Answer:
Y=20x+15 & 175 dollars
Step-by-step explanation:
The word problems says $20 per hour, so that means 20 times the amount of hours. If yo multiply 20 times 8 you get 160. Add 15 to 160, you end up with $175.
![\displaystyle\iint_R\sin(384x^2+486y^2)\,\mathrm dA](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Ciint_R%5Csin%28384x%5E2%2B486y%5E2%29%5C%2C%5Cmathrm%20dA)
Notice that Given that
is an ellipse, consider a conversion to polar coordinates:
![\begin{cases}x(r,\theta)=\frac r8\cos\theta\\y(r,\theta)=\frac r9\sin\theta\end{cases}](https://tex.z-dn.net/?f=%5Cbegin%7Bcases%7Dx%28r%2C%5Ctheta%29%3D%5Cfrac%20r8%5Ccos%5Ctheta%5C%5Cy%28r%2C%5Ctheta%29%3D%5Cfrac%20r9%5Csin%5Ctheta%5Cend%7Bcases%7D)
The Jacobian for this transformation is
![J=\begin{bmatrix}\frac18\cos\theta&-\frac r8\sin\theta\\\frac19\sin\theta&\frac r9\cos t\end{bmatrix}](https://tex.z-dn.net/?f=J%3D%5Cbegin%7Bbmatrix%7D%5Cfrac18%5Ccos%5Ctheta%26-%5Cfrac%20r8%5Csin%5Ctheta%5C%5C%5Cfrac19%5Csin%5Ctheta%26%5Cfrac%20r9%5Ccos%20t%5Cend%7Bbmatrix%7D)
with determinant ![\det J=\frac r{72}](https://tex.z-dn.net/?f=%5Cdet%20J%3D%5Cfrac%20r%7B72%7D)
Then the integral in polar coordinates is
![\displaystyle\frac1{72}\int_0^{\pi/2}\int_0^1\sin(6r^2\cos^2t+6r^2\sin^2t)r\,\mathrm dr\,\mathrm d\theta=\int_0^{\pi/2}\int_0^1r\sin(6r^2)\,\mathrm dr\,\mathrm d\theta=\boxed{\frac{\pi\sin^23}{864}}](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Cfrac1%7B72%7D%5Cint_0%5E%7B%5Cpi%2F2%7D%5Cint_0%5E1%5Csin%286r%5E2%5Ccos%5E2t%2B6r%5E2%5Csin%5E2t%29r%5C%2C%5Cmathrm%20dr%5C%2C%5Cmathrm%20d%5Ctheta%3D%5Cint_0%5E%7B%5Cpi%2F2%7D%5Cint_0%5E1r%5Csin%286r%5E2%29%5C%2C%5Cmathrm%20dr%5C%2C%5Cmathrm%20d%5Ctheta%3D%5Cboxed%7B%5Cfrac%7B%5Cpi%5Csin%5E23%7D%7B864%7D%7D)
where you can evaluate the remaining integral by substituting
and
.
Answer:
6.3 Kwhr
Step-by-step explanation:
Given :
Power = 8827 watts
Time in minutes = 43 minutes
To obtain the amount of CO2 that was created :, which is the energy :
Recall
Energy = power * time
Energy in kw/hr = (8827/100) * (43/60)
Energy = 8.827 * 0.7166666
Energy = 6.326 Kwhr
Let us break it down. A sum of ten. That is just
+10
Then, we will add that to the quotient (which is the number after dividing) of a number x and 6. We can write that as
+ x/6
The slash means division here. Thus your final answer is
10 + x/6
Part A.
*To find the sales tax (6%) amount: $18.50 x .06 = $1.11 is the sales tax on a dozen carnations
Part B.
*To find the total cost of a dozen carnations plus the sales tax: $18.50 + $1.11 = $19.61 this is the total cost