The paths of two runners cross at a stop sign. One runner is heading south at a constant rate of 6.5 miles per hour while the other runner is heading west at a constant rate of 7 miles per hour. How fast is the distance between them changing after 10 minutes?

Answers

Answer 1

Answer:

Answer:

The distance between them changing after 10 minutes will be 9.553 mph.

Step-by-step explanation:

The paths of two runners cross at a stop sign (O). One runner is heading south at a constant rate of 6.5 miles per hour towards A while the other runner is heading west at a constant rate of 7 miles per hour towards B.

So, after 10 minutes the first runner covers a distance of $6.5 * (10)/(60) = 1.083$ miles and the second runner covers a distance of $7 * (10)/(60) = 1.167$ miles.

Therefore, after 10 minutes their distance will be $\sqrt{(1.083)^(2) + (1.167)^(2)} = 1.592$ miles.

Now, the distance between them is given by

AB² = OA² + OB²

Now, differentiating this equation with respect to time t (in hours) we get

$2(AB) (d(AB))/(dt) = 2(OA) (d(OA))/(dt) + 2(OB) (d(OB))/(dt)$

⇒ $(AB) (d(AB))/(dt) = (OA) (d(OA))/(dt) + (OB) (d(OB))/(dt)$

⇒ $1.592 * (d(AB))/(dt) = 1.083 * 6.5 + 1.167 * 7 = 15.208$

⇒ $(d(AB))/(dt) = 9.553$ mph.

Therefore, the distance between them changing after 10 minutes will be 9.553 mph. (Answer)

Answer 2

Answer:

Final answer:

The distance between the two runners is not changing after 10 minutes.

Explanation:

To find the rate of change of the distance between the two runners, we can use the concept of relative velocity. The distance is changing due to the motion of both runners, so we need to find the rate at which each runner is approaching or moving away from the other. Since one runner is heading south and the other is heading west, their velocities are perpendicular to each other. We can use the Pythagorean theorem to find their combined velocity and then calculate the rate of change of the distance between them.

Let's consider the southward runner as Runner A and the westward runner as Runner B. The velocity of A is 6.5 miles per hour, and the velocity of B is 7 miles per hour. After 10 minutes, the distance traveled by A can be calculated as (6.5 miles/hour) * (10/60) hours = 1.083 miles. The distance traveled by B can be calculated as (7 miles/hour) * (10/60) hours = 1.167 miles.

Using the Pythagorean theorem, we can calculate the distance between the two runners after 10 minutes:

Distance = sqrt((1.083 miles)^2 + (1.167 miles)^2) ≈ 1.563 miles

To find the rate of change of the distance between them, we can differentiate the equation for the distance with respect to time:

d(Distance)/dt = (1/2)*((2*(1.083 miles)*(0))/(sqrt((1.083 miles)^2 + (1.167 miles)^2))) + (1/2)*((2*(1.167 miles)*(0))/(sqrt((1.083 miles)^2 + (1.167 miles)^2))) = 0

Therefore, the distance between the two runners is not changing after 10 minutes.

Learn more about Relative velocity here:

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Answers

Answer: 24(?)

Step-by-step explanation:

I think it might be 24 cause line EB is 12 (?) and line AE is equal to line EB but my answer may not be correct please wait till someone else answers before submitting your answer

Put the following events in order from least to most likely. Please help me in this

Answers

Answer:

Colorado Bronze wins

I Am Pat wins

Good Legs Lance wins

Step-by-step explanation:

Put them all as decimals and THEN put them in order. Hope this helps :)

Final answer:

When ordering events from least to most likely, you rank them based on their probabilities which typically range from 0 (impossible event) to 1 (certain event). The event with the smallest value is considered the least likely and the event with the largest value is considered the most likely.

Explanation:

Without specific events provided in your question, I'm unable to put them in order from least to most likely. However, to help you understand how to do this yourself: probabilities of events typically range from 0 (impossible event) to 1 (certain event). Let's use an example. Say we have the following events and their probabilities: A: It will rain tomorrow (0.9), B: A tossed coin will land heads (0.5), C: Drawing a red card from a deck (0.5), and D: Winning the lottery (0.0000001).

You arrange these from least to most likely as follows: D (least likely), B and C (equally likely), and A (most likely).

Learn more about Probability here:

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Write the number in order starting with the smallest 1.06, 1.031,1.306,1.36

Answers

1.031, 1.06, 1.306, 1.36

If it helps, when you have something that only goes to the hundredths place, add a 0 to the end.
for example, 1.63= 1.630

1.031, 1.06, 1.306, 1.36

The face of a clock has a circumference of 63 in. What is the area of the face of the clock?

Answers

Answer:

The area of the clock $= 315.41\ inch^(2)$

Step-by-step explanation:

We have been given the face of the clock that is $63\ in$

So that is also the circumference of the clock.

Since the clock is circular in shape.

So $2\pi(r)=63\ inch$

From here we will calculate the value of radius $(r)$ of the clock that is circular in shape.

Then $2\pi(r)=63\ inch =(63)/(2\pi) = 10.02\ in$

Now to find the area of the clock we will put this value of (r) in the equation of area of the circle.

Now $\pi (r)^(2)=\pi(10.02)^(2)=315.41\ in^(2)$

So the area of the face of the clock = $315.41\ in^(2)$

Answer:

The answer is 316

Step-by-step explanation:

I did a test it is the right answer everyone els is wrong :/

Calculate the average speed of a car stuck in traffic that drives 12 kilometers in 2 hours

Answers

Average speed = (total distance) / (time for the distance)

Average speed= (12 km) / (2 hours) = 6 km per hour

$v_M=(d)/(t)\n \n v_M=(12 \ km)/(2 \ h)=6 \ km/h$

What is the estimate of 74.75

Answers

Well if you are referring to rounding you answer is 74.8 because if it is 5 or more you raise the score one point. If it is 4 or less you let it rest.
hope that helped:)

rounded it would be 75 if your rounding to the full number

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