Quadratic equations are used for many applications. The formula to solve quadratic equations can be used to solve all quadratic equations, even those that cannot be factored. A common application of quadratic equations is the height of a thrown object over time, which takes the earth's gravity and the velocity of the throw into account. For example, if someone throws a ball down from a height of 100 meters, the ball's distance from the ground can be modeled by the equation: d = − 9.8 t 2 − 15 t + 100 where t is the time in seconds and d is the distance in meters.At what time (t) will the ball hit the ground? (Hint: what does this mean for d=distance?)You will get two answers. Do both make sense? (Explain in detail Why or Why not)...

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Asked Oct 25, 2019
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Quadratic equations are used for many applications. The formula to solve quadratic equations can be used to solve all quadratic equations, even those that cannot be factored. A common application of quadratic equations is the height of a thrown object over time, which takes the earth's gravity and the velocity of the throw into account. For example, if someone throws a ball down from a height of 100 meters, the ball's distance from the ground can be modeled by the equation: d = − 9.8 t 2 − 15 t + 100 where t is the time in seconds and d is the distance in meters.

  1. At what time (t) will the ball hit the ground? (Hint: what does this mean for d=distance?)
  2. You will get two answers. Do both make sense? (Explain in detail Why or Why not)...
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Expert Answer

Step 1

When the ball hits the ground then d=0

From there we have to solve for t.

Before that we simplify the equation to remove the decimal.

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-9.8 15t100 0 Multiply both sides by 10 -9.810 15t - 10+100 10 = 0 10 Refine -98/150r1000 = 0

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Step 2

Then we solve for t using quadratic formula.

t= -4.05 and t=2.52

Time can not be negative ...

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-(-160) ± V (-150)- - 4(-98)1000 2(-98) For a= -98, b= -150, c = 1000: 12= 5(15 145 -(-150) 150)- 4(-98)1000 2(-98) t= 98 -(-150) V150)-4(-98)1000 2(-98) 51415) 98 t= The solutions to the quadratic equation are: 5(15+ 4145 98 5414515) t= t= 98 t- -4.05 t-2.52

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