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3 years ago

6

Real numbers are always rational numbers

1 answer:

DiKsa [7]3 years ago

8 0

Yes, real numbers are always rational numbers

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Drag the numbers to order them from greatest to least, with the greatest at the top. 5.03709 4.923935 17 12

Bond [772]

I think 4.923935; 5,03709; 12; 17

7 0

3 years ago

Find an equation in slope-intercept form of the line that has slope 9 and passes through point A(-9, -1).

Step2247 [10]

Answer:

y = 9x+80

Step-by-step explanation:

We can use the slope intercept form of a line

y = mx+b where m is the slope and b is the y intercept

y = 9x+b

Substitute the point in for x and y

-1 = 9(-9) +b

-1 = -81 +b

Add 81 to each side

-1+81 = b

80 =b

The equation is y = 9x+80

3 0

3 years ago

A buoy floating in the sea is bobbing in simple harmonic motion with period 2 seconds and amplitude 8 in. Its displacement d fro

Mrac [35]

Answer:

The equation of the displacement $d$ as a function of time $t$ is :

$d(t)=8sin(\pi t+\pi )$

Step-by-step explanation:

Generally , A simple harmonic wave is a sinusoidal function that is it can be expressed in simple $sin$ or $cos$ terms.

Thus,

$d(t) = Asin(wt+c)$

is the general form of displacement of a SHM.

where,

<em> $d(t)$ is the displacement with respect to the mean position at any time $t$ </em>
<em> $A$ is amplitude </em>
<em> $w$ is the natural frequency of oscillation ( $rads^{-1}$ )</em>
<em> $c$ is the phase angle which indicates the initial position of the object in SHM ( $rad$ )</em>

given,

Time period ( $T$ ) = $2s$
$A=8$
The natural frequency ( $w$ ) and time period ( $T$ ) is :

$w=\frac{2\pi} {T}$

∴

$w$ = $\frac{2\pi }{2} = \pi$ $rads^{-1}$

∴

the equation :

<em>⇒ $d(t)=8sin(\pi t+c)$ </em> ------1

since $d=0$ when $t=o$ ,

<em>⇒ $0=8sinc\\c=n\pi$ ------2</em>

where n is an integer ;

<u>⇒since the bouy immediately moves in the negative direction , $x$ must be negative or c must be an odd multiple of $\pi$ .</u>

<em>⇒ $d(t) = 8sin(\pi t+(2k+1)\pi )$ ------3</em>

where k is also an integer ;

the least value of $k=0$ ;

thus ,

the equation is :

$d(t)=8sin(\pi t+\pi )$

<em></em>

7 0

3 years ago

Explain how you can use a number line to show that 5/8isgreater than 3/8

Rina8888 [55]

Here is what I did....

8 0

4 years ago

The Vertex of a parabola is at (8-1), and it's why intercept is negative 17, which function represents the parabola

suter [353]

Answer:

The function is equal to $y=-(1/4)(x-8)^{2}-1$

Step-by-step explanation:

we know that

The equation of a vertical parabola in vertex form is equal to

$y=a(x-h)^{2}+k$

where

a is a coefficient

(h,k) is the vertex

In this problem we have

(h,k)=(8,-1)

substitute

$y=a(x-8)^{2}-1$

<u><em>Find the value of a</em></u>

Remember that we have the y-intercept

The y-intercept is the point (0,-17)

substitute

x=0,y=-17

$-17=a(0-8)^{2}-1$

$-17=64a-1$

$64a=-17+1$

$64a=-16$

$a=-16/64$

$a=-1/4$

therefore

The function is equal to

$y=-(1/4)(x-8)^{2}-1$

see the attached figure to better understand the problem

4 0

4 years ago