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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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Jakes truck can tow a max weight of 5,000 pounds. What is the max number of horses he can take in his trailer at one time withou
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Answer:

He can take 5 Horses at max in his trailer at one time without going over the max weight his truck can tow. (Assuming the average weight of one horse to be equal to 1000 pounds)

Step-by-step explanation:

The no. of horses that can be carried by the truck can be found by simply dividing the maximum weight, that the truck can tow by the weight of a horse.

Max. No of Horses = (Max weight truck can tow)/(Average weight of one    horse)

The weight of a horse is not given in the question .Thus, we assume the average weight of one horse, to be equal to 1000 pounds, we get:

Max. No of Horses = 5000 pounds/ 1000 pounds

<u>Max. No of Horses = 5</u>

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3 years ago
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Answer:

<2 and <8

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Step-by-step explanation:

The Alternate Interior Angles Theorem states that, when two parallel lines are cut by a transversal , the resulting alternate interior angles are congruent .

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Similar polygons have corresponding sides that are proportional and corresponding angles that are -
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company with a large fleet of cars hopes to keep gasoline costs down and sets a goal of attaining a fleet average of at least 26
podryga [215]

Answer:

t=\frac{25.02-26}{\frac{4.83}{\sqrt{50}}}=-1.435    

p_v =P(t_{(49)}  

If we compare the p value and the significance level assumed \alpha=0.05 we see that p_v>\alpha so we can conclude that we have enough evidence to fail reject the null hypothesis, so we can't conclude that the height of men actually its significant lower than 26 so then the specification is satisfied.

Step-by-step explanation:

Data given and notation  

\bar X=25.02 represent the sample mean

s=4.83 represent the sample standard deviation

n=50 sample size  

\mu_o =26 represent the value that we want to test

\alpha represent the significance level for the hypothesis test.  

t would represent the statistic (variable of interest)  

p_v represent the p value for the test (variable of interest)  

State the null and alternative hypotheses.  

We need to conduct a hypothesis in order to check if the mean is at least 26 mpg, the system of hypothesis would be:  

Null hypothesis:\mu \geq 26  

Alternative hypothesis:\mu < 26  

If we analyze the size for the sample is > 30 but we don't know the population deviation so is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:  

t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}  (1)  

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".  

Calculate the statistic

We can replace in formula (1) the info given like this:  

t=\frac{25.02-26}{\frac{4.83}{\sqrt{50}}}=-1.435    

P-value

The first step is calculate the degrees of freedom, on this case:  

df=n-1=50-1=49  

Since is a one sided test the p value would be:  

p_v =P(t_{(49)}  

Conclusion  

If we compare the p value and the significance level assumed \alpha=0.05 we see that p_v>\alpha so we can conclude that we have enough evidence to fail reject the null hypothesis, so we can't conclude that the height of men actually its significant lower than 26 so then the specification is satisfied.

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ollegr [7]

Answer:

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