a sailboat with a sick passenger aboard is following a parabolic path given by the equation y=-2x+8. the boat’s captain sent out a distress signal. a speedboat is trying to catch the sailboat to provide medical aid and is on a path given by the linear equation y=x^2-6x+8. do the paths of the two boats cross?

solve in graphically and

answer

Explanation:

1. Graphical solution

First, understand that the descriptions of the two equations are exchanged, i.e. the linear equation is y = - 2x + 8 and the quadratic equation is y = x² - 6x + 8, but that does not change the solution.

The graphical method consist in drawing the two equations in the same coordinate plane and the intersection of the curves are the solutions to the system of equations.

a) Graph of the linear equation, y = - 2x + 8

A line may be easily drawn using two points. You can choose the intercepts. You do it in this way:

b) Graph of the quadratic equation,  y = x² - 6x + 8

        x² - 6x + 8 = 0

        (x - a) (x - b) = 0, where - a - b = - 6 and (- a) × (- b) = 8

        (x - 4) (x - 2) = 0 ⇒ x = 4 and x = 2.

        ⇒ points (2, 0) and (4, 0)

        (2 + 4) / 2 = 3 ⇒ x = 3 is the axis of symetry.

        y = 3² - 6(3) + 8 = 9 - 18 + 8 = - 1 ⇒ vertex ( 3, -1).

Now you have plenty information to sketch the curve.

The graph of the two curves is in the diagram attached. It was drawn witha graphical tool but you can do it in a sheet of paper using the features of the curves found.

The intersection points on the graph are (0,8) and (4,0), meaning tha the solutions to the paths of the two boats cross at those coordinates.

2. Algebraic solution.

a) equal the two equations:

b) Solve:

Meaning that the two paths cross at x = 0 and x = 4.

Thus, you can find the y-coordinates substituting those x-coordinates in either equation of the paths. I will use y = -2x +8

Thus, the paths of the two boats cross at (0,8) and (4,0), such as we found with the graphical method.

the solution is h=10 because you add 9 to each side of the equation.

3x + 18 = 147°

step-by-step explanation:

3x + 18 = 147°, because the value of the central angle is equal to the value of the arc formed by it.

i hope i you.