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swat32
3 years ago
9

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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\displaystyle \int_{-2}^2 \sqrt 3(x^2-4)^2 \, dx = \frac{\sqrt3}4 \times 8 \int_0^2 (x^2-4)^2 \, dx = \boxed{\frac{512}{5\sqrt3}}

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8 0
3 years ago
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