Let's say that FH and EG intersection is O,
So we have the following:
OF = 2
OH = 5
Just because F and H are midpoints it means that EO = OG = x
And as it's given the area S=35
On the other hand
S = OF*OG/2 + OG*OH/2 + OH*OE/2 + OE*OF/2 = 2*x/2 + x*5/2 + 5*x/2 + x*2/2 = 2*x + 5*x = 7*x = 35
7x = 35 so x = 35/7 = 5
Answer: 5 units
You can name a vector<span> by its length and direction</span>
You can compute both the mean and second moment directly using the density function; in this case, it's
Then the mean (first moment) is
![E[X]=\displaystyle\int_{-\infty}^\infty x\,f_X(x)\,\mathrm dx=\frac1{80}\int_{670}^{750}x\,\mathrm dx=710](https://tex.z-dn.net/?f=E%5BX%5D%3D%5Cdisplaystyle%5Cint_%7B-%5Cinfty%7D%5E%5Cinfty%20x%5C%2Cf_X%28x%29%5C%2C%5Cmathrm%20dx%3D%5Cfrac1%7B80%7D%5Cint_%7B670%7D%5E%7B750%7Dx%5C%2C%5Cmathrm%20dx%3D710)
and the second moment is
![E[X^2]=\displaystyle\int_{-\infty}^\infty x^2\,f_X(x)\,\mathrm dx=\frac1{80}\int_{670}^{750}x^2\,\mathrm dx=\frac{1,513,900}3](https://tex.z-dn.net/?f=E%5BX%5E2%5D%3D%5Cdisplaystyle%5Cint_%7B-%5Cinfty%7D%5E%5Cinfty%20x%5E2%5C%2Cf_X%28x%29%5C%2C%5Cmathrm%20dx%3D%5Cfrac1%7B80%7D%5Cint_%7B670%7D%5E%7B750%7Dx%5E2%5C%2C%5Cmathrm%20dx%3D%5Cfrac%7B1%2C513%2C900%7D3)
The second moment is useful in finding the variance, which is given by
![V[X]=E[(X-E[X])^2]=E[X^2]-E[X]^2=\dfrac{1,513,900}3-710^2=\dfrac{1600}3](https://tex.z-dn.net/?f=V%5BX%5D%3DE%5B%28X-E%5BX%5D%29%5E2%5D%3DE%5BX%5E2%5D-E%5BX%5D%5E2%3D%5Cdfrac%7B1%2C513%2C900%7D3-710%5E2%3D%5Cdfrac%7B1600%7D3)
You get the standard deviation by taking the square root of the variance, and so
![\sqrt{V[X]}=\sqrt{\dfrac{1600}3}\approx23.09](https://tex.z-dn.net/?f=%5Csqrt%7BV%5BX%5D%7D%3D%5Csqrt%7B%5Cdfrac%7B1600%7D3%7D%5Capprox23.09)
Answer:
Center = (5, -2) and radius = √33
Step-by-step explanation:
The equation of a circle is given by the formula;
(x-a)² + (y-b)² = r² ; where (a,b) is the center of the circle and r is the radius of the circle.
In this case;
2x² - 20x + 2y² + 8y =40 ;
Dividing both sides of the equation by 2 we get;
x² - 10x + y² + 4y = 20
we can then use the completing the square on both x and y terms.
x² - 10x + y² + 4y = 20
x² + 2(-5)x + 25 + y² + 2(2) y + 4 = 20 +9 + 4
In standard form we get;
(x-5)² + (y+2)² = 33
Therefore;
Center = (5, -2) and radius = √33
