contestada

50. HOW DO YOU SEE IT? The object of a computer game
is to break bricks by deflecting y ball toward them
using a paddle. The graph shows the current path of
the ball and the location of the last brick.
brick
6
paddle
0
a. You can move the paddle up, down, left, and right.
At what coordinates should you place the paddle
to break the last brick? Assume the ball deflects at
a right angle.
b. You move the paddle to the coordinates in part (a),
and the ball is deflected. How can you write an
absolute value function that describes the path of
the ball?

50 HOW DO YOU SEE IT The object of a computer game is to break bricks by deflecting y ball toward them using a paddle The graph shows the current path of the ba class=

Respuesta :

The initial path of the ball and the path of the deflected ball are

perpendicular to each other.

  • a. The coordinates at which the paddle should be placed is [tex]\underline{(7, \, 1)}[/tex]
  • b. The absolute value function is; [tex]\underline{y = |x - 7| + 1}[/tex]

Reasons:

a. Points along the path of the ball are; (0, 8), and (2, 6)

Therefore;

[tex]\displaystyle Slope \ of \ the \ path, \, m = \frac{2 - 0}{6 - 8} = -1[/tex]

The y-intercept is 8, the equation of the path of the ball is therefore;

y = -x + 8

The initial location of the brick = (14, 8)

The direction of the ball after deflection = At right angle (perpendicular) to initial path

Which gives;

The slope of the ball after deflection, m', is given by the equation;

  • [tex]\displaystyle m' = -\frac{1}{m}[/tex]

Which gives;

The slope of the ball after deflection is therefore;

[tex]\displaystyle m' = -\frac{1}{(-1)} = 1[/tex]

Equation of the ball to reach the brick, y - 8 = 1·(x - 14)

y = x - 14 + 8 = x - 6

y = x - 6

The coordinate of the paddle, is given by the equation;

x - 6 = -x + 8

∴ 2·x = 14

[tex]\displaystyle x = \frac{14}{2} = 7[/tex]

y = -x + 8

y = -7 + 8 = 1

The coordinates at which the paddle should be placed is [tex]\underline{(7, \, 1)}[/tex]

b. The absolute value function that describes the path of the ball can be

written in the form;

f(x) = a·|x - h| + k

Where;

(h, k) = The coordinate of the vertex = (7, 1)

a = The slope = 1

Which gives;

The absolute value function is; f(x) = [tex]\underline{y = \mathbf{ |x - 7| + 1}}[/tex]

Learn more here:

https://brainly.com/question/10538556

Otras preguntas