Answer:
Q5- B
Q6- H
Q7- C
Step-by-step explanation:
Here,
Angle F = 180 – ( 90 + 60 )
Or, Angle F = 180 – 150
Or, Angle F = 30 °
Here,
- Angle G is directly proportional to the Side EF.
- Angle F is directly proportional to the Side GE.
- Angle E is directly proportional to the side FG.
Now,
EF = 10√2 Units
Then, FG = 60 / 90 × 10√2
Finally, EG = 30 / 90 × 10√2
Hence,
Answer:
one solution i think
Step-by-step explanation:
Answer:
The center is the point (3,1) and the radius is 3 units
Step-by-step explanation:
we know that
The equation of a circle in standard form is equal to
![(x-h)^{2}+(y-k)^{2}=r^{2}](https://tex.z-dn.net/?f=%28x-h%29%5E%7B2%7D%2B%28y-k%29%5E%7B2%7D%3Dr%5E%7B2%7D)
we have
![x^{2}+y^{2}-6x-2y+1=0](https://tex.z-dn.net/?f=x%5E%7B2%7D%2By%5E%7B2%7D-6x-2y%2B1%3D0)
Convert to standard form
Group terms that contain the same variable, and move the constant to the opposite side of the equation
![(x^{2}-6x)+(y^{2}-2y)=-1](https://tex.z-dn.net/?f=%28x%5E%7B2%7D-6x%29%2B%28y%5E%7B2%7D-2y%29%3D-1)
Complete the square twice. Remember to balance the equation by adding the same constants to each side.
![(x^{2}-6x+9)+(y^{2}-2y+1)=-1+9+1](https://tex.z-dn.net/?f=%28x%5E%7B2%7D-6x%2B9%29%2B%28y%5E%7B2%7D-2y%2B1%29%3D-1%2B9%2B1)
![(x^{2}-6x+9)+(y^{2}-2y+1)=9](https://tex.z-dn.net/?f=%28x%5E%7B2%7D-6x%2B9%29%2B%28y%5E%7B2%7D-2y%2B1%29%3D9)
Rewrite as perfect squares
![(x-3)^{2}+(y-1)^{2}=9](https://tex.z-dn.net/?f=%28x-3%29%5E%7B2%7D%2B%28y-1%29%5E%7B2%7D%3D9)
The center is the point (3,1) and the radius is 3 units
Answer:
.
Step-by-step explanation:
We have been given an indefinite integral
. We are asked to find the value of the integral using integration by parts.
Let
,
.
Now, we will find du and v as shown below:
![\frac{du}{dx}=\frac{d}{dx}(\text{ln}(x))](https://tex.z-dn.net/?f=%5Cfrac%7Bdu%7D%7Bdx%7D%3D%5Cfrac%7Bd%7D%7Bdx%7D%28%5Ctext%7Bln%7D%28x%29%29)
![\frac{du}{dx}=\frac{1}{x}](https://tex.z-dn.net/?f=%5Cfrac%7Bdu%7D%7Bdx%7D%3D%5Cfrac%7B1%7D%7Bx%7D)
![du=\frac{1}{x}dx](https://tex.z-dn.net/?f=du%3D%5Cfrac%7B1%7D%7Bx%7Ddx)
![v=\frac{x^{3+1}}{3+1}=\frac{x^{4}}{4}](https://tex.z-dn.net/?f=v%3D%5Cfrac%7Bx%5E%7B3%2B1%7D%7D%7B3%2B1%7D%3D%5Cfrac%7Bx%5E%7B4%7D%7D%7B4%7D)
Upon substituting our values in integration by parts formula, we will get:
![\int \:x^3\:\text{ln}\:(x)\:dx=\text{ln}(x)*\frac{x^4}{4}-\int\: \frac{x^4}{4}*\frac{1}{x}dx](https://tex.z-dn.net/?f=%5Cint%20%5C%3Ax%5E3%5C%3A%5Ctext%7Bln%7D%5C%3A%28x%29%5C%3Adx%3D%5Ctext%7Bln%7D%28x%29%2A%5Cfrac%7Bx%5E4%7D%7B4%7D-%5Cint%5C%3A%20%5Cfrac%7Bx%5E4%7D%7B4%7D%2A%5Cfrac%7B1%7D%7Bx%7Ddx)
![\int \:x^3\:\text{ln}\:(x)\:dx=\frac{\text{ln}(x)x^4}{4}-\int\: \frac{x^3}{4}dx](https://tex.z-dn.net/?f=%5Cint%20%5C%3Ax%5E3%5C%3A%5Ctext%7Bln%7D%5C%3A%28x%29%5C%3Adx%3D%5Cfrac%7B%5Ctext%7Bln%7D%28x%29x%5E4%7D%7B4%7D-%5Cint%5C%3A%20%5Cfrac%7Bx%5E3%7D%7B4%7Ddx)
![\int \:x^3\:\text{ln}\:(x)\:dx=\frac{\text{ln}(x)x^4}{4}-\frac{1}{4}\int\: x^3dx](https://tex.z-dn.net/?f=%5Cint%20%5C%3Ax%5E3%5C%3A%5Ctext%7Bln%7D%5C%3A%28x%29%5C%3Adx%3D%5Cfrac%7B%5Ctext%7Bln%7D%28x%29x%5E4%7D%7B4%7D-%5Cfrac%7B1%7D%7B4%7D%5Cint%5C%3A%20x%5E3dx)
![\int \:x^3\:\text{ln}\:(x)\:dx=\frac{\text{ln}(x)x^4}{4}-\frac{1}{4}*\frac{x^{3+1}}{3+1}+C](https://tex.z-dn.net/?f=%5Cint%20%5C%3Ax%5E3%5C%3A%5Ctext%7Bln%7D%5C%3A%28x%29%5C%3Adx%3D%5Cfrac%7B%5Ctext%7Bln%7D%28x%29x%5E4%7D%7B4%7D-%5Cfrac%7B1%7D%7B4%7D%2A%5Cfrac%7Bx%5E%7B3%2B1%7D%7D%7B3%2B1%7D%2BC)
![\int \:x^3\:\text{ln}\:(x)\:dx=\frac{\text{ln}(x)x^4}{4}-\frac{1}{4}*\frac{x^4}{4}+C](https://tex.z-dn.net/?f=%5Cint%20%5C%3Ax%5E3%5C%3A%5Ctext%7Bln%7D%5C%3A%28x%29%5C%3Adx%3D%5Cfrac%7B%5Ctext%7Bln%7D%28x%29x%5E4%7D%7B4%7D-%5Cfrac%7B1%7D%7B4%7D%2A%5Cfrac%7Bx%5E4%7D%7B4%7D%2BC)
![\int \:x^3\:\text{ln}\:(x)\:dx=\frac{\text{ln}(x)x^4}{4}-\frac{x^4}{16}+C](https://tex.z-dn.net/?f=%5Cint%20%5C%3Ax%5E3%5C%3A%5Ctext%7Bln%7D%5C%3A%28x%29%5C%3Adx%3D%5Cfrac%7B%5Ctext%7Bln%7D%28x%29x%5E4%7D%7B4%7D-%5Cfrac%7Bx%5E4%7D%7B16%7D%2BC)
Therefore, our required integral would be
.