Answer:
-47
Step-by-step explanation:
For this problem, we can use the rule "two negatives make a positive".
-81-(-34)
= -81 + 34
If you subtract 34 from 81, you find the opposite positive/negative answer.
81 - 34 = 47
Change all of the positive/negative signs:
-81 + 34 = -47
If you fill in the last coordinates with the x and y you get (1,7)
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
.
The answer is the second image from left to right (B). Examples of direct and inverse variations are showed in the image below. :)
25 because 29 and 34 are in the middle so on the other side the middle number will be 25