Question

2
Type the correct answer in the box. Use numerals instead of words.
A ball is kicked with an initial height of 0.75 meters and initial upward velocity of 22 meters/second. This inequality represents the time, t in
seconds, when the ball's height is greater than 10 meters.
-4.9t2 + 22t + 0.75 > 10
and
seconds.
The ball's height is greater than 10 meters when t is approximately between blank and blank seconds
​

Answer 1

Answer:

t is between 0 seconds and 4.878

Step-by-step explanation:

Given:

Inequality: $-4.9t^2 + 22t + 0.75 > 10$

Required

Determine the value(s) of t

To answer this question, we simply solve the inequality

$-4.9t^2 + 22t + 0.75 > 10$

Subtract 10 from both sides

$-4.9t^2 + 22t + 0.75 - 10> 10 - 10$

$-4.9t^2 + 22t -9.25> 0$

Multiply through by -1

$4.9t^2 - 22t + 9.25 < 0$

Solve the value of t using quadratic formula

$t = \frac{-b \± \sqrt{b^2 - 4ac}}{2a}$

Where

a = 4.9; b = -22 and c = -9.25

So:

$t = \frac{-(-22) \± \sqrt{(-22)^2 - 4 * 4.9 * -9.25}}{2 * 4.9}$

$t = \frac{22 \± \sqrt{484 + 181.3}}{9.8}$

$t = \frac{22 \± \sqrt{665.3}}{9.8}$

$t = \frac{22 \± 25.80}{9.8}$

Split the expression

$t = \frac{22 + 25.80}{9.8}$    or      $t = \frac{22 - 25.80}{9.8}$

$t = \frac{47.8}{9.8}$    or     $t = \frac{-3.8}{9.8}$

$t = 4.878$   or  $t = -0.388$

Since t cannot be negative; Then

$t < 4.878$

Hence; t is between 0 seconds and 4.878

Answer 2

Answer:

c

Step-by-step explanation:

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