Question

In a game of cornhole, Sasha tossed a bean bag and it landed at the edge of the hole. The hole can be represented by the equation x2 + y2 = 5, and the path of the bean bag can be represented by y = 0.5x2 + 1.5x – 4. To which points could she have tossed her bean bag? (–1, –2) or (–2, 1) (1, –2) or (2, 1) (–1, 2) or (–2, –1) (1, 2) or (2, –1)

Answer 1

In the game of cornhole, when Sasha tossed a bean bag to the edge of the hole, in which the equations of the hole and bean bag's path are x² + y² = 5 and y = 0.5x² + 1.5x - 4, respectively, she could have tossed her bean bag to the points (1, -2) or (2, 1).              

 

To find the points in which she could have tossed her bean bag, we need to intersect the two equations of the function as follows.

The equation for the hole

$x^{2} + y^{2} = 5$   (1)

The equation for the path of the bean bag

$y = 0.5x^{2} + 1.5x - 4$    (2)

By entering equation (2) into (1) we have:  

$x^{2} + (0.5x^{2} + 1.5x - 4)^{2} = 5$

$x^{2} + 0.25x^{4} + 1.5x^{3} - 4x^{2} + 2.25x^{2} - 12x + 16 = 5$    

$0.25x^{4} + 1.5x^{3} - 0.75x^{2} - 12x + 11 = 0$

By solving for x, we have:

x₁ = 1

x₂ = 2

Now, for y we have (eq 2):

• x₁ = 1    

$y_{1} = 0.5(1)^{2} + 1.5(1) - 4 = -2$

• x₂ = 2

$y_{2} = 0.5(2)^{2} + 1.5(2) - 4 = 1$                                              

Therefore, the points are (1, -2) or (2, 1).

To find more about intersections, go here: brainly.com/question/4977725?referrer=searchResults        

I hope it helps you!