P represents the original per pound price3p represents the cost of three pounds 3p + 3(0.75) = 5.88 multiply3p + 2.25 = 5.88 subtract 2.55 from both sides3p = 3.63 divide both sidesby 3p = 1.21 The original price was $1.21 per pound. 1.21 = 0.751.963(1.96)5.88
X is 3
y is 2
you have to replace x with a zero and divide 12 by it and then you do the same for y
Attached is a plot of the base with one of the cross sections (at
![x=0.6](https://tex.z-dn.net/?f=x%3D0.6)
).
The area of any one cross section is given by
![\dfrac{\pi r^2}2](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cpi%20r%5E2%7D2)
, where
![r](https://tex.z-dn.net/?f=r)
is the radius of the circular cross section. In terms of the sections' diameters
![d=2r](https://tex.z-dn.net/?f=d%3D2r)
, the area would be
![\dfrac{\pi\left(\frac d2\right)^2}2=\dfrac{\pi d^2}8](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cpi%5Cleft%28%5Cfrac%20d2%5Cright%29%5E2%7D2%3D%5Cdfrac%7B%5Cpi%20d%5E2%7D8)
.
Each section's diameter is determined by the vertical distance (in the x-y plane) between the curve
![y=3-x^5](https://tex.z-dn.net/?f=y%3D3-x%5E5)
and the x-axis (
![y=0](https://tex.z-dn.net/?f=y%3D0)
), or simply
![d=3-x^5](https://tex.z-dn.net/?f=d%3D3-x%5E5)
. So the area of any one cross-section for a given
![x](https://tex.z-dn.net/?f=x)
is
![\dfrac{\pi(3-x^5)^2}8](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cpi%283-x%5E5%29%5E2%7D8)
.
The region extends from
![x=0](https://tex.z-dn.net/?f=x%3D0)
to
![x=3^{1/5}](https://tex.z-dn.net/?f=x%3D3%5E%7B1%2F5%7D)
(the positive root of
![3-x^5](https://tex.z-dn.net/?f=3-x%5E5)
), so the volume of the solid would be
![\displaystyle\int_0^{3^{1/5}}\frac{\pi(3-x^5)^2}8\,\mathrm dx=\frac\pi8\int_0^{3^{1/5}}(3-x^5)^2\,\mathrm dx](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Cint_0%5E%7B3%5E%7B1%2F5%7D%7D%5Cfrac%7B%5Cpi%283-x%5E5%29%5E2%7D8%5C%2C%5Cmathrm%20dx%3D%5Cfrac%5Cpi8%5Cint_0%5E%7B3%5E%7B1%2F5%7D%7D%283-x%5E5%29%5E2%5C%2C%5Cmathrm%20dx)
You can compute this by expanding the integrand, then integrating term by term. You should find a volume of
![\dfrac{75\times3^{1/5}\pi}{88}\approx3.335](https://tex.z-dn.net/?f=%5Cdfrac%7B75%5Ctimes3%5E%7B1%2F5%7D%5Cpi%7D%7B88%7D%5Capprox3.335)
.
I believe the answer is either iscoceles or scalene