Um.... you gave no expression to rewrite ^^ maybe re ask it and ill answer?
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
.
Answer:
The number of ways of selecting a combination of 8 marbles from a bag containing 20 marbles is 125970
Step-by-step explanation:
The number of selecting 8 marbles from a bag of 20 marbles
A combination gives the number of possible order or arrangement in a collection of k items selected from a set of n items
![C_{n,k} = \dbinom{n}{k}= \dfrac{n!}{k!\cdot \left ( n - k \right )!}](https://tex.z-dn.net/?f=C_%7Bn%2Ck%7D%20%3D%20%5Cdbinom%7Bn%7D%7Bk%7D%3D%20%5Cdfrac%7Bn%21%7D%7Bk%21%5Ccdot%20%5Cleft%20%28%20n%20-%20k%20%5Cright%20%29%21%7D)
In the question, k = 8, and n = 20
Substituting the values of n and k in the above equation gives;
![C_{20,8} = \dbinom{20}{8}= \dfrac{20!}{8!\times\left ( 20 - 8 \right )!} = 125,970](https://tex.z-dn.net/?f=C_%7B20%2C8%7D%20%3D%20%5Cdbinom%7B20%7D%7B8%7D%3D%20%5Cdfrac%7B20%21%7D%7B8%21%5Ctimes%5Cleft%20%28%2020%20-%208%20%5Cright%20%29%21%7D%20%3D%20125%2C970)
Therefore, the number of ways of selecting 8 marbles from a bag containing 20 marbles is given by the combination C₂₀, ₈ = 125970.
H = height of triangle
b = length of triangle base
A = area of triangle
Recall the formula for area of a triangle :
A = 1/2 bh
Plug in what was given in the problem :
h = b - 5
A = 42
A = 1/2 bh
42 = 1/2 b (b-5)
Answer:
D. Undefined
Step-by-step explanation:
The graph of x=3 is a straight, vertical line. Therefore, the slope will be undefined.