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3 years ago

HELP ME DO THIS PLZ

Mathematics

1 answer:

cestrela7 [59]3 years ago

3 0

Answer:

It landed at a height of 14 feet

Step-by-step explanation:

Given

$y = -\frac{1}{8}x^2 +4x$ --- Path of a t-shirt

$3y = 2x - 14$ --- height of bleachers

Required

Height when t-shirts land in bleachers

$3y = 2x - 14$

Make y the subject

$y = \frac{2}{3}x - \frac{14}{3}$

Substitute $y = \frac{2}{3}x - \frac{14}{3}$ in $y = -\frac{1}{8}x^2 +4x$

$\frac{2}{3}x - \frac{14}{3} = -\frac{1}{8}x^2 +4x$

Multiply through by 24

$16x- 112 = -3x^2 +96x$

Express as:

$3x^2 + 16x -96x- 112 = 0$

$3x^2 -80x- 112 = 0$

Using a calculator:

$x = 28$ or $x = -\frac{4}{3}$

x can not be negative:

So:

$x = 28$

Substitute $x = 28$ in $y = -\frac{1}{8}x^2 +4x$ to calculate the height it landed

$y = -\frac{1}{8} * 28^2 + 4 * 28$

$y = 14$

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