Which table represents a direct variation function?

If 40% of a number is 32, what is 25% of that number?

Mekhanik [1.2K]

Well what I would do is split the 40% into 20% so from 40% to 20% that is /2. So 32/2=16 so 20% of a number is 16, we know there is 5, 20% in 100% so multiply 16 and 5 which gives you 80. Now 25% of 80 is the same as 80*.25 or 80/4 which is 20

Your Answer 20

7 0

2 years ago

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Use Stokes' Theorem to evaluate S curl F · dS. F(x, y, z) = x2 sin(z)i + y2j + xyk, S is the part of the paraboloid z = 9 − x2 −

Korolek [52]

The vector field

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

has curl

$\nabla\times\vec F(x,y,z)=x\,\vec\imath+(x^2\cos z-y)\,\vec\jmath$

Parameterize $S$ by

$\vec s(u,v)=x(u,v)\,\vec\imath+y(u,v)\,\vec\jmath+z(u,v)\,\vec k$

where

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

with $0\le u\le3$ and $0\le v\le2\pi$ .

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:

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

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

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

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

4 0

1 year ago

Which polynomial is prime? x3 + 3x2 – 2x – 6 x3 – 2x2 + 3x – 6 4x4 + 4x3 – 2x – 2 2x4 + x3 – x + 2

alexandr1967 [171]

D. 2x4+x3–x+2 <span>is prime</span>

4 0

2 years ago

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Jose wants to start a restaurant and is writing a business proposal. His rent is $1,000 per month. The monthly operating costs a

Harman [31]

Answer:

Revenue = 5( 1000 + w+ k)

Step-by-step explanation:

Lets calculate expenses first

rent = $1000

wages = w

overhead cost = k

Total cost = rent + wage+ overhead

Total cost = 1000 + w+ k

Given Jose wants his monthly sales revenue, x, to be 4 times greater than the operating costs

Let revenue be R

Thus, putting the statement mathematically

revenue - total cost = 4 * operating cost

R - ( 1000 + w+ k) = 4( 1000 + w+ k)

R = 4( 1000 + w+ k) + ( 1000 + w+ k)

R = 5( 1000 + w+ k)

Thus, revenue should be 5( 1000 + w+ k).

4 0

2 years ago

The height h of the equilateral triangle below is given by y= 5 cot theta where theta = 30 degrees

brilliants [131]

To solve this we can take two different approaches:

1. We can substitute theta by 30° and evaluate our expression using a calculator:
$y=5cot( \alpha )$
$y=5cot(30)$
$y=8.7$

2. We can use the unitary circle and the fact that $cot \alpha = \frac{cos( \alpha }{sin( \alpha )}$ , so we can rewrite our expression as follows:
$y=5cot( \alpha )$
$y=5 \frac{cos( \alpha )}{sin( \alpha )}$
$y= \frac{cos(30)}{sin(30)}$
From our unitary circle we can check that $cos(30)= \frac{ \sqrt{3} }{2}$ and $sin(30)= \frac{1}{2}$ .
Lets replace those values in our expression and simplify:
$y= \frac{ 5(\frac{ \sqrt{3} }{2})}{ \frac{1}{2} }$
$y=5 \sqrt{3}$
$y=8.7$

Either way we can conclude that the correct answer is: D)8.7

6 0

1 year ago