It sounds like <em>R</em> is the region (in polar coordinates)
<em>R</em> = {(<em>r</em>, <em>θ</em>) : 2 ≤ <em>r</em> ≤ 3 and 0 ≤ <em>θ</em> ≤ <em>π</em>/2}
Then the integral is
![\displaystyle \iint_R\frac{\mathrm dx\,\mathrm dy}{\sqrt{x^2+y^2}} = \int_0^{\pi/2}\int_2^3 \frac{r\,\mathrm dr\,\mathrm d\theta}{\sqrt{r^2}} \\\\ = \int_0^{\pi/2}\int_2^3 \mathrm dr\,\mathrm d\theta \\\\ = \frac\pi2\int_2^3 \mathrm dr \\\\ = \frac\pi2r\bigg|_2^3 = \frac\pi2 (3-2) = \boxed{\frac\pi2}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Ciint_R%5Cfrac%7B%5Cmathrm%20dx%5C%2C%5Cmathrm%20dy%7D%7B%5Csqrt%7Bx%5E2%2By%5E2%7D%7D%20%3D%20%5Cint_0%5E%7B%5Cpi%2F2%7D%5Cint_2%5E3%20%5Cfrac%7Br%5C%2C%5Cmathrm%20dr%5C%2C%5Cmathrm%20d%5Ctheta%7D%7B%5Csqrt%7Br%5E2%7D%7D%20%5C%5C%5C%5C%20%3D%20%5Cint_0%5E%7B%5Cpi%2F2%7D%5Cint_2%5E3%20%5Cmathrm%20dr%5C%2C%5Cmathrm%20d%5Ctheta%20%5C%5C%5C%5C%20%3D%20%5Cfrac%5Cpi2%5Cint_2%5E3%20%5Cmathrm%20dr%20%5C%5C%5C%5C%20%3D%20%5Cfrac%5Cpi2r%5Cbigg%7C_2%5E3%20%3D%20%5Cfrac%5Cpi2%20%283-2%29%20%3D%20%5Cboxed%7B%5Cfrac%5Cpi2%7D)
Answer:
80 mph
Step-by-step explanation:
![\boxed{\sf Distance=Speed \times Time}](https://tex.z-dn.net/?f=%5Cboxed%7B%5Csf%20Distance%3DSpeed%20%5Ctimes%20Time%7D)
<u>First leg of trip</u>
- Speed = 64 mph
- Time = 3 hours
![\implies \sf Distance =64\times 3 = 192\:miles](https://tex.z-dn.net/?f=%5Cimplies%20%5Csf%20Distance%20%3D64%5Ctimes%203%20%3D%20192%5C%3Amiles)
<u>Second leg of trip</u>
- Speed = 92 mph
- Time = 4 hours
![\implies \sf Distance=92 \times 4 = 368\:miles](https://tex.z-dn.net/?f=%5Cimplies%20%5Csf%20Distance%3D92%20%5Ctimes%204%20%3D%20368%5C%3Amiles)
![\boxed{\sf Speed=\dfrac{Distance}{Time}}](https://tex.z-dn.net/?f=%5Cboxed%7B%5Csf%20Speed%3D%5Cdfrac%7BDistance%7D%7BTime%7D%7D)
To find the average speed:
![\begin{aligned}\implies \sf Average\:speed & = \sf \dfrac{Total\:distance}{Total\:time}\\\\ & = \sf \dfrac{192+368}{3+4}\\\\& = \sf \dfrac{560}{7}\\\\ & = \sf 80\:mph\end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7D%5Cimplies%20%5Csf%20Average%5C%3Aspeed%20%26%20%3D%20%5Csf%20%5Cdfrac%7BTotal%5C%3Adistance%7D%7BTotal%5C%3Atime%7D%5C%5C%5C%5C%20%26%20%3D%20%5Csf%20%5Cdfrac%7B192%2B368%7D%7B3%2B4%7D%5C%5C%5C%5C%26%20%3D%20%5Csf%20%5Cdfrac%7B560%7D%7B7%7D%5C%5C%5C%5C%20%26%20%3D%20%5Csf%2080%5C%3Amph%5Cend%7Baligned%7D)
Answer:
The number is -3
Step-by-step explanation:
Write an equation
2x+4=-10
add 4 on both sides
2x=-6
divide 2 on both sides to isolate variable
x=-3
Answer: 2/3 or 1/3
Step-by-step explanation: If we have a cake that has a total of 12 pieces, and we gave four to someone else we would have 8/12 pieces left. Now if we simplify then we would have 2/3 left.
Alternate explanation: Now if we just want to divide 4/12 then we would have 1/3.
I'm happy to help let me know if I'm wrong!