Answer:
∠P = 39º
∠Q=120º
∠R = 21º
Step-by-step explanation:
m∠P+m∠Q+m∠R=180º (sum of ∠s in a triangle)
2x-3+6x-6+x=180º (substitution)
9x-9=180º (algebra)
9x=189º (algebra)
x=21º (algebra) (this is ∠R)
(2x-3)=39º (algebra) (this is ∠P)
6x-6=120º (algebra) (this is ∠Q)
To solve the question we proceed as follows:
Distance is the integral of the velocity. Thus given:
v(t)=3.5t+0.25t^2
d(t)=1.75t^2+0.08333t^3.....i
v(t)=1.2t+0.03t^2
d(t)=0.6t^2+0.01t^3.......ii
From equation i and ii, we conclude that using strategy i will cover greater distance
Answer:
![\dfrac{d}{dx}f(x)=\dfrac{e^{2x}+e^{-2x}}{2}](https://tex.z-dn.net/?f=%5Cdfrac%7Bd%7D%7Bdx%7Df%28x%29%3D%5Cdfrac%7Be%5E%7B2x%7D%2Be%5E%7B-2x%7D%7D%7B2%7D)
Step-by-step explanation:
It is given that
![\sinh x=\dfrac{e^x-e^{-x}}{2}](https://tex.z-dn.net/?f=%5Csinh%20x%3D%5Cdfrac%7Be%5Ex-e%5E%7B-x%7D%7D%7B2%7D)
![\cosh x=\dfrac{e^x+e^{-x}}{2}](https://tex.z-dn.net/?f=%5Ccosh%20x%3D%5Cdfrac%7Be%5Ex%2Be%5E%7B-x%7D%7D%7B2%7D)
![f(x)=\sinh x\cosh x=](https://tex.z-dn.net/?f=f%28x%29%3D%5Csinh%20x%5Ccosh%20x%3D)
Using the given hyperbolic functions, we get
![f(x)=\dfrac{e^x-e^{-x}}{2}\times \dfrac{e^x+e^{-x}}{2}](https://tex.z-dn.net/?f=f%28x%29%3D%5Cdfrac%7Be%5Ex-e%5E%7B-x%7D%7D%7B2%7D%5Ctimes%20%5Cdfrac%7Be%5Ex%2Be%5E%7B-x%7D%7D%7B2%7D)
![f(x)=\dfrac{(e^x)^2-(e^{-x})^2}{4}](https://tex.z-dn.net/?f=f%28x%29%3D%5Cdfrac%7B%28e%5Ex%29%5E2-%28e%5E%7B-x%7D%29%5E2%7D%7B4%7D)
![f(x)=\dfrac{e^{2x}-e^{-2x}}{4}](https://tex.z-dn.net/?f=f%28x%29%3D%5Cdfrac%7Be%5E%7B2x%7D-e%5E%7B-2x%7D%7D%7B4%7D)
Differentiate both sides with respect to x.
![\dfrac{d}{dx}f(x)=\dfrac{d}{dx}\left(\dfrac{e^{2x}-e^{-2x}}{4}\right )](https://tex.z-dn.net/?f=%5Cdfrac%7Bd%7D%7Bdx%7Df%28x%29%3D%5Cdfrac%7Bd%7D%7Bdx%7D%5Cleft%28%5Cdfrac%7Be%5E%7B2x%7D-e%5E%7B-2x%7D%7D%7B4%7D%5Cright%20%29)
![\dfrac{d}{dx}f(x)=\left(\dfrac{2e^{2x}-(-2)e^{-2x}}{4}\right )](https://tex.z-dn.net/?f=%5Cdfrac%7Bd%7D%7Bdx%7Df%28x%29%3D%5Cleft%28%5Cdfrac%7B2e%5E%7B2x%7D-%28-2%29e%5E%7B-2x%7D%7D%7B4%7D%5Cright%20%29)
![\dfrac{d}{dx}f(x)=\left(\dfrac{2(e^{2x}+e^{-2x})}{4}\right )](https://tex.z-dn.net/?f=%5Cdfrac%7Bd%7D%7Bdx%7Df%28x%29%3D%5Cleft%28%5Cdfrac%7B2%28e%5E%7B2x%7D%2Be%5E%7B-2x%7D%29%7D%7B4%7D%5Cright%20%29)
![\dfrac{d}{dx}f(x)=\dfrac{e^{2x}+e^{-2x}}{2}](https://tex.z-dn.net/?f=%5Cdfrac%7Bd%7D%7Bdx%7Df%28x%29%3D%5Cdfrac%7Be%5E%7B2x%7D%2Be%5E%7B-2x%7D%7D%7B2%7D)
Hence,
.
The mean is calculated by dividing the total sum of all the numbers, by the number of numbers. or in this case...
Mean=(total score)/(number of categories)
plug in the data that we know
7.25=(total score)/(8)
multiply both sides by 8
58=(total score)
Answer=58
The coordinates for your circle (showed in you last question) are (3,0).