Mathematics: 1) a projectile is thrown upward so that its distance above the ground after t seconds ish=-10t2 +440 t. after how many seconds does it reach its maximum height?

Including the 3 at the beginning, it d be 2. But if you re talking about the 7th number after the decimal, it d be 6. :)...

1) a projectile is thrown upward so that its distance

aweller3898

09.01.2022

After 22 seconds the projectile reach its maximum height of 4,840 units

Step-by-step explanation:

we have

$h(t)=-10t^{2}+440t$

This is a vertical parabola downward (because the leading coefficient is negative)

The vertex is a maximum

Find out the coordinates of the vertex

Convert the quadratic equation in vertex form

Factor -10

$h(t)=-10(t^{2}-44t)$

Complete the square

$h(t)=-10(t^{2}-44t+22^2)+(10)(22^2)$

$h(t)=-10(t^{2}-44t+22^2)+4,840$

Rewrite as perfect squares

$h(t)=-10(t-22)^{2}+4,840$

The vertex is the point (22,4,840)

therefore

After 22 seconds the projectile reach its maximum height of 4,840 units

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