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?

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 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?

A. the camera will not capture her jump
B. 3 feet
C. 7 feet
D. 8 feet

Answer 1

Neither is correct. The answer was 8 feet.

Answer 2

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

Setting f(x) equal to g(x) gives:

-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

This is a quadratic equation that can be solved using the quadratic formula. The solutions are x ≈ 3.476 and x ≈ 6.524.

Since Jada dives into the water before 6.524 feet horizontally, the camera will not be able to capture her jump. The answer is:

A. the camera will not capture her jump.

Answer 3

is this right

Answer 4

I apologize for the error in my previous response.

To find out at what point the camera will capture Jada's jump, we need to equate the two functions f(x) and g(x) and solve for x:

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

Expanding both sides:

-0.1(x^2 - 6x + 9) + 10 = 0.67x + 3
-0.1x^2 + 0.6x - 0.9 + 10 = 0.67x + 3
-0.1x^2 + 0.6x + 9.1 = 0.67x + 3

Combining like terms:

-0.1x^2 - 0.07x + 6.1 = 0

Now we need to solve for x by setting the equation equal to zero and solving for x. This can be done using the quadratic formula:

x = (0.07 ± √(0.07^2 - 4 * (-0.1) * 6.1)) / (2 * (-0.1))

x = (0.07 ± √(0.0049 + 2.44)) / -0.2
x = (0.07 ± √2.4449) / -0.2
x ≈ -16.7 or x ≈ 23.4

Since the camera function is g(x) = 0.67x + 3, Jada will be captured by the camera at x ≈ 23.4 feet horizontally.

Therefore, to the nearest integer, the camera will capture Jada when she is approximately 23 feet above the surface of the water. So, the correct answer is:

D. 23 feet

Answer 5

which is right

Answer 6

I made a mistake in my previous response. I apologize for the confusion.

Let's revisit the solution:

We previously found that the point of intersection between the two functions is:

x ≈ -16.7 or x ≈ 23.4

Since the negative value does not make sense in this context, we will consider the positive value of x, which is approximately 23.4 feet horizontally.

Therefore, to the nearest integer, the camera will capture Jada when she is approximately 23 feet above the surface of the water.

The correct answer is:

D. 23 feet