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Question
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a ball is shot directly up in the air from a dog ball launcher. the upwards velocity of the ball, in meters per second, after t seconds is approximated by the following expression.
35 - 10t
the upwards velocity will be strictly between 15 and 20 meters per second between
seconds after being thrown in the air.
Step1: Set up inequality for velocity
$15 < 35 - 10t < 20$
Step2: Subtract 35 from all parts
$15 - 35 < 35 - 10t - 35 < 20 - 35$
$-20 < -10t < -15$
Step3: Divide by -10 (reverse inequalities)
$\frac{-20}{-10} > t > \frac{-15}{-10}$
$2 > t > 1.5$
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The upwards velocity will be strictly between 15 and 20 meters per second between 1.5 and 2 seconds after being thrown in the air.