Jada dives off a cliff into the ocean. The vertical path of her dive, in feet, is modeled by the function f(x) = - 0.1 * (x - 3) ^ 2 + 10 , where x is the horizontal distance and f(x) is the vertical distance. To capture her experience, Jada asks a friend to record her on a video camera. The camera's view is modeled by the function g(x) = 0.67x + 3 where x is the horizontal distance, in feet, and g(x) is the vertical distance, in feet, that the camera can captureGraph the equations to determine whether the camera will be able to capture Jada's jump before she hits the waterIf so, how far above the surface of the water, to the nearest integer, will the camera capture her jump? (1 point) The camera will not capture her jump feet feet feet

Question

Jada dives off a cliff into the ocean. The vertical path of her dive, in feet, is modeled by the function f(x) = - 0.1 * (x - 3) ^ 2 + 10 , where x is the horizontal distance and f(x) is the vertical distance. To capture her experience, Jada asks a friend to record her on a video camera. The camera's view is modeled by the function g(x) = 0.67x + 3 where x is the horizontal distance, in feet, and g(x) is the vertical distance, in feet, that the camera can captureGraph the equations to determine whether the camera will be able to capture Jada's jump before she hits the waterIf so, how far above the surface of the water, to the nearest integer, will the camera capture her jump? (1 point) The camera will not capture her jump feet feet feet

Answer 1

To determine whether the camera will be able to capture Jada's jump before she hits the water, we need to find the point where the two functions intersect.

Setting f(x) = g(x), we have:

-0.1 * (x - 3)^2 + 10 = 0.67x + 3

Simplifying, we get:

-0.1x^2 + 0.6x - 0.1 = 0.67x + 3
-0.1x^2 - 0.07x - 3.1 = 0

Using the quadratic formula to solve for x, we get:

x ≈ 9.57 or x ≈ -27.43

Since we're only interested in the positive value, Jada will be captured by the camera at approximately 9.57 feet above the water's surface. Rounded to the nearest integer, the camera will capture her jump at a height of 10 feet above the water.