Answer:
The value of
is
.
Step-by-step explanation:
The given equation is
![x^4=8y^5-240](https://tex.z-dn.net/?f=x%5E4%3D8y%5E5-240)
We need to find the value of
.
Differentiate with respect to t.
![[\because \frac{d}{dx}x^n=nx^{n-1},\frac{d}{dx}C=0]](https://tex.z-dn.net/?f=%5B%5Cbecause%20%5Cfrac%7Bd%7D%7Bdx%7Dx%5En%3Dnx%5E%7Bn-1%7D%2C%5Cfrac%7Bd%7D%7Bdx%7DC%3D0%5D)
![4x^3\frac{dx}{dt}=40y^4\frac{dy}{dt}](https://tex.z-dn.net/?f=4x%5E3%5Cfrac%7Bdx%7D%7Bdt%7D%3D40y%5E4%5Cfrac%7Bdy%7D%7Bdt%7D)
It is given that y=2 and dy/dt=1, substitute these values in the above equation.
![4x^3\frac{dx}{dt}=40(2)^4(1)](https://tex.z-dn.net/?f=4x%5E3%5Cfrac%7Bdx%7D%7Bdt%7D%3D40%282%29%5E4%281%29)
![4x^3\frac{dx}{dt}=40(16)(1)](https://tex.z-dn.net/?f=4x%5E3%5Cfrac%7Bdx%7D%7Bdt%7D%3D40%2816%29%281%29)
![4x^3\frac{dx}{dt}=640](https://tex.z-dn.net/?f=4x%5E3%5Cfrac%7Bdx%7D%7Bdt%7D%3D640)
Divide both sides by 4x³.
![\frac{dx}{dt}=\frac{640}{4x^3}](https://tex.z-dn.net/?f=%5Cfrac%7Bdx%7D%7Bdt%7D%3D%5Cfrac%7B640%7D%7B4x%5E3%7D)
![\frac{dx}{dt}=\frac{160}{x^3}](https://tex.z-dn.net/?f=%5Cfrac%7Bdx%7D%7Bdt%7D%3D%5Cfrac%7B160%7D%7Bx%5E3%7D)
Therefore the value of
is
.
1. 99, 98.05, 62, and 0
2. 67, 65, 64, 6
Explanation: When you see the | | around a number what ever symbol before is irrelevant
For example |-6| would just be 6
Point-slope form is (y-y1)=m(x-x1)
We are given that m=5 and (x1,y1)=(1,9) so
y-9=5(x-1)
No solutions.
To solve, set the two equations equal to each other.
6x +9 = 6x +2
cross out the 6x
9 = 2
there are no instances where 9 = 2, so there are no solutions.