The path of a diver diving into the water is approximately parabolic. diving timelapse the function h(t)=-2t^2+3t+9 h ( t ) = − 2 t 2 + 3 t + 9 most closely represents the height (h) of the diver in feet after t seconds. how high does the diver reach? round to the nearest tenth. hint: make sure you include units. a space is needed between the number and unit. example: 34.8 feet

10.125 feet

Step-by-step explanation:

h(t) = -2t² + 3t + 9

The maximum height is at the vertex of the parabola.  For a parabola ax² + bx + c, the vertex is at x = -b/(2a).

t = -3 / (2×-2)

t = 3/4

h(3/4) = -2(3/4)² + 3(3/4) + 9

h(3/4) = -9/8 + 9/4 + 9

h(3/4) = 81/8

h(3/4) = 10.125 feet

answer: ratio of volume of cone (with 3 times the height and equal diameter) to volume of cylinder is 2 to 1. the value of π is not used.

step-by-step explanation:

radius is diameter/2 = 4.

area of circle is π r^2.

volume of cylinder is height × area of base = hπr^2 = 3(4^2) π = 48π cubic inches.

not knowing the formula for volume of cone, i calculate it using calculus (which is for calculating things).

volume of cone is integral 0 to h area(y) dy. area(y) is π r(y)^2. r(y) runs r to zero as y runs zero to h, r(0) = r, r(h) = 0.

r(y) = r - r/h y

area(y) = π (r - r/h y)^2 = π (r^2 - 2r^2y/h + r^2y^2/h^2) = π r^2(1-2y/h+y^2/h^2)

antiderivative area(y) = π r^2 (y-y^2/h+y^3/(3h^2))

integral 0 to h = π r^2(h-h^2/h+h^3/(3h^2) - (0)) = π r^2(h - h + h/3) = π r^2(h/3) = π/3 r^2 h

volume of this cone is π/3(4^2)18 cubic inches.

= 6 16 π = 96π cubic inches.

cone has twice the volume, 96/48.

cone height is 6 times the cylinder.

ratio of volume formula: π r^2 cancels.

cone over cylinder ratio is 6h/3 to h, 2 to 1.

my guess would be b and d, but i didn’t actually get out the pen and paper. lol