Answer:
108 deg. These are vertically opposite angles.
Step-by-step explanation:
Corresponding angles are for example EFB and ABC.
Alternate angles are for example EFB and FBD.
All three angle options describe equal angles.
This question is saying that all the dimension of the statue are multiplied by a certain value in order to get to the scaled dimensions.
We can do 6/18 to find the scale value to be 1/3
Answer:
The required answer is
.
Step-by-step explanation:
The given differential equation is
![\frac{dy}{dx}=(x-y+1)^2](https://tex.z-dn.net/?f=%5Cfrac%7Bdy%7D%7Bdx%7D%3D%28x-y%2B1%29%5E2)
Substitute u=x-y+1 in the above equation.
![\frac{du}{dx}=1-\frac{dy}{dx}](https://tex.z-dn.net/?f=%5Cfrac%7Bdu%7D%7Bdx%7D%3D1-%5Cfrac%7Bdy%7D%7Bdx%7D)
![\frac{dy}{dx}=1-\frac{du}{dx}](https://tex.z-dn.net/?f=%5Cfrac%7Bdy%7D%7Bdx%7D%3D1-%5Cfrac%7Bdu%7D%7Bdx%7D)
![1-\frac{du}{dx}=u^2](https://tex.z-dn.net/?f=1-%5Cfrac%7Bdu%7D%7Bdx%7D%3Du%5E2)
![1-u^2=\frac{du}{dx}](https://tex.z-dn.net/?f=1-u%5E2%3D%5Cfrac%7Bdu%7D%7Bdx%7D)
Using variable separable method, we get
![dx=\frac{du}{1-u^2}](https://tex.z-dn.net/?f=dx%3D%5Cfrac%7Bdu%7D%7B1-u%5E2%7D)
Integrate both the sides.
![\int dx=\int \frac{du}{1-u^2}](https://tex.z-dn.net/?f=%5Cint%20dx%3D%5Cint%20%5Cfrac%7Bdu%7D%7B1-u%5E2%7D)
![[\because \int \frac{dx}{a^2-x^2}=\frac{1}{2a}\n|\frac{a+x}{a-x}|+C]](https://tex.z-dn.net/?f=%5B%5Cbecause%20%5Cint%20%5Cfrac%7Bdx%7D%7Ba%5E2-x%5E2%7D%3D%5Cfrac%7B1%7D%7B2a%7D%5Cn%7C%5Cfrac%7Ba%2Bx%7D%7Ba-x%7D%7C%2BC%5D)
Substitute u=x-y+1 in the above equation.
![x+C=\frac{1}{2}\ln|\frac{1+x-y+1}{1-(x-y+1)}|](https://tex.z-dn.net/?f=x%2BC%3D%5Cfrac%7B1%7D%7B2%7D%5Cln%7C%5Cfrac%7B1%2Bx-y%2B1%7D%7B1-%28x-y%2B1%29%7D%7C)
![x+C=\frac{1}{2}\ln|\frac{2+x-y}{y-x}|](https://tex.z-dn.net/?f=x%2BC%3D%5Cfrac%7B1%7D%7B2%7D%5Cln%7C%5Cfrac%7B2%2Bx-y%7D%7By-x%7D%7C)
Therefore the required answer is
.
7b + 4 (-b +3)
= 7b +4*(-b)+ 4*3
= 7b -4b+ 12
= 3b + 12
The final answer is 3b+12.
Hope this helps~
Proportional and linear functions are almost identical in form. The only difference is the addition of the “b” constant to the linear function. Indeed, a proportional relationship is just a linear relationship where b = 0, or to put it another way, where the line passes through the origin