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spin [16.1K]
3 years ago
5

PLEASE help me??

Mathematics
1 answer:
ivolga24 [154]3 years ago
4 0

Let x = 5


f(5) = 4(5) - 11


f(5) = 20 - 11


f(5) = 9


Choice C


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Answer:

irrational

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Step-by-step explanation:

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3 years ago
Evaluate the integral e^xy w region d xy=1, xy=4, x/y=1, x/y=2
LUCKY_DIMON [66]
Make a change of coordinates:

u(x,y)=xy
v(x,y)=\dfrac xy

The Jacobian for this transformation is

\mathbf J=\begin{bmatrix}\dfrac{\partial u}{\partial x}&\dfrac{\partial v}{\partial x}\\\\\dfrac{\partial u}{\partial y}&\dfrac{\partial v}{\partial y}\end{bmatrix}=\begin{bmatrix}y&x\\\\\dfrac1y&-\dfrac x{y^2}\end{bmatrix}

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The integral then changes to

\displaystyle\iint_{\mathcal W_{(x,y)}}e^{xy}\,\mathrm dx\,\mathrm dy=\iint_{\mathcal W_{(u,v)}}\dfrac{e^u}{|\det\mathbf J|}\,\mathrm du\,\mathrm dv
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8 0
3 years ago
7.
Iteru [2.4K]

Answer:

a. 45 π

b. 12 π

c. 16 π

Step-by-step explanation:

a.

If a 3×5 rectangle is revolved about one of its sides of length 5 to create a solid of revolution, we can see a cilinder with:

Radius: 3

Height: 5

Then the volume of the cylinder is:

V=π*r^{2} *h= π*(3)^{2} *(5) = π*(9)*(5)=45 π

b. If a 3-4-5 right triangle is revolved about a leg of length 4 to create a solid of revolution. We can see a cone with:

Radius: 3

Height: 4

Then the volume of the cone is:

V=(1/3)*π*r^{2} *h= (1/3)*π*(3)^{2} *(4) = (1/3)*π*(9)*(4)=12 π

c. We can answer this item using the past (b. item) and solving for the other leg revolution (3):

Then we will have:

Radius: 4

Height: 3

Then the volume of the cone is:

V=(1/3)*π*r^{2} *h= (1/3)*π*(4)^{2} *(3) = (1/3)*π*(16)*(3)=16 π

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Answer:

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