On a certain day, the temperature changed at a rate of 3°F per hour. How long did it take for the change in temperature to be -3

Answer:

1) The calculated average rate of change is 6.

2) The average rate of change across an interval is computed by taking the ratio of the total variation in the dependent variable or function values to the changes in the independent variable or input function values.

Step-by-step explanation:

1) The average change in the function can be determined as follows;

At x = 0.75, y = -0.5, at x = 1.125, y = 1.75

Thus, the average rate of change = (1.75 - (-0.5))/(1.125 - 0.75) = 6.

2) To find the average rate of change for a segment on a graph or curve, one divides the difference in the y-values of the selected points by the difference in their x-values.

*Refer to the image attached below

Answer:

346.4 ft

Step-by-step Explanation:

The distance between the boats, CD = BD - BC

Using trigonometry, find the length of BD in triangle ∆ABD and also calculate the length of BC in triangle ABC.

Length of BD in triangle ABD:

Opposite side to <30° = 300 ft

Adjacent side = BD

Divide both sides by tan(30)

(rounded to nearest tenth)

Length of BC in triangle ABC:

Opposite side to <60° = 300 ft

Adjacent side = BC

Divide both sides by tan(60)

(rounded to nearest tenth)

The distance, CD, between the boats is calculated as BD - BC

= 519.6 - 173.2 = 346.4 ft

The y-intercept is the location where any graph meets the y-axis.

Conversely, the x-intercept is where a graph intersects the x-axis.

This indicates that the coordinates at the intercept will always have the x-value as 0. Therefore, points of the format (0, y) represent y-intercepts, while points in the format (x, 0) indicate x-intercepts.

The provided points are:

(0,-6): y-intercept

(-2,0): x-intercept

(-6,0): x-intercept

(0,-2): y-intercept