An airplane started at point X, traveled 320 miles to point Y, adjusted its route, and traveled another 400 miles to point Z. If the airplane is currently 599 miles from its starting position at point X, by how many degrees did it adjust its route at point Y?

67.88°

Step-by-step explanation:

If three sides of a triangle are known and you want to determine one angle, this can be done using cosine rule.

Given sides x, y, and z and the angle Y is opposite to side y, the cosine formula is given as:

y² = x² + z² - 2xzcosY

For this problem, x = 400 miles, y = 599 miles, z = 320 miles.

Using the cosine formula:

Degree to adjust its route at point Y = 180° - 112.12° = 67.88°

It needs to adjust by 67.88° at point Y

the required function is .

step-by-step explanation:

from the given table it is noticed that the graph passing through (-3,7), (0,4), (3,1) and (8,-4).

it is a linear function because the value of y is decrease by one as the value of x increase by 1.

the slope of the function is

the slope of the function is -1 and the y-intercept is 4.

the slope intercept form is

where, m is slope and b is y-intercept.

therefore the required function is . the graph of this function is shown below.

answer is x<