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3 years ago

Determine the equation of the graph

Mathematics

1 answer:

laila [671]3 years ago

4 0

There is no graph here

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What's the slope of -4,6 and 3,-8

notsponge [240]

Answer:

The slope is -2

Step-by-step explanation:

(-4,6) (3,-8)

(y₂ - y₁) / (x₂ - x₁)

((-8) - (6)) / ((3) - (-4))

(-8 - 6) / (3 + 4)

-14/7 = -2

4 0

3 years ago

A Ferris wheel has a radius of 10 m, and the bottom of the wheel passes 1 m above the ground. If the Ferris wheel makes one comp

Volgvan

Answer: $1+10(1-\cos (\frac{\pi t}{9}))$

Step-by-step explanation:

Given

radius of wheel $r=10 m$

Time period of Wheel $T=18 s$

and $T\cdot \omega =2\pi$ , where $\omega =angular velocity of wheel$

$\omega =\frac{2\pi }{18}$

Let at any angle $\theta$ with vertical position of a point is given by

$x=r\sin \theta$

$y=y_0+r(1-\cos \theta )$

and $\theta =\omega \times t$

for velocity differentiate x and y to get

$v_x=r\cos \theta =r\cos (\omega t)$

$v_y=0+r(\sin \theta )=r\sin (\omeag t)$

Height at any time t is given by

$h=1+10(1-\cos \theta )=1+10(1-\cos (\frac{\pi t}{9}))$

7 0

3 years ago

4sin²<img src="https://tex.z-dn.net/?f=%5Cfrac%7Bx%7D%7B2%7D" id="TexFormula1" title="\frac{x}{2}" alt="\frac{x}{2}" align="absm

raketka [301]

Answer:

$\displaystyle x=\left \{\frac{2\pi}{3}+2\pi k,\frac{4\pi}{3}+2\pi k, \frac{8\pi}{3}+2\pi k, \frac{10\pi}{3}+2\pi k\right \}k\in \mathbb{Z}$

Step-by-step explanation:

Hi there!

We want to solve for $x$ in:

$4\sin^2(\frac{x}{2})=3$

Since $x$ is in the argument of $\sin^2$ , let's first isolate $\sin^2$ by dividing both sides by 4:

$\displaystyle \sin^2\left(\frac{x}{2}\right)=\frac{3}{4}$

Next, recall that $\sin^2x$ is just shorthand notation for $(\sin x)^2$ . Therefore, take the square root of both sides:

$\displaystyle \sqrt{\sin^2\left(\frac{x}{2}\right)}=\sqrt{\frac{3}{4}},\\\sin\left(\frac{x}{2}\right)=\pm \sqrt{\frac{3}{4}}$

Simplify using $\displaystyle \sqrt{\frac{a}{b}}=\frac{\sqrt{a}}{\sqrt{b}}$ :

$\displaystyle \sin\left(\frac{x}{2}\right)=\pm \sqrt{\frac{3}{4}},\\\sin\left(\frac{x}{2}\right)=\pm \frac{\sqrt{3}}{\sqrt{4}}=\pm \frac{\sqrt{3}}{2}$

Let $\phi = \frac{x}{2}$ .

<h3><u>Case 1 (positive root):</u></h3>

$\displaystyle \sin(\phi)=\frac{\sqrt{3}}{2},\\\phi = \frac{\pi}{3}+2\pi k, k\in \mathbb{Z}, \\\\\phi =\frac{2\pi}{3}+2\pi k, k\in \mathbb{Z}$

Therefore, we have:

$\displaystyle \frac{x}{2}=\phi = \frac{\pi}{3}+2\pi k, k\in \mathbb{Z}, \\\\\frac{x}{2}=\phi =\frac{2\pi}{3}+2\pi k, k\in \mathbb{Z},\\\\\begin{cases}x=\boxed{\frac{2\pi}{3}+2\pi k, k\in \mathbb{Z}},\\x=\boxed{\frac{4\pi}{3}+2\pi k , k \in \mathbb{Z}}\end{cases}$

<h3><u>Case 2 (negative root):</u></h3>

$\displaystyle \sin(\phi)=-\frac{\sqrt{3}}{2},\\\phi = \frac{4\pi}{3}+2\pi k, k\in \mathbb{Z}, \\\\\phi =\frac{5\pi}{3}+2\pi k, k\in \mathbb{Z},\\\begin{cases}x=\boxed{\frac{8\pi}{3}+2\pi k, k\in \mathbb{Z}},\\x=\boxed{\frac{10\pi}{3}+2\pi k , k \in \mathbb{Z}}\end{cases}$

8 0

2 years ago

Please help with this!!!

RSB [31]

Answer:

Step-by-step explanation:

So to graph an inverse of the function given we have to switch the x and y values of the function:

So Ill do some points and the rest of the points the same process is applicable.

So our first point is (-1,1)

So our inverse point would be (1,-1)

The second point is (-2,2)

So our inverse point would be (2,-2)

The third point is (-3,3)

So our inverse point would be (3,-3)

Hope this helps!

5 0

3 years ago

What is the sum of the exterior angles of a 54-gon?

oksian1 [2.3K]

Answer: The sum of the exterior angles of a 54-gon should be 360°.

Step-by-step explanation:

A polygon is a closed figure made up of straight lines like triangle (3-gon) , quadrilateral (4-gon) , square(4-gon), pentagon (5-gon) , octagon(8-gon) etc.

The sum of exterior angles of any polygon with n sides ( or n-gon ) is always 360 degrees.

A 54-gon is a polygon with 54 sides.

Therefore , the sum of the exterior angles of a 54-gon should be 360°.

5 0

3 years ago