Answer:
Graph is attached below.
Step-by-step explanation:
If you want to solve for the variable x,
x = −4 / 5y + 7 / 5
Determine the general rule (Tn)
1 answer:
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So hmm check the picture below, that's the silo, notice the top of the cylinder is inside with grain... and the bottom, well, that's the (base no included)
so
![\bf \textit{now, let's check the critical points}\\\\ \cfrac{dc}{dr}=-\cfrac{28000}{r^2}+\cfrac{16\pi r}{3}\implies \cfrac{dc}{dr}=\cfrac{16\pi r^3-84000}{3r^2} \\\\\\ 0=\cfrac{16\pi r^3-84000}{3r^2}\implies 84000=16\pi r^3\implies 5250=\pi r^3 \\\\\\ \boxed{\sqrt[3]{\cfrac{5250}{\pi }}=r}](https://tex.z-dn.net/?f=%5Cbf%20%5Ctextit%7Bnow%2C%20let%27s%20check%20the%20critical%20points%7D%5C%5C%5C%5C%0A%5Ccfrac%7Bdc%7D%7Bdr%7D%3D-%5Ccfrac%7B28000%7D%7Br%5E2%7D%2B%5Ccfrac%7B16%5Cpi%20r%7D%7B3%7D%5Cimplies%20%5Ccfrac%7Bdc%7D%7Bdr%7D%3D%5Ccfrac%7B16%5Cpi%20r%5E3-84000%7D%7B3r%5E2%7D%0A%5C%5C%5C%5C%5C%5C%0A0%3D%5Ccfrac%7B16%5Cpi%20r%5E3-84000%7D%7B3r%5E2%7D%5Cimplies%2084000%3D16%5Cpi%20r%5E3%5Cimplies%205250%3D%5Cpi%20r%5E3%0A%5C%5C%5C%5C%5C%5C%0A%5Cboxed%7B%5Csqrt%5B3%5D%7B%5Ccfrac%7B5250%7D%7B%5Cpi%20%7D%7D%3Dr%7D)
now, I'd like to point out, we also get critical points from the denominator being zero, so 3r²=0, gives us r=0, which is a critical point, however, with a radius of 0, well, there's no volume, so, the is not feasible for the phenomena, so is not applicable, though is a valid critical point
critical points from the denominator being zero, are usually asymptotic or "cusps", the function reaches an extrema, however the tangent is not horizontal and thus is not differentiable at that point, even though is an extrema.
so
now, I'd like to point out, we also get critical points from the denominator being zero, so 3r²=0, gives us r=0, which is a critical point, however, with a radius of 0, well, there's no volume, so, the is not feasible for the phenomena, so is not applicable, though is a valid critical point
critical points from the denominator being zero, are usually asymptotic or "cusps", the function reaches an extrema, however the tangent is not horizontal and thus is not differentiable at that point, even though is an extrema.
9514 1404 393
Answer:
11 7/16
Step-by-step explanation:
The integration resolves into finding the area of two triangles. The left has a height of (-3/8(-2/3)+2) = 2 1/4, and a width of (16/3-(-2/3)) = 6. Then its area is ...
A = (1/2)bh = (1/2)(6)(2 1/4) = 6 3/4
__
The right triangle has a height of |(-3/8)(31/3) +2| = |-31/8+16/8| = 15/8. Its width is (31/3) -(16/3) = 5, so its area is ...
A = (1/2)(5)(15/8) = 75/16 = 4 11/16
Then the total area, the value of the integral, is ...
6 3/4 +4 11/16 = 10 23/16 = 11 7/16 . . . the value of the integral
