Find a b if a = 3i + 8j and b = -0.5i -4j.

<span>D=20+50t 120=20+50t 50t=100 t=2 hours The time variable t ranges from t=-(2/5)hr to t=2hr. Given that they have already covered 20 miles. [-2/5,2]</span>

Answer:

Attached is the histogram illustrating the marathon runners’ times.

Step-by-step explanation:

The provided data is as follows;

2.21

2.25

2.76

3.1

3.3

3.5

3.6

3.77

3.8

4.23

4.25

4.25

4.6

4.9

From this data, we can determine;

The count of runners finishing between 0 and 1 hour = 0

The count of runners finishing between 1 and 2 hours = 0

The count of runners finishing between 2 and 3 hours = 3

The count of runners finishing between 3 and 4 hours = 6

The count of runners finishing between 4 and 5 hours = 5

Based on these frequencies across the various time ranges, the histogram for the provided data has been constructed and is attached.

The outcome is $7.54 for each book.

By adding 1137.5 and 1500, you obtain 2637.5.
Then, dividing 2637.5 by 350 gives 7.54.

Verifying the result
350 multiplied by 7.54 equals $2639.

Subtracting $1137.5 from $2639 results in $1501.5 (profit).

We can formulate the trajectory of the parabola using the vertex form equation: y = a (x – h)^2 + k. The coordinates for the vertex are at h and k, representing the peak height, thus h = 250 and k = 120. Consequently, the equation becomes y = a (x – 250)^2 + 120. At the starting point where x = 0 and y = 0, we find a: 0 = a (0 – 250)^2 + 120, which simplifies to 0 = a (62,500) + 120, leading to a = -0.00192. The complete equation is y = -0.00192 (x – 250)^2 + 120. To determine y when x = 400, we substitute: y = -0.00192 (400 - 250)^2 + 120, yielding y = 76.8 ft. Hence, the ball clears the tree by 76.8 ft – 60 ft = 16.8 ft.

Response:

The loop's length is roughly 49.58 km.

Step-by-step details:

Given:

Duration to cycle the loop = 2 hours and 30 minutes

It is known that;

60 minutes = 1 hour

30 minutes = 0.5 hour

therefore, 2 hours and 30 minutes =

∴ Time to cycle the loop = 2.5 hours

Let 's' denote the cycling speed.

Denote the total loop distance as 'd'

From our understanding;

Distance equals speed times time.

Representing this as an equation we have;

Given:

If her speed increased by 1 km/hr, the time taken around the loop would decrease by 7 minutes.

As a result, we can say;

Speed =

The time then will be shortened by 7 minutes.

7 minutes = 0.12 hours

Consequently, time = 2.5 - 0.12 = 2.38

Again, Distance is calculated as speed times time.

This can be expressed with equations;

The distances are equivalent in both scenarios, thus we will determine speed by equating the equations.

So, Speed = 19.83 km/hr

Loop length (d) =

Therefore, the loop length is approximately 49.58 km.