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melisa1 [442]
3 years ago
5

The sum of a number and 8 is no more than the square of the difference of the number and 4. Which of the following inequalities

can be used to determine the unknown number?
Mathematics
1 answer:
Lady bird [3.3K]3 years ago
6 0

Answer:

x + 8 ≤ (x − 4)2

Step-by-step explanation:

Let the number be x,

The sum of the number and 8 is

(x + 8)

The square of the difference of the number and 4 is

(x - 4) {}^{2}  

Hence the inequality is

(x + 8) \leqslant (x - 4) {}^{2}

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Use Stokes' Theorem to evaluate C F · dr where C is oriented counterclockwise as viewed from above. F(x, y, z) = 2yi + xzj + (x
Lady_Fox [76]

By Stokes' theorem, the line integral of \vec F over C is given by the surface integral of the curl of \vec F over S, where S is the region of intersection of the plane z=y+6 and the cylinder x^2+y^2=1 with S having positive/upward orientation.

Parameterize S by

\vec s(u,v)=u\cos v\,\vec\imath+u\sin v\,\vec\jmath+(u\sin v+6)\,\vec k

with 0\le u\le1 and 0\le v\le2\pi.

Take the normal vector to S to be

\vec s_u\times\vec s_v=-u\,\vec\jmath+u\,\vec k

The curl of \vec F is

\nabla\times\vec F(x,y,z)=(1-x)\,\vec\imath-\vec\jmath+(z-2)\,\vec k

Then the line integral is equivalent to

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

=\displaystyle\int_0^{2\pi}\int_0^1\bigg((1-u\cos v)\,\vec\imath-\vec\jmath+(u\sin v+4)\,\vec k\bigg)\cdot\bigg(-u\,\vec\jmath+u\,\vec k\bigg)\,\mathrm du\,\mathrm dv

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4 0
3 years ago
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GREYUIT [131]

Answer:

43in

it might be wrong but that's what I got

3 0
3 years ago
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Step-by-step explanation:

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3 years ago
Use the distributive property to solve the equation 2(m + 2) = 22. Describe what it means to distribute the 2 to each term insid
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Answer:

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It means that you are multiplying each of the values inside the parentheses by 2.

Step-by-step explanation:

2(m + 2) = 22

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3 0
3 years ago
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