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Rudiy27
3 years ago
6

Find the slope of the line that goes through (1, 3) and (-2,-6).

Mathematics
1 answer:
monitta3 years ago
3 0

Answer:

m= -3

Step-by-step explanation:

slope intercept formula

(y2-y1)/ (x2-x1)

-6-3= -9

-2-1=-3

-9/3 =-3

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The equation of a line is -6x - 2y = -18. What is the x-intercept & y-intercept of the line?
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Step-by-step explanation:

In slope intercept form, the equation is y=-3x+9. In the formula y=mx+b, we know b is the y intercept, so our y int. is 9. To find our x intercept, we set y=0. So, 0=-3x+9=>3x=9=>x=3

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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,

  1. Time period (T) = 2s
  2. A=8
  3. 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>

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D.) is the right answer
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