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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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John invests $200 at 4.5% compounded annually. About how long will it take for John’s investment to double in value?
Gekata [30.6K]

Answer:

The number of years needed is 15.75 years.

Step-by-step explanation:

The investment amount (present value) = $200

Interest rate =4.5%

Double of investment = $400

Now we have to find the time or number of years in which the investment amount will be doubled. So, just use the below formula to find the number of years.

Future value = present value ×(1+interest rate)^n

400 = 200×(1+4.5%)^n

N = 15.75 years

The number of years required to double the amount is 15.75 years.

8 0
3 years ago
Which quadratic function has one real solution? 0 = 2(x + 7)(x – 5) 0 = (x – 3)(x – 3) 0 = 2.4(x – 2)(x + 2) 0 = (x – 2)(x – 1)
NikAS [45]

0 = (x – 3)(x – 3)

x - 3 = 0

x = 3

Solution is x = 3 (one real solution)

Answer

0 = (x – 3)(x – 3)

6 0
3 years ago
Read 2 more answers
On a coordinate plane, a circle has a center at (0, 0). Point (3, 0) lies on the circle.
9966 [12]

Answer:

The correct option is;

No, the distance from (0, 0) to (2, √6) is not 3 units

Step-by-step explanation:

The given parameters of the question are as follows;

Circle center (h, k) = (0, 0)

Point on the circle (x, y) = (3, 0)

We are required to verify whether point (2, √6) lie on the circle

We note that the radius of the circle is given by the equation of the circle as follows;

Distance \, formula = \sqrt{\left (x_{2}-x_{1}  \right )^{2} + \left (y_{2}-y_{1}  \right )^{2}}

Distance² = (x - h)² + (y - k)² = r² which gives;

(3 - 0)² + (0 - 0)² = 3²

Hence r² = 3² and r = 3 units

We check the distance of the point (2, √6) from the center of the circle (0, 0) as follows;

\sqrt{\left (x_{2}-x_{1}  \right )^{2} + \left (y_{2}-y_{1}  \right )^{2}} = Distance

Therefore;

(2 - 0)² + (√6 - 0)² = 2² + √6² = 4 + 6 = 10 = √10²

\sqrt{\left (2-0 \right )^{2} + \left (\sqrt{6} -0 \right )^{2}} = 10

Which gives the distance of the point (2, √6) from the center of the circle (0, 0) = √10

Hence the distance from the circle center (0, 0) to (2, √6) is not √10 which s more than 3 units hence the point  (2, √6), does not lie on the circle.

4 0
3 years ago
Read 2 more answers
HELPPP WILL MARK BRAINLIEST
leva [86]

Answer:

Step-by-step explanation:

y - z+6

7 0
3 years ago
Read 2 more answers
Calculate the angle of depression, x, if the boat is 850 ft. away from the lighthouse and the lighthouse is 250 ft. high. Round
trapecia [35]

Firstly , we can draw diagram

we can see that

adjacent = 850

opposite =250

so, we can use tan formula

tan(x)=\frac{250}{850}

x=tan^{-1}(\frac{250}{850})

16.38

x=16.38

so,

angle of depression is 16.38 degree........Answer

6 0
3 years ago
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