SOLUTION: The speed of a car was tracked by radar in a police helicopter over a period of 10 minutes. The police found that the car's speed could be represented by the equation: s = 3t squar

Question 166463: The speed of a car was tracked by radar in a police helicopter over a period of 10 minutes. The police found that the car's speed could be represented by the equation: s = 3t squared - 30t + 135
where s is the speed of the car in kilometers per hour after t minutes have passed.
a. When was the car travelling at 80km/h?
b. When was the car travelling at 120km/h?
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
I'll do the first part to get you started

a)

Start with the given equation

Plug in

Subtract 80 from both sides.

Combine like terms.

Notice we have a quadratic equation in the form of where , , and

Let's use the quadratic formula to solve for t

Start with the quadratic formula

Plug in , , and

Negate to get .

Square to get .

Multiply to get

Subtract from to get

Multiply and to get .

Simplify the square root (note: If you need help with simplifying square roots, check out this solver)

or Break up the expression.

So the answers are or

which approximate to or

So the this means that at 2.418 seconds or at 7.582 seconds, the car was traveling at 80 km/h
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