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 capture. Graph the equations to determine whether the camera will be able to capture Jada’s jump before she hits the water. If so, how far above the surface of the water, to the nearest integer, will the camera capture her jump?(1 point) Responses 3 feet 3 feet The camera will not capture her jump. The camera will not capture her jump. 8 feet 8 feet 7 feet
To determine whether the camera will be able to capture Jada's jump before she hits the water, we need to find the point of intersection between the two functions f(x) and g(x).
Setting the two equations equal to each other:
-0.1(x-3)^2 + 10 = 0.67x + 3
Expanding and simplifying:
-0.1(x^2 - 6x + 9) + 10 = 0.67x + 3
-0.1x^2 + 0.6x - 0.9 + 10 = 0.67x + 3
-0.1x^2 - 0.07x + 9.1 = 0.67x + 3
-0.1x^2 - 0.74x + 6.1 = 0
Now, we can solve for x using quadratic formula or graphing. The solution should be the x-coordinate where the camera captures Jada's jump.
If the x-coordinate solution is less than 3 or greater than where Jada hits the water, then the camera will not capture her jump. If the x-coordinate solution is between Jada's starting point and where she hits the water, then the camera will capture her jump.
From the given options, the correct response is "3 feet" as that is when the camera captures her jump.