if the ellipse has a major axis of 12 inches, that means its major radius is half that, or 6, and if its minor axis is 7, then its minor radius is half that, 3.5.
![\bf \textit{volume of an elliptical cylinder}\\\\ V=\pi ab h~~ \begin{cases} a=\textit{major axis radius}\\ b=\textit{minor axis radius}\\ h=height\\[-0.5em] \hrulefill\\ a=6\\ b=3.5\\ h=21 \end{cases} \\\\\\ V=\pi (6)(3.5)(21)\implies V\approx 1385.44236023309881816203](https://tex.z-dn.net/?f=%5Cbf%20%5Ctextit%7Bvolume%20of%20an%20elliptical%20cylinder%7D%5C%5C%5C%5C%0AV%3D%5Cpi%20ab%20h~~%0A%5Cbegin%7Bcases%7D%0Aa%3D%5Ctextit%7Bmajor%20axis%20radius%7D%5C%5C%0Ab%3D%5Ctextit%7Bminor%20axis%20radius%7D%5C%5C%0Ah%3Dheight%5C%5C%5B-0.5em%5D%0A%5Chrulefill%5C%5C%0Aa%3D6%5C%5C%0Ab%3D3.5%5C%5C%0Ah%3D21%0A%5Cend%7Bcases%7D%0A%5C%5C%5C%5C%5C%5C%0AV%3D%5Cpi%20%286%29%283.5%29%2821%29%5Cimplies%20V%5Capprox%201385.44236023309881816203)
Answer:
10kg
Step-by-step explanation:
For UPS;
express fee = $10
If one kg costs $2, then x kg of package will coat $2x
Total cost of shipping xkg of package will be 10+2x
For FedEx;
Fixed express fee = $20
If one kg costs $1, then x kg of package will coat $1x
Total cost of shipping x kg of package is 20+x
If the total costs of the two options are the same, then;
10+2x = 20+x
2x-x = 20-10
x = 10.
Hence Eric sent 10kg of package
Answer:
answer is 90
Explanation:
Here 5 is one of the 4 prime factors, so dividing the lower (80) and upper limit (100) by 5 we have new lower limit 16 and new upper limit 20.
So the product of other 3 factors should be greater than 16 and less than 20.
And we can have it from 18 only. Hence the number is 90.
The numbers between 80 and 100 having factor 5 are
<span>80,85,90,95,100</span>
<span>16=<span>24</span></span>
<span>17=17</span>
<span>18=2×3×3</span>
<span>19=19</span>
<span>20=<span>22</span>×5</span>
<span>90=2×<span>32</span>×<span>5</span></span>
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Answer:

Step-by-step explanation:
We have a separable equation, first let's rewrite the equation as:

But:

So:

Multiplying both sides by dx and dividing both sides by 3a+y:

Integrating both sides:

Evaluating the integrals:

Where C1 is an arbitrary constant.
Solving for y:


So:

Finally, let's evaluate the initial condition in order to find C1:

Solving for C1:

Therefore:
