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)
hello
Step-by-step explanation:
![l = 2b \\ \\( 2b + b)2 = 6480 \\ 3b = 3240 \\ b = 1080](https://tex.z-dn.net/?f=l%20%3D%202b%20%5C%5C%20%20%5C%5C%28%202b%20%2B%20b%292%20%3D%206480%20%5C%5C%203b%20%3D%203240%20%5C%5C%20b%20%3D%201080)
l=2160
<h2>
<u>ques</u><u>tion</u><u> </u><u>is</u><u> </u><u>incomplete</u><u>.</u><u>.</u><u>.</u></h2>
Answer:
A. Ariel wants to find the difference of a number and 13.
Step-by-step explanation:
Just took the test
Answer:
![=8\sqrt{15}b^{\frac{7}{2}}](https://tex.z-dn.net/?f=%3D8%5Csqrt%7B15%7Db%5E%7B%5Cfrac%7B7%7D%7B2%7D%7D)
Step-by-step explanation:
![\sqrt{24b^3}\sqrt{40b^2}\sqrt{b^2}](https://tex.z-dn.net/?f=%5Csqrt%7B24b%5E3%7D%5Csqrt%7B40b%5E2%7D%5Csqrt%7Bb%5E2%7D)
![=\sqrt{40}\sqrt{b^2}\sqrt{b^2}\sqrt{24b^3}](https://tex.z-dn.net/?f=%3D%5Csqrt%7B40%7D%5Csqrt%7Bb%5E2%7D%5Csqrt%7Bb%5E2%7D%5Csqrt%7B24b%5E3%7D)
![=\sqrt{40}b^2\sqrt{24b^3}](https://tex.z-dn.net/?f=%3D%5Csqrt%7B40%7Db%5E2%5Csqrt%7B24b%5E3%7D)
![\sqrt{24b^3}](https://tex.z-dn.net/?f=%5Csqrt%7B24b%5E3%7D)
![=\sqrt{24}\sqrt{b^3}](https://tex.z-dn.net/?f=%3D%5Csqrt%7B24%7D%5Csqrt%7Bb%5E3%7D)
![=\sqrt{24}b^{\frac{3}{2}}](https://tex.z-dn.net/?f=%3D%5Csqrt%7B24%7Db%5E%7B%5Cfrac%7B3%7D%7B2%7D%7D)
![=\sqrt{24}b^{\frac{3}{2}}\sqrt{40}b^2](https://tex.z-dn.net/?f=%3D%5Csqrt%7B24%7Db%5E%7B%5Cfrac%7B3%7D%7B2%7D%7D%5Csqrt%7B40%7Db%5E2)
![=\sqrt{2^3\cdot \:3}b^{\frac{3}{2}}\sqrt{40}b^2](https://tex.z-dn.net/?f=%3D%5Csqrt%7B2%5E3%5Ccdot%20%5C%3A3%7Db%5E%7B%5Cfrac%7B3%7D%7B2%7D%7D%5Csqrt%7B40%7Db%5E2)
![=\sqrt{2^3}\sqrt{3}b^{\frac{3}{2}}\sqrt{40}b^2](https://tex.z-dn.net/?f=%3D%5Csqrt%7B2%5E3%7D%5Csqrt%7B3%7Db%5E%7B%5Cfrac%7B3%7D%7B2%7D%7D%5Csqrt%7B40%7Db%5E2)
![\sqrt{2^3}](https://tex.z-dn.net/?f=%5Csqrt%7B2%5E3%7D)
![=2^{3\cdot \frac{1}{2}](https://tex.z-dn.net/?f=%3D2%5E%7B3%5Ccdot%20%5Cfrac%7B1%7D%7B2%7D)
![=2^{3\cdot \frac{1}{2}}\sqrt{3}b^{\frac{3}{2}}\sqrt{40}b^2](https://tex.z-dn.net/?f=%3D2%5E%7B3%5Ccdot%20%5Cfrac%7B1%7D%7B2%7D%7D%5Csqrt%7B3%7Db%5E%7B%5Cfrac%7B3%7D%7B2%7D%7D%5Csqrt%7B40%7Db%5E2)
![=2^{\frac{3}{2}}\sqrt{3}b^{\frac{3}{2}}\sqrt{40}b^2](https://tex.z-dn.net/?f=%3D2%5E%7B%5Cfrac%7B3%7D%7B2%7D%7D%5Csqrt%7B3%7Db%5E%7B%5Cfrac%7B3%7D%7B2%7D%7D%5Csqrt%7B40%7Db%5E2)
![=2^{\frac{3}{2}}\sqrt{3}b^{\frac{3}{2}}\sqrt{2^3\cdot \:5}b^2](https://tex.z-dn.net/?f=%3D2%5E%7B%5Cfrac%7B3%7D%7B2%7D%7D%5Csqrt%7B3%7Db%5E%7B%5Cfrac%7B3%7D%7B2%7D%7D%5Csqrt%7B2%5E3%5Ccdot%20%5C%3A5%7Db%5E2)
![=2^{\frac{3}{2}}\sqrt{3}b^{\frac{3}{2}}\sqrt{2^3}\sqrt{5}b^2](https://tex.z-dn.net/?f=%3D2%5E%7B%5Cfrac%7B3%7D%7B2%7D%7D%5Csqrt%7B3%7Db%5E%7B%5Cfrac%7B3%7D%7B2%7D%7D%5Csqrt%7B2%5E3%7D%5Csqrt%7B5%7Db%5E2)
![=2^{\frac{3}{2}}\sqrt{3}b^{\frac{3}{2}}\cdot \:2^{\frac{3}{2}}\sqrt{5}b^2](https://tex.z-dn.net/?f=%3D2%5E%7B%5Cfrac%7B3%7D%7B2%7D%7D%5Csqrt%7B3%7Db%5E%7B%5Cfrac%7B3%7D%7B2%7D%7D%5Ccdot%20%5C%3A2%5E%7B%5Cfrac%7B3%7D%7B2%7D%7D%5Csqrt%7B5%7Db%5E2)
![=\sqrt{3}b^{\frac{3}{2}}\cdot \:2^{\frac{3}{2}+\frac{3}{2}}\sqrt{5}b^2](https://tex.z-dn.net/?f=%3D%5Csqrt%7B3%7Db%5E%7B%5Cfrac%7B3%7D%7B2%7D%7D%5Ccdot%20%5C%3A2%5E%7B%5Cfrac%7B3%7D%7B2%7D%2B%5Cfrac%7B3%7D%7B2%7D%7D%5Csqrt%7B5%7Db%5E2)
![=\sqrt{3}\cdot \:2^{\frac{3}{2}+\frac{3}{2}}\sqrt{5}b^{\frac{3}{2}+2}](https://tex.z-dn.net/?f=%3D%5Csqrt%7B3%7D%5Ccdot%20%5C%3A2%5E%7B%5Cfrac%7B3%7D%7B2%7D%2B%5Cfrac%7B3%7D%7B2%7D%7D%5Csqrt%7B5%7Db%5E%7B%5Cfrac%7B3%7D%7B2%7D%2B2%7D)
![2^{\frac{3}{2}+\frac{3}{2}}](https://tex.z-dn.net/?f=2%5E%7B%5Cfrac%7B3%7D%7B2%7D%2B%5Cfrac%7B3%7D%7B2%7D%7D)
![=2^3](https://tex.z-dn.net/?f=%3D2%5E3)
![=2^3\sqrt{3}\sqrt{5}b^{\frac{3}{2}+2}](https://tex.z-dn.net/?f=%3D2%5E3%5Csqrt%7B3%7D%5Csqrt%7B5%7Db%5E%7B%5Cfrac%7B3%7D%7B2%7D%2B2%7D)
![b^{\frac{3}{2}+2}](https://tex.z-dn.net/?f=b%5E%7B%5Cfrac%7B3%7D%7B2%7D%2B2%7D)
![=b^{\frac{7}{2}}](https://tex.z-dn.net/?f=%3Db%5E%7B%5Cfrac%7B7%7D%7B2%7D%7D)
![=2^3\sqrt{3}\sqrt{5}b^{\frac{7}{2}}](https://tex.z-dn.net/?f=%3D2%5E3%5Csqrt%7B3%7D%5Csqrt%7B5%7Db%5E%7B%5Cfrac%7B7%7D%7B2%7D%7D)
![=2^3\sqrt{3\cdot \:5}b^{\frac{7}{2}}](https://tex.z-dn.net/?f=%3D2%5E3%5Csqrt%7B3%5Ccdot%20%5C%3A5%7Db%5E%7B%5Cfrac%7B7%7D%7B2%7D%7D)
![=8\sqrt{15}b^{\frac{7}{2}}](https://tex.z-dn.net/?f=%3D8%5Csqrt%7B15%7Db%5E%7B%5Cfrac%7B7%7D%7B2%7D%7D)