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4 years ago

Is 3 a rational number

Mathematics

1 answer:

Shkiper50 [21]4 years ago

4 0

3 is a rational number because it can be written in the ratio of 3/1 or 6/2.

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Daniel [21]

equation in slope-intercept form is:

$y=9x+7$

Step-by-step explanation:

The general form of slope-intercept form is:

$y=mx+b$

where m is the slope and b is the y-intercept

In the question we are given slope m=9 and a point(0,7)

We will find b i.e y-intercept

$y=mx+b\\7=9(0)+b\\7=0+b\\b=7$

So, value of b=7 and value of slope m=9

So, equation in slope-intercept form is:

$y=9x+7$

Keywords: slope-intercept form

Learn more about slope-intercept form at:

#learnwithBrainly

8 0

3 years ago

Find the surface area of x^2+y^2+z^2=9 that lies above the cone z= sqrt(x^@+y^2)

Mashcka [7]

The cone equation gives

$z=\sqrt{x^2+y^2}\implies z^2=x^2+y^2$

which means that the intersection of the cone and sphere occurs at

$x^2+y^2+(x^2+y^2)=9\implies x^2+y^2=\dfrac92$

i.e. along the vertical cylinder of radius $\dfrac3{\sqrt2}$ when $z=\dfrac3{\sqrt2}$ .

We can parameterize the spherical cap in spherical coordinates by

$\mathbf r(\theta,\varphi)=\langle3\cos\theta\sin\varphi,3\sin\theta\sin\varphi,3\cos\varphi\right\rangle$

where $0\le\theta\le2\pi$ and $0\le\varphi\le\dfrac\pi4$ , which follows from the fact that the radius of the sphere is 3 and the height at which the sphere and cone intersect is $\dfrac3{\sqrt2}$ . So the angle between the vertical line through the origin and any line through the origin normal to the sphere along the cone's surface is

$\varphi=\cos^{-1}\left(\dfrac{\frac3{\sqrt2}}3\right)=\cos^{-1}\left(\dfrac1{\sqrt2}\right)=\dfrac\pi4$

Now the surface area of the cap is given by the surface integral,

$\displaystyle\iint_{\text{cap}}\mathrm dS=\int_{\theta=0}^{\theta=2\pi}\int_{\varphi=0}^{\varphi=\pi/4}\|\mathbf r_u\times\mathbf r_v\|\,\mathrm dv\,\mathrm du$
$=\displaystyle\int_{u=0}^{u=2\pi}\int_{\varphi=0}^{\varphi=\pi/4}9\sin v\,\mathrm dv\,\mathrm du$
$=-18\pi\cos v\bigg|_{v=0}^{v=\pi/4}$
$=18\pi\left(1-\dfrac1{\sqrt2}\right)$
$=9(2-\sqrt2)\pi$

3 0

3 years ago

HELP HELP HELP OMGOMG

user100 [1]

Answer:

Direct variation

Step-by-step explanation:

It's not iverse because the line is curved so it's direct variation

6 0

3 years ago

Which data set is the most spread from its mean?<br>14. 26 24 28<br>22 16 18 36<br>24 19 27.25

xenn [34]

Answer:

22 16 18 36

Step-by-step explanation:

4 0

4 years ago

Question 95 pts

garri49 [273]

The correct answer is “hasn’t” probably maybe

5 0

3 years ago