Answer:
7m^2 - 11m - 2
Step-by-step explanation:
Subtract (-3m^2 + 10m + 4) from 4m^2 - m + 2:
4m^2 - m + 2
- (-3m^2 + 10m + 4) Now distribute the negative sign:
4m^2 - m + 2
+ 3m^2 - 10m - 4
--------------------------
7m^2 - 11m - 2 is the final answer.
Set
![\begin{cases}x=r\cos\theta\\y=r\sin\theta\end{cases}\implies\mathrm dA=r\,\mathrm dr\,\mathrm d\theta](https://tex.z-dn.net/?f=%5Cbegin%7Bcases%7Dx%3Dr%5Ccos%5Ctheta%5C%5Cy%3Dr%5Csin%5Ctheta%5Cend%7Bcases%7D%5Cimplies%5Cmathrm%20dA%3Dr%5C%2C%5Cmathrm%20dr%5C%2C%5Cmathrm%20d%5Ctheta)
The region
is given in polar coordinates by the set
![R=\left\{(r,\theta)\mid2\le r\le3,0\le\theta\le\dfrac\pi2\right\}](https://tex.z-dn.net/?f=R%3D%5Cleft%5C%7B%28r%2C%5Ctheta%29%5Cmid2%5Cle%20r%5Cle3%2C0%5Cle%5Ctheta%5Cle%5Cdfrac%5Cpi2%5Cright%5C%7D)
So we have
![\displaystyle\iint_R\sin(x^2+y^2)\,\mathrm dA=\int_0^{\pi/2}\int_2^3r\sin(r^2)\,\mathrm dr\,\mathrm d\theta=\boxed{\frac\pi4(\cos4-\cos9)}](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Ciint_R%5Csin%28x%5E2%2By%5E2%29%5C%2C%5Cmathrm%20dA%3D%5Cint_0%5E%7B%5Cpi%2F2%7D%5Cint_2%5E3r%5Csin%28r%5E2%29%5C%2C%5Cmathrm%20dr%5C%2C%5Cmathrm%20d%5Ctheta%3D%5Cboxed%7B%5Cfrac%5Cpi4%28%5Ccos4-%5Ccos9%29%7D)
Answer:
24.
Step-by-step explanation:
Substitute each instance of x with a 3.
That leaves us with 3^2 + 3x - 5 + 3^2 - 3x + 11.
Combine like terms.
2(3^2) + 6.
Simplify.
2(9) + 6
18 + 6
24.
Answer:
She will ride an average of 5 miles
Step-by-step explanation:
To calculate the average, add all the values together and divide by the amount of values:
3 + 5 + 4 + 8 = 20
20 ÷ 4 = 5
Average of 5 miles