The distance that Sarah travels varies directly to how long she drives. She travels 440 miles in 8 hours. Write the equation that relates the distance, d, to the time, t.
How many miles can Sarah travel in 6 hours

Answers

Answer 1

Answer:

The equation relating distance, d, to time, t, is given by d = 55t, where 55 is the constant of variation. Sarah can travel 330 miles in 6 hours by substituting t = 6 into the equation d = 55t.

The equation that relates the distance, d, to the time, t, when they vary directly is:

d = k * t

where k represents the constant of variation.

To find the value of k, we can use the given information. Sarah travels 440 miles in 8 hours. Substituting these values into the equation:

440 = k * 8

Dividing both sides by 8:

k = 440 / 8

k = 55

Therefore, the equation that relates the distance, d, to the time, t, is:

d = 55t

To find how many miles Sarah can travel in 6 hours, we substitute t = 6 into the equation:

d = 55 * 6

d = 330

Therefore, Sarah can travel 330 miles in 6 hours.

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Answer 2

Answer:

Answer:

d=55t Sara travels 330 miles

Step-by-step explanation:

We are given that distance, d, Sarah drives varies directly to the time, t. This means

d=k⋅t

for some constant, k. Since Sarah travels 440 miles in 8 hours, we substitute these values into the formula for direct variation to find

440=k⋅8

Dividing by 8 gives k=55, so an equation that relates d and t is

d=55t

Substituting t=6 yields

55(6)=330

So Sarah can travel 330 miles in 6 hours.

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Theodore says there are 2 weeks 5 days left in a year how many days are left in the year

Answers

Answer:19 days because there are 7 days in a week and 7+7=14 and 14+7=19

Step-by-step explanation:

There are 7 days in a week so there is 14 days in 2 weeks.

2 weeks and 5 days is the same as 14 days + 5 days, or C) 19 days

How many 3/8 cup servings are in a pitcher containing 6 3/4 cup of orange juice?

Answers

You can solve this problem in multiple ways, but you'll have to divide the total volume with the amount per servings to find the number of servings (makes sense logically if you think about it).

The first way is to just use the fractions given. This will usually be your method in handling this if you're not familiar with it.

Convert 6 3/4 into an improper fraction. To do this, we need to put the 6 into the numerator somehow. We can approach this by multiplying the whole number (6) with the denominator (4) and adding it to (3). Basically, 6 x 4 + 3 = 27. This will be our new numerator. If you are not familiar with this concept, please let me know.

Our new fraction for the total amount of juice is $(27)/(4)$ . Divide this with the amount per serving, $(3)/(8)$

$(27)/(4) / (3)/(8)$
We flip the second fraction over and multiply it.

$(27)/(4) * (8)/(3) = (9)/(1) * (2)/(1) = 18 servings$ (I crossed out common numbers here, unfortunately I don't know how to do that here so let me know if my explanation was not clear enough. I skipped a few steps.)

18 servings would be your answer.

Or you can convert 6 3/4 into decimal, which would be 6.75. 3/8 in decimal is .375 and you can do long division from there. That way is a bit more tedious in my opinion, but sometimes more convenient.

Cheers!

992×16=? show work please

Answers

      9 9 2
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      1 5,8 7 2    <==

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:

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)

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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:
The slope of the line that passes through the points (5,10) and (2,12) is

Answers

Answer:

m = -2/3; b = 13 1/3

Step-by-step explanation:

ΔX = 2 – 5 = -3

ΔY = 12 – 10 = 2

2/-3 = -2/3

Equation for b:

$10 = -(2)/(3) (5)+b\n10 = -3 (1)/(3) +b\n13 (1)/(3) =b$

Answer:

-2/3

Step-by-step explanation:

To find the slope, you use rise over run. so 12 - 10 over 2 - 5. That is 2 over negative 3. so negative two thirds. I hope this helps and please mark me brainliest!

Write (1/3i)-(-6+2/3i) as a complex number in standard form