Cred%7B%5Csf%20I%20%3D%20%20%5Cdfrac%7B1%7D%7B3%7Dsin%283x%29%20%20-%203cos%28x%29%20%2B%20C%20%7D%7D%7D%7D%7D)
8% = 0.08
150 x 0.08 = 12
Answer = 12
Answer:
![\pi -irrational](https://tex.z-dn.net/?f=%5Cpi%20-irrational)
![-\frac{2}{3}-rational](https://tex.z-dn.net/?f=-%5Cfrac%7B2%7D%7B3%7D-rational)
![\sqrt{16} -rational](https://tex.z-dn.net/?f=%5Csqrt%7B16%7D%20-rational)
![\sqrt{3} -irrational](https://tex.z-dn.net/?f=%5Csqrt%7B3%7D%20-irrational)
![18-rational](https://tex.z-dn.net/?f=18-rational)
![0.625-rational](https://tex.z-dn.net/?f=0.625-rational)
![0.987987987...-rational](https://tex.z-dn.net/?f=0.987987987...-rational)
Step-by-step explanation:
Rational numbers:
-are all numbers you can write as a quotient of integers
, ![b\neq 0](https://tex.z-dn.net/?f=b%5Cneq%200)
-include terminating decimals. For example, ![\frac{1}{8}=0.125](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B8%7D%3D0.125)
-include repeating decimals. For example, ![\frac{1}{3} =0.33333....](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B3%7D%20%3D0.33333....)
Irrational numbers:
-have decimal representations that neither terminate nor repeat. For example, ![\sqrt{2}=1.414213....](https://tex.z-dn.net/?f=%5Csqrt%7B2%7D%3D1.414213....)
-cannot be written as quotients of integers