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
.
Answer:
Y=60
Step-by-step explanation:
S+Y=90
S=(2*Y)-90
Y+2Y-90=90
3Y=180
Y=60
Plug back into S+Y=90
S+60=90
S=30
Answer:
Step-by-step explanation:
9
4:32 is the same as 2:16 and 12:96. A ratio is the same as a fraction, so you can reduce them the same way. 4/2 = 2, 32/2 = 16. 2*6 = 12, 16*6 = 96.
Can you do the second one on your own now?