Questions: A ball is thrown from an initial height of 2 feet with an initial upward velocity of 17 ft/s. The ball's height h (in feet) after t seconds is given by the following: h = -16t^2 + 17t + 2 Find all values of t for which the ball's height is 6 feet. (If there is more than one answer, use the "or" button.) t = (17 ± sqrt(17^2 - 4(-16)(2-6)))/(2(-16)) = (17 ± sqrt(289 + 256))/(-32) = (17 ± sqrt(545))/(-32) Round your answer(s) to the nearest hundredth. seconds

A ball is thrown from an initial height of 2 feet with an initial upward velocity of 17 ft/s. The ball's height h (in feet) after t seconds is given by the following:

h = -16t^2 + 17t + 2

Find all values of t for which the ball's height is 6 feet.

(If there is more than one answer, use the "or" button.)

t = (17 ± sqrt(17^2 - 4(-16)(2-6)))/(2(-16)) = (17 ± sqrt(289 + 256))/(-32) = (17 ± sqrt(545))/(-32)

Round your answer(s) to the nearest hundredth.

seconds
Transcript text: A ball is thrown from an initial height of 2 feet with an initial upward velocity of 17 ft/s. The ball's height h (in feet) after t seconds is given by the following: h = -16t^2 + 17t + 2 Find all values of t for which the ball's height is 6 feet. (If there is more than one answer, use the "or" button.) t = \frac{17 \pm \sqrt{17^2 - 4(-16)(2-6)}}{2(-16)} = \frac{17 \pm \sqrt{289 + 256}}{-32} = \frac{17 \pm \sqrt{545}}{-32} Round your answer(s) to the nearest hundredth. seconds
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Solution

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Solution Steps

Step 1: Set the equation equal to 6.

The given equation is h = 2 + 17t - 16t². We are looking for the time(s) when the height (h) is 6 feet. So, we set the equation equal to 6:

6 = 2 + 17t - 16t²

Step 2: Rearrange the equation into standard quadratic form.

Subtract 6 from both sides of the equation to get the equation in standard quadratic form (ax² + bx + c = 0):

0 = -16t² + 17t - 4

Step 3: Solve for _t_ using the quadratic formula.

The quadratic formula is: t = (-b ± √(b² - 4ac)) / 2a In our equation, a = -16, b = 17, and c = -4. Plug these values into the quadratic formula:

t = (-17 ± √(17² - 4_(-16)_(-4))) / (2 * -16) t = (-17 ± √(289 - 256)) / -32 t = (-17 ± √33) / -32

Step 4: Calculate the two possible values for _t_.

t = (-17 + √33) / -32 ≈ (-17 + 5.74) / -32 ≈ 0.35 t = (-17 - √33) / -32 ≈ (-17 - 5.74) / -32 ≈ 0.71

Final Answer

t ≈ 0.35 or t ≈ 0.71 seconds

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