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Nata [24]
2 years ago
8

Question

Mathematics
1 answer:
denpristay [2]2 years ago
7 0
V= π r^2 h

r= radius
h= height

If the radius was 10 ft and the height was 12ft then the answer be about 3769.91.

However if it was reversed and the radius was 12ft and the height was 10 ft then the answer would be about 4523.89.

3769.92≈ π 10^2 12

or

4523.89≈ π 12^2 10

(Question was not correctly specified)
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Show that the line integral is independent of path by finding a function f such that ?f = f. c 2xe?ydx (2y ? x2e?ydy, c is any p
Juli2301 [7.4K]
I'm reading this as

\displaystyle\int_C2xe^{-y}\,\mathrm dx+(2y-x^2e^{-y})\,\mathrm dy

with \nabla f=(2xe^{-y},2y-x^2e^{-y}).

The value of the integral will be independent of the path if we can find a function f(x,y) that satisfies the gradient equation above.

You have

\begin{cases}\dfrac{\partial f}{\partial x}=2xe^{-y}\\\\\dfrac{\partial f}{\partial y}=2y-x^2e^{-y}\end{cases}

Integrate \dfrac{\partial f}{\partial x} with respect to x. You get

\displaystyle\int\dfrac{\partial f}{\partial x}\,\mathrm dx=\int2xe^{-y}\,\mathrm dx
f=x^2e^{-y}+g(y)

Differentiate with respect to y. You get

\dfrac{\partial f}{\partial y}=\dfrac{\partial}{\partial y}[x^2e^{-y}+g(y)]
2y-x^2e^{-y}=-x^2e^{-y}+g'(y)
2y=g'(y)

Integrate both sides with respect to y to arrive at

\displaystyle\int2y\,\mathrm dy=\int g'(y)\,\mathrm dy
y^2=g(y)+C
g(y)=y^2+C

So you have

f(x,y)=x^2e^{-y}+y^2+C

The gradient is continuous for all x,y, so the fundamental theorem of calculus applies, and so the value of the integral, regardless of the path taken, is

\displaystyle\int_C2xe^{-y}\,\mathrm dx+(2y-x^2e^{-y})\,\mathrm dy=f(4,1)-f(1,0)=\frac9e
8 0
3 years ago
A line has this equation: y = -2x-5 Write an equation for the parallel line that goes through (-3,-5).​
zhuklara [117]

Answer:

Step-by-step explanation:

y + 5 = -2(x + 3)

y + 5 = -2x - 6

y = -2x - 11

3 0
3 years ago
Help pls .!!!!!!!!!!!
Igoryamba
A and C are the answer
4 0
2 years ago
Read 2 more answers
A shop has one-pound bags of peanuts for $2 and three-pound bags of peanuts for $5.50. If you buy 8 bags and spend $37, how many
Andrew [12]

Answer:

  • 6 3-lb bags
  • 2 1-lb bags

Step-by-step explanation:

Let x represent the number of 3-lb bags purchased. Then the total purchase was ...

  $2(8 -x) +$5.50(x) = $37

  16 +3.50x = 37 . . . . . . . . . divide by $, collect terms

  3.50x = 21 . . . . . . . . . . . . . subtract 16

  21/3.50 = x = 6 . . . . . . . . divide by the coefficient of x

You bought 6 3-lb bags of peanuts and 2 1-lb bags.

4 0
3 years ago
Which equation does not represent the percentage of the votes?
Vladimir [108]
I would say 92 * x = 115
5 0
3 years ago
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