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patriot [66]
2 years ago
13

Joey is running an experiment with a mass on a spring. Joey models the height of the mass above the table he is working on using

the equation h(t)=6.85cos(3.42t)+9, where the height is in inches and the time, t, is in seconds since he let the mass free. How many seconds, to the nearest tenth, will it take for the mass to return to its original position?
Mathematics
1 answer:
galben [10]2 years ago
5 0

Answer: 1.8 s

Step-by-step explanation:

Given

The height of the spring mass system above the table is given by

h(t)=6.85\cos (3.42t)+9

The mass is performing S.H.M with frequency \omega =3.42

and \omega T=2\pi

\therefore T=\dfrac{2\pi }{\omega}

time when mass returns to its original position

T=\dfrac{2\pi }{3.42}\\\\T=1.8\ s

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-        -
8       1

Simplify 24 and 8. (8 goes into 24 six times.)

5      6
-       -
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3 years ago
I WILL MARK YOU BRAINLYEST if you answer all of my problems !!!!!!!!!!!
Romashka [77]

First, let's convert each line to slope-intercept form to better see the slopes.

Isolate the y variable for each equation.

2x + 6y = -12

Subtract 2x from both sides.

6y = -12 - 2x

Divide both sides by 6.

y = -2 - 1/3x

Rearrange.

y = -1/3x - 2


Line b:

2y = 3x - 10

Divide both sides by 2.

y = 1.5x - 5


Line c:

3x - 2y = -4

Add 2y to both sides.

3x = -4 + 2y

Add 4 to both sides.

2y = 3x + 4

Divide both sides by 2.

y = 1.5x + 2


Now, let's compare our new equations:

Line a: y = -1/3x - 2

Line b: y = 1.5x - 5

Line c: y = 1.5x + 2

Now, the rule for parallel and perpendicular lines is as follows:

For two lines to be parallel, they must have equal slopes.

For two lines to be perpendicular, one must have the negative reciprocal of the other.

In this case, line b and c are parallel, and they have the same slope, but different y-intercepts.

However, none of the lines are perpendicular, as -1/3x is not the negative reciprocal of 1.5x, or 3/2x.

<h3><u>B and C are parallel, no perpendicular lines.</u></h3>
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5 0
2 years ago
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Answer:

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zimovet [89]

Given the expression (8+3i)+(-2+i)

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(8+3i)+(-2+i)

First we have to remove the parenthesis.

8+3i-2+i

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8-2 +3i+i

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We have got the required answer.

The simplified answer is 6+4i.

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