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3 years ago

The sum of twice a number and five is at most fourteen?

Mathematics

1 answer:

KatRina [158]3 years ago

3 0

2x+5<14 .................................

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Select all that apply

weeeeeb [17]

Answer:

The answer to this is both (3,0) and (0,-3). C and B

Step-by-step explanation:

This is because the points in which these two graphs meet is the solution of equations.

Please mark me Brainliest!

7 0

4 years ago

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

3 years ago

X^2+4x-7 what is the ordered pair

lisabon 2012 [21]

It would be y=4x-7. I hope this helped :)

6 0

3 years ago

Which expression can be substituted for x in the top equation of the following system to solve the system by substitution? 2x−7y

Ivanshal [37]

From the second equation:-
x = 6 - 4y
Substitute this for x in the top equation

6 0

3 years ago

Naina went on a trip. She covered a distance of 34 Kilometre 46 metre by car, 143 kilometre 92 metre by train, 5 kilometre 92 me

GaryK [48]

Answer:

185590 m

or 185 km 590 meters

Step-by-step explanation:

to calculate total distance covered, convert km to meter and adding the numbers together

1km = 1000m

34 Kilometre 46 metre = (34 x 1000) + 46 = 34046m

143 kilometre 92 metre = ( 143 x 1000) + 92 = 143,092m

5 kilometre 92 metre = (5 x 1000) + 92 = 5092

2 kilometre 60 metre = (2 x 1000) + 60 = 2060

1.3 km = 1.3 x 1000 = 1300

7 0

3 years ago