Question

You are shot out of a cannon at the fair. The equation y=-1/5(x+2) (x-28) models your flight path, where y is the height above the ground and x is the horizontal distance. Which of the following statements in the comments are true?

a) You reach a maximum height of 45 feet
b) You will land 11.2 feet from the cannon
c) The barrel of the cannon is about 11 feet above the ground.
d)At a point 13 feet from the cannon, you begin to descend.

Answer 1

The maximum height reached is 45 feet.

Step-by-step explanation:

The equation y=-1/5(x+2) (x-28) models your flight path, where y is the height above the ground and x is the horizontal distance. To find the maximum height, we can use the formula for the vertex of a parabola, which is given by (h, k), where h is the x-coordinate and k is the y-coordinate of the vertex. In this case, the maximum height is the y-coordinate of the vertex.

So, to find the maximum height, we need to find the vertex of the parabola represented by the equation y=-1/5(x+2) (x-28). The x-coordinate of the vertex can be found using the formula x = -b/2a, where a, b, and c are the coefficients of the quadratic equation. In this case, a = -1/5, b = 1/5(2-28) = 1/5(-26) = -26/5.

Plugging in these values, we get x = -(-26/5)/(2*(-1/5)) = 13. So, the maximum height is the y-coordinate of the vertex when x = 13. Evaluating the equation at x = 13, we get y = -1/5(13+2)(13-28) = -1/5(15)(-15) = 45.

Therefore, statement (a) is true.

Answer 2

Q: You are shot out of a cannon at the fair. The equation y=-1/5 * (x+2) (x-28) models your flight path, where y is the height above the ground and x is the horizontal distance. Which of the following statements in the comments are true?

a) You reach a maximum height of 45 feet,

b) You will land 11.2 feet from the cannon,

c) The barrel of the cannon is about 11 feet above the ground.

d)At a point 13 feet from the cannon, you begin to descend.

A: When y = 0, x = 28

y’ = 0 at x = 13 where Y is max = 15^2 / 5 = 45

Hence a is true, b is false, c is false, d is false .