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Richard needs to fly from San Diego to Halifax, Nova Scotia and back in order to give an important talk about mathematics. On the way to Halifax, he will get a speed boost from the wind which blows at 50 miles per hour (mph). On the way back, the plane must, unfortunately, fight this wind speed. If the talk lasts 2 hours, and if the distance between the two cities is 3000 miles, how fast must the plane fly in mph if the entire trip is to take 13 hours?

 

I'm at 11s^2 - 6000s - 27500. Could someone show me the steps of using the quadratic formula to find s?

 Nov 30, 2023
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The quadratic formula is given by:

x = (-b ± √(b^2 - 4ac)) / 2a

Now let's substitute the values into the formula:

s = (-(-6000) ± √((-6000)^2 - 4*11*(-27500))) / (2*11)

Simplifying further:

s = (6000 ± √(36000000 + 1210000)) / 22
s = (6000 ± √(37210000)) / 22
s = (6000 ± 7200) / 22


We need s to be positive, so s = (6000 + 7200)/22 = 600.

 

The answer is 600.

 Nov 30, 2023

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