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Marina CMI [18]
2 years ago
13

A ladder is leaning against a building, forming a 70 degree angle with the ground. The base of the ladder is 8.2 ft from the bas

e of the building.
What is the length of the ladder?
Mathematics
2 answers:
ankoles [38]2 years ago
8 0
Cosine (70) = 8.2 / ladder
ladder = 8.2 / cosine (70)
ladder = 8.2 / 0.3420201
<span><span><span>ladder length = 23.9751991184 </span> </span> </span>


serious [3.7K]2 years ago
3 0

Answer:

24.0

Step-by-step explanation:

I took the test. While I also got the other answer, this is the one the test is telling me is correct.

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The vector field

\vec F(x,y,z)=x^2\sin z\,\vec\imath+y^2\,\vec\jmath+xy\,\vec k

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Parameterize S by

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where

\begin{cases}x(u,v)=u\cos v\\y(u,v)=u\sin v\\z(u,v)=(9-u^2)\end{cases}

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Take the normal vector to S to be

\dfrac{\partial\vec s}{\partial u}\times\dfrac{\partial\vec s}{\partial v}=2u^2\cos v\,\vec\imath+2u^2\sin v\,\vec\jmath+u\,\vec k

Then by Stokes' theorem we have

\displaystyle\int_{\partial S}\vec F\cdot\mathrm d\vec r=\iint_S(\nabla\times\vec F)\cdot\mathrm d\vec S

=\displaystyle\int_0^{2\pi}\int_0^3(\nabla\times\vec F)(\vec s(u,v))\cdot\left(\dfrac{\partial\vec s}{\partial u}\times\dfrac{\partial\vec s}{\partial v}\right)\,\mathrm du\,\mathrm dv

=\displaystyle\int_0^{2\pi}\int_0^3u^3(2u\cos^3v\sin(u^2-9)+\cos^3v\sin v+2u\sin^3v+\cos v\sin^3v)\,\mathrm du\,\mathrm dv

which has a value of 0, since each component integral is 0:

\displaystyle\int_0^{2\pi}\cos^3v\,\mathrm dv=0

\displaystyle\int_0^{2\pi}\sin v\cos^3v\,\mathrm dv=0

\displaystyle\int_0^{2\pi}\sin^3v\,\mathrm dv=0

\displaystyle\int_0^{2\pi}\cos v\sin^3v\,\mathrm dv=0

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2 years ago
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Hi there
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Answer:

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Maura swims the length of a pool 8 times .The pool is 17.4 meters long .How many meters does Maura swim in all
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What is the range of the function graphed below?
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<h2>Answer:</h2>

Option: B is the correct answer.

The range of the function is:

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<h2>Step-by-step explanation:</h2>

Range of a function--

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          Hence, the answer is:

                Option: B

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2 years ago
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