Aprojectile is shot into the air following the path, h(x) = -3x^2 + 30x + 300. at what time, value of x, will it reach a maximum height?
x = 1
x = 2
x = 4
x = 5

maximum at x=5

Step-by-step explanation:

This path is parabolic (represented by a parabola since it is given by a quadratic expression).The parabola has the branches down since its leading coefficient is negative (-3), so the maximum value of this function will correspond to the vertex of the parabola.

We can use the definition for the vertex of a parabola to find it.

For a general parabola of the form: ,

the x-value of its vertex is given by the expression:

In our case, (since = -3,  and = 30) it becomes:

Therefore, the projectile will reach its maximum at x=5

34.5 cm

step-by-step explanation:

generally for a circular segment of angle, θ° and radius r

arc length

= (θ/360) x circumference

= (θ/360) x 2πr

in our case, θ = 60°, π=3.142 and r = 33 cm

substitute into above formula

arc length

= (60/360) x 2(3.142)( 33) = 34.5 cm