Mathematics: A person is shot out of a cannon at a circus. The height of the person flying through the air is described by the equation h (t) = -6t² + 48t , where t is the seconds after the person leaves the Cannon. What is the height of the person after 4 seconds? Use feet as the unit.

A person is shot out of a cannon at a circus. The

BePaige

30.01.2022

The height of the person is 96 feet.

Step-by-step explanation:

Hi, to answer this question we simply have to substitute t=4 seconds in the equation given:

h (t) = -6t² + 48t

Replacing and solving:

h(4) = -6 (4)² + 48 (4)

h(4) = -6 (16) + 192

h(4) = -96 + 192

h(4) = 96 ft

The height of the person after 4 seconds is 96 feet.

Feel free to ask for more if needed or if you did not understand something.

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natalie2sheffield

13.11.2022

31.64 feet

Step-by-step explanation:

The height is given by the equation:

$h(x) = -32x^2/45^2 + x +210 = -\frac{32}{45^2}x^2 + x +210$

where x is the horizontal distance of the projectile from the face of the cliff.

If the height is maximum, then its derivative must be h'(x)=0. Remembering that the derivative of x^n is $nx^{n-1}$ , we have:

$h'(x) = (-\frac{32}{45^2}x^2 + x +210)' = (-\frac{32}{45^2}x^2)' + (x)' +(210)'=-2\frac{32}{45^2}x+1$

And we want h'(x)=0, so:

$-2\frac{32}{45^2}x+1=0$

This will give us the horizontal distance from the face of the cliff when the height of the projectile is at its maximum. We then do:

$2\frac{32}{45^2}x=1$

$x=\frac{1}{2}\frac{45^2}{32}=31.64$

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