Mathematics, 31.03.2020 21:16 brittnum9044

The height of an object after it is released can be modeled by the function f(t) = -16t^2 + vt + s, where t is the number of seconds after the object is released, v is the upward speed at release, and s is the starting heightIf a quarterback throws a ball from his hand 6 feet in the air at a speed of 25 feet per second, how much time does his teammate have to catch the ball?

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Answer from: cody665

1.7739 seconds

Step-by-step explanation:

In the problem, v = 25 and s = 6, (we are counting height in feets). We want t such that f(t) = 0. We can solve it with the quadratic formula

$r_1,r_2 = \frac{-b ^+_- \, \sqrt{b^2-4ac} }{2a}$

Here, a = -16, b = 25 and s = 6, thsu

$r_1,r_2 = \frac{-25 ^+_- \, \sqrt{25^2-4(-16)6} }{2(-16)} = \frac{-25 ^+_- 31.76}{-32}$

We take only the - before the square root because if we sum we would obtain a negative root. Thus, r = (-25-31.76)/-32 = 1.7739.

His teammate have to catch the ball in the second 1.7739

Answer from: bri2008

The teammate of the quarterback has 1.774 seconds to catch the ball.

Step-by-step explanation:

Given the height of the object to be:

f(t) = -16t² + vt + s

Given that the quarterback throws the ball in his hand 6 fts in the air, at a speed of 25ft/s.

We want to find how much time his teammate have to catch the ball.

This is the same as finding the value of f(t) = 0

That is

-16t² + vt + s = 0

With s = 6ft, v = 25 ft/s

So, we solve

-16t² + 25t + 6 = 0

Using the quadratic formula

t = [-b ± √(b² - 4ac)]/2a

Where a = -16, b = 25, and c = 6

t = [-25 ± √(25² - 4×(-16)×6)]/2(-16)

= 25/32 ± √(625 + 384)/(-32)

= 25/32 ± (-1/32)√1009

= 25/32 ± (-0.993)

= 0.781 ± 0.993

t = 0.781 + 0.993

= 1.774

t = 0.781 - 0.993

= -0.212

We take the positive value for time, which is t = 1.774s

Answer from: Quest

10120202020000000304040404

Answer from: Quest

answer: the answer is one of

$f=\dfrac{1}{2},~\dfrac{1}{4},~\dfrac{3}{4},~\dfrac{1}{6},~\dfrac{5}{6},~\dfrac{1}{8},~\dfrac{3}{8},~\dfrac{5}{8},~\dfrac{7}{8}.$

step-by-step explanation: we are given to write a proper fraction where the whole is divided into an even number of equal parts less than ten, and an odd number of those parts exist.

an even number less than 10 may be one of 2, 4, 6 or 8. so, the whole may be one of these four evens.

now, an odd number of these parts must exist, so the numerator must be an odd number, one of 1, 3, 5 or 7. it cannot be 9 because then the fraction will become improper.

thus, our fraction may be one of the following

$f=\dfrac{1}{2},~\dfrac{1}{4},~\dfrac{3}{4},~\dfrac{1}{6},~\dfrac{5}{6},~\dfrac{1}{8},~\dfrac{3}{8},~\dfrac{5}{8},~\dfrac{7}{8}.$

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