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adell [148]
3 years ago
15

A tortoise and a hare are competing in a 2000-meter race. The arrogant hare decides to let the tortoise have a 510-meter head st

art. When the start gun is fired the hare begins running at a constant speed of 8 meters per second and the tortoise begins crawling at a constant speed of 5 meters per second. Define a function f to represent the tortoise's distance from the finish line (in meters) in terms of the number of seconds t since the start of the race.
Mathematics
1 answer:
Nataliya [291]3 years ago
8 0

The distance covered by the hare and the tortoise in t seconds are 8t and 5t respectively. (Simple Speed-Distance-Time relation)

The tortoise gets a 510m headstart so at t=0 is 1490m.

The functions representing the distance of both of them from the finish line is,

F(x)=2000-8t,. for hare

G(x)=1490-5t,. for tortoise

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Answer: Option C.

Step-by-step explanation:

We have functions of r(θ)

In our graph, we can see that the minimum value of r is when θ = 0°, and the maximum value is when θ = 180°.

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Then let's analyze the options:

A) r = 3 - 2*cos(θ)

the maximum is at the right angle, but the maximum is:

r = 3 -2*(-1) = 5, so this maximum value is bigger than the one in the graph.

B) r = 3 - sin(θ)

For the sin functions, the maximum and minimum do not correspond with the values i write earlier, so we can discard this option.

C) r = 3 - cos(θ)

The maximum is: r = 3 - (-1) = 4, so this may be the correct answer.

the minimum is r = 3 - 1 = 2,

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D) r = 2 - 2*cos(θ)

Here, when θ = 0, we have: r = 2 - 2*1 = 0, but in the graph we can see that the radius is not 0 when θ = 0, so we can discard this option.

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3 years ago
Which of the following conditions must be met in order to make a statistical inference about a population based on a sample
klasskru [66]

Answer:

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For this case the condition required in order to consider a sample size large is that n>30, then the best solution would be:

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Step-by-step explanation:

For this case if we want to conclude that  the sample does not come from a normally distributed population we need to satisfy the condition that the sample size would be large enough in order to use the central limit theoream and approximate the sample mean with the following distribution:

\bar X \sim (\mu, \frac{\sigma}{\sqrt{n}})

For this case the condition required in order to consider a sample size large is that n>30, then the best solution would be:

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Step-by-step explanation:

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Answer:

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Step-by-step explanation:

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