<span>I think it's x=<span>419 well i could be wrong just an elementary eight year old</span></span>
The answer to the equation is approximately 536.91
Step-by-step explanation:
Answers
= 80 square feet
Answer:
Radius=2.09 cm
Height,h=14.57 cm
Step-by-step explanation:
We are given that
Volume of cylinderical shaped can=200 cubic cm.
Cost of sides of can=0.02 cents per square cm
Cost of top and bottom of the can =0.07 cents per square cm
Curved surface area of cylinder=![2\pi rh](https://tex.z-dn.net/?f=2%5Cpi%20rh)
Area of circular base=Area of circular top=![\pi r^2](https://tex.z-dn.net/?f=%5Cpi%20r%5E2)
Total cost,C(r)=![0.02\times 2\pi rh+2\pi r^2\times 0.07](https://tex.z-dn.net/?f=0.02%5Ctimes%202%5Cpi%20rh%2B2%5Cpi%20r%5E2%5Ctimes%200.07)
Volume of cylinder,![V=\pi r^2 h](https://tex.z-dn.net/?f=V%3D%5Cpi%20r%5E2%20h)
![200=\pi r^2 h](https://tex.z-dn.net/?f=200%3D%5Cpi%20r%5E2%20h)
![h=\frac{200}{\pi r^2}](https://tex.z-dn.net/?f=h%3D%5Cfrac%7B200%7D%7B%5Cpi%20r%5E2%7D)
Substitute the value of h
![C(r)=0.02\times 2\pi r\times \frac{200}{\pi r^2}+2\pi r^2\times 0.07](https://tex.z-dn.net/?f=C%28r%29%3D0.02%5Ctimes%202%5Cpi%20r%5Ctimes%20%5Cfrac%7B200%7D%7B%5Cpi%20r%5E2%7D%2B2%5Cpi%20r%5E2%5Ctimes%200.07)
![C(r)=\frac{8}{r}+0.14\pi r^2](https://tex.z-dn.net/?f=C%28r%29%3D%5Cfrac%7B8%7D%7Br%7D%2B0.14%5Cpi%20r%5E2)
Differentiate w.r.t r
![C'(r)=-\frac{8}{r^2}+0.28\pi r](https://tex.z-dn.net/?f=C%27%28r%29%3D-%5Cfrac%7B8%7D%7Br%5E2%7D%2B0.28%5Cpi%20r)
![C'(r)=0](https://tex.z-dn.net/?f=C%27%28r%29%3D0)
![-\frac{8}{r^2}+0.28\pi r=0](https://tex.z-dn.net/?f=-%5Cfrac%7B8%7D%7Br%5E2%7D%2B0.28%5Cpi%20r%3D0)
![0.28\pi r=\frac{8}{r^2}](https://tex.z-dn.net/?f=0.28%5Cpi%20r%3D%5Cfrac%7B8%7D%7Br%5E2%7D)
![r^3=\frac{8}{0.28\pi}=9.095](https://tex.z-dn.net/?f=r%5E3%3D%5Cfrac%7B8%7D%7B0.28%5Cpi%7D%3D9.095)
![r=(9.095)^{\frac{1}{3}}=2.09](https://tex.z-dn.net/?f=r%3D%289.095%29%5E%7B%5Cfrac%7B1%7D%7B3%7D%7D%3D2.09)
Again, differentiate w.r.t r
![C''(r)=\frac{16}{r^3}+0.28\pi](https://tex.z-dn.net/?f=C%27%27%28r%29%3D%5Cfrac%7B16%7D%7Br%5E3%7D%2B0.28%5Cpi)
Substitute the value of r
![C''(2.09)=\frac{16}{(2.09)^3}+0.28\pi=2.63>0](https://tex.z-dn.net/?f=C%27%27%282.09%29%3D%5Cfrac%7B16%7D%7B%282.09%29%5E3%7D%2B0.28%5Cpi%3D2.63%3E0)
Therefore,the product cost is minimum at r=2.09
h=![\frac{200}{\pi (2.09)^2}=14.57](https://tex.z-dn.net/?f=%5Cfrac%7B200%7D%7B%5Cpi%20%282.09%29%5E2%7D%3D14.57)
Radius of can,r=2.09 cm
Height of cone,h=14.57 cm
<span>5/5 ÷ 1/2 =
5/5 is the same as 1 so 1/2 of 1 = 1/2
</span>