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Makovka662 [10]
3 years ago
14

Stephen is making curtains for several windows in his aunt’s house. He determines that he needs 8.5 yards of fabric for each win

dow.
a. Write an equation to represent the number of yards of fabric needed given a certain number of windows.

Answer y = 8.5x

b. What is the rate of change in this situation?

Answer _______
Mathematics
1 answer:
bogdanovich [222]3 years ago
7 0

Answer: x which is the windows

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Use Stokes' Theorem to evaluate C F · dr F(x, y, z) = xyi + yzj + zxk, C is the boundary of the part of the paraboloid z = 1 − x
Serggg [28]

I assume C has counterclockwise orientation when viewed from above.

By Stokes' theorem,

\displaystyle\int_C\vec F\cdot\mathrm d\vec r=\iint_S(\nabla\times\vec F)\cdot\mathrm d\vec S

so we first compute the curl:

\vec F(x,y,z)=xy\,\vec\imath+yz\,\vec\jmath+xz\,\vec k

\implies\nabla\times\vec F(x,y,z)=-y\,\vec\imath-z\,\vec\jmath-x\,\vec k

Then parameterize S by

\vec r(u,v)=\cos u\sin v\,\vec\imath+\sin u\sin v\,\vec\jmath+\cos^2v\,\vec k

where the z-component is obtained from

1-(\cos u\sin v)^2-(\sin u\sin v)^2=1-\sin^2v=\cos^2v

with 0\le u\le\dfrac\pi2 and 0\le v\le\dfrac\pi2.

Take the normal vector to S to be

\vec r_v\times\vec r_u=2\cos u\cos v\sin^2v\,\vec\imath+\sin u\sin v\sin(2v)\,\vec\jmath+\cos v\sin v\,\vec k

Then the line integral is equal in value to the surface integral,

\displaystyle\iint_S(\nabla\times\vec F)\cdot\mathrm d\vec S

=\displaystyle\int_0^{\pi/2}\int_0^{\pi/2}(-\sin u\sin v\,\vec\imath-\cos^2v\,\vec\jmath-\cos u\sin v\,\vec k)\cdot(\vec r_v\times\vec r_u)\,\mathrm du\,\mathrm dv

=\displaystyle-\int_0^{\pi/2}\int_0^{\pi/2}\cos v\sin^2v(\cos u+2\cos^2v\sin u+\sin(2u)\sin v)\,\mathrm du\,\mathrm dv=\boxed{-\frac{17}{20}}

6 0
3 years ago
Describe how the shapes moves to get from its position in each frame from the next.
Colt1911 [192]

Answer:

Mark me as brain list plz for fun I need to get my expert rank

Step-by-step explanation:

There is no attachment to see any grams post then I will answer

3 0
2 years ago
What is the answer to this
LekaFEV [45]
4 \dfrac{3}{5} \times \dfrac{5}{12} =

= \dfrac{23}{5} \times \dfrac{5}{12}

You changed the mixed numeral into a fraction correctly.
Now you need to multiply the fractions.
Multiply the numerators together, and multiply the denominators together.

= \dfrac{23 \times 5}{5 \times 12}

Now we could multiply out the numerator and denominator, and then we'd need to reduce the fraction, but before we multiply, we see there is a factor of 5 both in the numerator and in the denominator, so we can reduce before we multiply.

= \dfrac{23 \times 5}{12 \times 5}

= \dfrac{23}{12}

= 1 \dfrac{11}{12}
6 0
3 years ago
HELP
Oksi-84 [34.3K]

the answer is D :) i hope you have a good day

4 0
3 years ago
Read 2 more answers
Midpoint of the line segment (-1,6), (-6,5)
zepelin [54]
The answer is:

(-7/2 , 11/2)

5 0
3 years ago
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