Weird that the only choices are given as integrals with respect to
![x](https://tex.z-dn.net/?f=x)
. (Integration along the
![y](https://tex.z-dn.net/?f=y)
axis would be way easier, but whatever)
The fourth option should do it.
Answer:
Step-by-step explanation:
From the given information:
The domain D of integration in polar coordinates can be represented by:
D = {(r,θ)| 0 ≤ r ≤ 6, 0 ≤ θ ≤ 2π) &;
The partial derivates for z = xy can be expressed as:
![y =\dfrac{\partial z}{\partial x} , x = \dfrac{\partial z}{\partial y}](https://tex.z-dn.net/?f=y%20%3D%5Cdfrac%7B%5Cpartial%20z%7D%7B%5Cpartial%20x%7D%20%2C%20x%20%3D%20%5Cdfrac%7B%5Cpartial%20z%7D%7B%5Cpartial%20y%7D)
Thus, the area of the surface is as follows:
![\iint_D \sqrt{(\dfrac{\partial z}{\partial x})^2+ (\dfrac{\partial z}{\partial y})^2 +1 }\ dA = \iint_D \sqrt{(y)^2+(x)^2+1 } \ dA](https://tex.z-dn.net/?f=%5Ciint_D%20%5Csqrt%7B%28%5Cdfrac%7B%5Cpartial%20z%7D%7B%5Cpartial%20x%7D%29%5E2%2B%20%28%5Cdfrac%7B%5Cpartial%20z%7D%7B%5Cpartial%20y%7D%29%5E2%20%2B1%20%7D%5C%20dA%20%3D%20%5Ciint_D%20%5Csqrt%7B%28y%29%5E2%2B%28x%29%5E2%2B1%20%7D%20%5C%20dA)
![= \iint_D \sqrt{x^2 +y^2 +1 } \ dA](https://tex.z-dn.net/?f=%3D%20%5Ciint_D%20%5Csqrt%7Bx%5E2%20%2By%5E2%20%2B1%20%7D%20%5C%20dA)
![= \int^{2 \pi}_{0} \int^{6}_{0} \ r \sqrt{r^2 +1 } \ dr \ d \theta](https://tex.z-dn.net/?f=%3D%20%5Cint%5E%7B2%20%5Cpi%7D_%7B0%7D%20%5Cint%5E%7B6%7D_%7B0%7D%20%5C%20r%20%20%5Csqrt%7Br%5E2%20%2B1%20%7D%20%5C%20dr%20%5C%20d%20%5Ctheta)
![=2 \pi \int^{6}_{0} \ r \sqrt{r^2 +1 } \ dr](https://tex.z-dn.net/?f=%3D2%20%5Cpi%20%5Cint%5E%7B6%7D_%7B0%7D%20%5C%20r%20%20%5Csqrt%7Br%5E2%20%2B1%20%7D%20%5C%20dr)
![= 2 \pi \begin {bmatrix} \dfrac{1}{3}(r^2 +1) ^{^\dfrac{3}{2}} \end {bmatrix}^6_0](https://tex.z-dn.net/?f=%3D%202%20%5Cpi%20%5Cbegin%20%7Bbmatrix%7D%20%5Cdfrac%7B1%7D%7B3%7D%28r%5E2%20%2B1%29%20%5E%7B%5E%5Cdfrac%7B3%7D%7B2%7D%7D%20%5Cend%20%7Bbmatrix%7D%5E6_0)
![= 2 \pi \times \dfrac{1}{3} \Bigg [ (37)^{3/2} - 1 \Bigg]](https://tex.z-dn.net/?f=%3D%202%20%5Cpi%20%5Ctimes%20%5Cdfrac%7B1%7D%7B3%7D%20%20%5CBigg%20%5B%20%2837%29%5E%7B3%2F2%7D%20-%201%20%5CBigg%5D)
![= \dfrac{2 \pi}{3} \Bigg [37 \sqrt{37} -1 \Bigg ]](https://tex.z-dn.net/?f=%3D%20%5Cdfrac%7B2%20%5Cpi%7D%7B3%7D%20%5CBigg%20%5B37%20%5Csqrt%7B37%7D%20-1%20%5CBigg%20%5D)
Answer:
I think grater then?
Step-by-step explanation:
Answer:
The independent variable is the amount of miles walked, and the dependent is the total from home.
Step-by-step explanation:
Answer:
(
)
Step-by-step explanation:
The fastest way to do this is to convert both equations into slope-intercept form and graph it to find the solution point. If you wanted to do this algebraically, you might want to start out by getting rid of the fractions and using either substitution or elimination to find x and y.