The true question should be like this:
<span>What is the center and radius of the following circle: x^2 + (y _ 6)^2 = 50,
circle quation formula is (x-a)^2 + (y-b)^2 = R², so by identifying each term, we find </span>(x-a)^2=x^2 = (x-0)^2, (y-b)^2= (y _ 6)^2, R² = 50, implies R =5sqrt(2),
it is easy to identify that the center is (a,b)= (0, 6)
the radius is R =5sqrt(2),
x-37= 4
move -37 to the other side
sign changes from -37 to +37
x-37+37= 4+37
x= 4+37
Answer:
x= 41
Answer:
The dimensions of the box are 38.48 x 14.48 x 5.26 in.
Step-by-step explanation:
We will have a piece of cardboard with squares of side x cut from the corners to make a open box.
The volume of the box can be written as:
![V=A\cdot B\cdot x\\\\V=(49-2x)\cdot (25-2x)\cdot x\\\\V=x\cdot (4x^2-2x*(49+25)+49*25)\\\\V=4x^3-148x^2+1225x](https://tex.z-dn.net/?f=V%3DA%5Ccdot%20B%5Ccdot%20x%5C%5C%5C%5CV%3D%2849-2x%29%5Ccdot%20%2825-2x%29%5Ccdot%20x%5C%5C%5C%5CV%3Dx%5Ccdot%20%284x%5E2-2x%2A%2849%2B25%29%2B49%2A25%29%5C%5C%5C%5CV%3D4x%5E3-148x%5E2%2B1225x)
To calculate the maximum volume, we derive and equal to zero
![dV/dx=12x^2-296x+1225=0](https://tex.z-dn.net/?f=dV%2Fdx%3D12x%5E2-296x%2B1225%3D0)
We apply the quadratic equation to know the roots of the equation
![x=\frac{-b\pm\sqrt{b^24ac}}{2a}\\\\x=\frac{296\pm\sqrt{296^2-4*12*1225}}{2*12} =\frac{296\pm\sqrt{87616-58800}}{24}= \frac{296\pm\sqrt{28816}}{24}\\\\x=\frac{296\pm169.75}{24}= 12.333\pm7.073\\\\\\x_1=12.333+7.073=19.406\\\\x_2=12.333-7.073=5.26](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B-b%5Cpm%5Csqrt%7Bb%5E24ac%7D%7D%7B2a%7D%5C%5C%5C%5Cx%3D%5Cfrac%7B296%5Cpm%5Csqrt%7B296%5E2-4%2A12%2A1225%7D%7D%7B2%2A12%7D%20%20%3D%5Cfrac%7B296%5Cpm%5Csqrt%7B87616-58800%7D%7D%7B24%7D%3D%20%5Cfrac%7B296%5Cpm%5Csqrt%7B28816%7D%7D%7B24%7D%5C%5C%5C%5Cx%3D%5Cfrac%7B296%5Cpm169.75%7D%7B24%7D%3D%2012.333%5Cpm7.073%5C%5C%5C%5C%5C%5Cx_1%3D12.333%2B7.073%3D19.406%5C%5C%5C%5Cx_2%3D12.333-7.073%3D5.26)
The first solution is physically impossible, as the side that is cut would be bigger than 25.
So the real solution is for x=5.26 in.
Then, the dimensions of the box are:
![A=49-2x=49-2*5.26=49-10.52=38.48\\\\B=25-2x=25-10.52=14.48](https://tex.z-dn.net/?f=A%3D49-2x%3D49-2%2A5.26%3D49-10.52%3D38.48%5C%5C%5C%5CB%3D25-2x%3D25-10.52%3D14.48)
Hi,
To find population of the city you have to multiply people per square mile (population density) and area.
![87 \times 3517 = 305979](https://tex.z-dn.net/?f=87%20%5Ctimes%203517%20%3D%20305979)
Answer: 305979 people live in the city.
Hope this helps.
r3t40