parabolic path that can be reprsented by the function y=-0.1x^2 +2.9x, where x represents the horizontal distance and y represents the vertical distance of the football. As the ball is rising, a Louisanna lineman jumps in a linear path that can be represented by the equation y=-x+10 and blocks the kick... Graphically determine the height, to the nearest tenth of a meter, at which the lineman blocks the ball?

Question

parabolic path that can be reprsented by the function y=-0.1x^2 +2.9x, where x represents the horizontal distance and y represents the vertical distance of the football. As the ball is rising, a Louisanna lineman jumps in a linear path that can be represented by the equation y=-x+10 and blocks the kick... Graphically determine the height, to the nearest tenth of a meter, at which the lineman blocks the ball?

Answer 1

graphically? Draw the graphs, where do they intersect?

Answer 2

I graphed your functions using Wolfram and they don't intersect at a negative x and a value of showing which would show a negative height.

check your equations, or else the question is bogus

http://www.wolframalpha.com/input/?i=plot+y%3D-0.1x%5E2+%2B2.9x%2C+y+%3D+-x%2B10

Answer 3

I meant to say:

".. they intersect at a negative x and a value of x which would result in a negative height."

Answer 4

To graphically determine the height at which the lineman blocks the ball, we need to find the point of intersection between the parabolic path of the football and the linear path of the lineman.

Step 1: Set the two equations equal to each other since the y-coordinates are equal at the point of intersection:
-0.1x^2 + 2.9x = -x + 10

Step 2: Rearrange the equation to be in standard form:
-0.1x^2 + 2.9x + x - 10 = 0
-0.1x^2 + 3.9x - 10 = 0

Step 3: Solve the quadratic equation. You can use various methods to solve it such as factoring, completing the square, or using the quadratic formula. In this case, let's use the quadratic formula:
x = (-b ± √(b^2-4ac))/(2a)

Using the quadratic formula:
x = (-3.9 ± √(3.9^2-4(-0.1)(-10)))/(2(-0.1))

Simplifying further:
x = (-3.9 ± √(15.21-4(0.1)(-10)))/(-0.2)
x = (-3.9 ± √(15.21-4))/(-0.2)
x = (-3.9 ± √11.21)/(-0.2)

Step 4: Calculate the x-coordinate (horizontal distance) at the point of intersection by using the positive value of x:
x = (-3.9 + √11.21)/(-0.2)

Using a calculator, we find:
x ≈ 5.1

Step 5: Substitute the value of x back into one of the original equations to find the corresponding y-coordinate (vertical distance):
y = -x + 10

Substituting x = 5.1:
y = -(5.1) + 10
y ≈ 4.9

Step 6: Therefore, the height (y-coordinate) at which the lineman blocks the ball is approximately 4.9 meters.