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tester [92]
2 years ago
7

A strobe light is located at the center of a square dance room. the rotating light is 40 feet from each of the square walls and

complete 1 full rotation every 6 sec.
a) write an equation, representing the distance, d, in feet that the center of the circle of light, is a light source at t time.
Mathematics
1 answer:
Effectus [21]2 years ago
5 0

The equation of the rotating light is an illustration of a secant function

The equation that represents the distance between the center of the circle and the light source is d(t) = 40\sec(\frac{\pi}{3}t)

<h3>How to determine the equation</h3>

The equation is a secant function represented by

y =A\sec(Bt)

Where:

A represents the amplitude

So, we have:

A = 40 --- the distance of the light from each square wall

B represents the period, and it is calculated as:

B = \frac{2\pi}{T}

The light completes its full rotation every 6 seconds.

This means that,

T = 6

So, we have:

B = \frac{2\pi}{6}

Simplify

B = \frac{\pi}{3}

Substitute values for A and B in y =A\sec(Bt)

y = 40\sec(\frac{\pi}{3}t)

Rewrite as a function

d(t) = 40\sec(\frac{\pi}{3}t)

Hence, the equation that represents the distance between the center of the circle and the light source is d(t) = 40\sec(\frac{\pi}{3}t)

Read more about trigonometry functions at:

brainly.com/question/1143565

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Answer:

B

Step-by-step explanation:

To find the y-intercept, plug in x=0 in the original equation. (You want to find what y is when x=0)

2x + 3y = -12

2(0) + 3y = -12 (Plug in x=0)

3y = -12 (2*0=0, so you can ignore that part)

y = -4 (Divide both sides by 3)

This narrows down our choices to either A or B.


To find the x-intercept, plug in y=0 into the original equation. (You want to find what x is when y=0)

2x + 3y = -12

2x + 3(0) = -12 (Plug in y=0)

2x = -12 (3*0=0, so you can ignore that part)

x = -6 (Divide both sides by 2)


If our x intercept is -6 and our y intercept is -4, that makes our answer B.

4 0
3 years ago
A blimp provides aerial television views of a tennis game. The television camera sights the stadium at a 17degrees angle of depr
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Answer:

1379.31meters  is the​ line-of-sight distance from the television camera to the base of the stadium​ .

Step-by-step explanation:

As given

A blimp provides aerial television views of a tennis game.

The television camera sights the stadium at a 17degrees angle of depression. The altitude of the blimp is 400m.

Now by using the trignometric identity .

sin\theta = \frac{Perpendicular}{Hypotenuse}

As the figure is given below .

Perpendicular = AC = 400 m

Hypotenuse = AB

\theta = 17^{\circ}

Putting all the values in the identity .

sin17^{\circ} = \frac{400}{AB}

0.29\ (Approx)= \frac{400}{AB}

AB= \frac{400}{0.29}

AB = 1379.31 meters

Therefore the 1379.31 meters  is the​ line-of-sight distance from the television camera to the base of the stadium​ .

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Answer:

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Step-by-step explanation:

Slope is:

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Since there is no change of the y value, there is no slope.

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3 years ago
A golfer attempts to hit a golf ball over a valley from a platform above the groun
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Answer: NO

Step-by-step explanation:

The functions that models the height of the ball is given as

h(t) = -5t2 + 40t + 100

Where

a = -5, b = 40, c = 100

The time the ball will reach the maximum height will be the vertex of the parabola. At the line of symmetry, the time t will be:

t = -b/2a

Substitute b and a into the formula above.

t = - 40 / -5 = 8

Substitute 8 for t in the function f(t)

h(t) = - 5(8)^2 + 40(8) + 100

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Open the bracket

h(t) = -320 + 320 + 100

h(t) = 100

The maximum height of the ball is 100m

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3 years ago
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1-7
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Hope this helps!
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