Penelope drove 27 kilometers. Which expression finds the distance she drove in centimeters?

Mathematics

1 answer:

MaRussiya [10]3 years ago

7 0

27km* 10^6= 2,700,000cm
Or
1km is 1,000,000 cm, so that means 27 km is 2,700,000 cm

Hope this helps :)

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1. The function $h(t)=-16t^{2}+48t$ is a parabola of the form $ax^{2}+bx$ . The the formula for the axis of symmetry of a parabola is $x= \frac{-b}{2a}$ . We can infer from our function that $a=-16$ and $b=48$ , so lets replace those values in our formula:
$x= \frac{-b}{2a}$
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$x= \frac{-48}{-32}$
$x= \frac{3}{2}$
$x=1.5$
We can conclude that to the left of the line of symmetry the ball is reaching its maximum height, and to the right of the line of symmetry the ball is falling.

2. Lets check how much time the ball takes to reach its maximum height and return to the ground. To do that we are going to set the height equal to zero:
$0=-16t^{2}+48t$
$-16t(t-3)=0$
$t=0$ or $t-3=0$
$t=0$ or $t=3$
From our previous point we know that the ball reaches its maximum time at $t=1.5$ , which means that it takes 1.5 seconds to reach the maximum height and 1.5 seconds to fall back to the ground.