The path that a ball follows when thrown into the air from a height of 5 feet is given by the formula h=-0.1d^2 + 1.5d + 5, where h is the height of the ball and d is the time in second. How long will it take the ball to reach 10 feet? Please help it needs to be solved algebraically.

Question

anonymous · Answer

$$10=-.1d^2+1.5d+5$$
first get all everything to one side

$$10-10=-.1d^2+1.5d+5-10$$
$$0=-.1d^2+1.5d-5$$

anonymous · Answer

now use the quadratic formula which you can use when you have

$$0=ax^2+bx+c$$

anonymous · Answer

$$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$$

anonymous · Answer

does this hep?

anonymous · Answer

yes thank you so much!

anonymous · Answer

btw you need to take the lower value, because it will reach 10 feet on it's way down too!

anonymous · Answer

oh okay! thanks!

anonymous · Answer

i have a question what do ou do after the quadratic formula?

anonymous · Answer

you should get 2 values for d

anonymous · Answer

did you find them?

anonymous · Answer

after you put everything in, you should be able to evaluate it.... so since there is a plus or minus after negative b, you'll get two answers

one
$$\frac{-b+\sqrt{b^2-4ac}}{2a}$$

and


$$\frac{-b-\sqrt{b^2-4ac}}{2a}$$

anonymous · Answer

so does x=10 and x=5?

anonymous · Answer

not quite sure let me check ... http://www.wolframalpha.com/input/?i=-.1x%5E2%2B1.5x-5%3D0 yep you're correct so x=d=t so thats your time

anonymous · Answer

so 5 seconds after you toss it, it gets to 10 feet then goes higher. Another 5 seconds later the ball fall back to 10 feet.

anonymous · Answer

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