A pendulum is swinging next to a wall. The distance from the bob of the swinging pendulum to the wall varies in a periodic way that can be modeled by a trigonometric function.

The function has period 0.80.80, point, 8 seconds, amplitude 6 \text{ cm}6 cm6, start text, space, c, m, end text, and midline H = 15 \text{ cm}H=15 cmH, equals, 15, start text, space, c, m, end text. At time t = 0.5t=0.5t, equals, 0, point, 5 seconds, the bob is at its midline, moving towards the wall.

Find the formula of the trigonometric function that models the distance HHH from the pendulum's bob to the wall after t seconds. Define the function using radians.

  H(t) = 15 -6sin(2.5π(t -0.5))

Step-by-step explanation:

For midline M, amplitude A, period T and time t0 at which the function is decreasing from the midline, the function can be written as ...

  H(t) = M -Asin(2π/T(t -t0))

Using the given values of M=15, A=6, T=0.8 and t0 = 0.5, the equation is ...

  H(t) = 15 -6sin(2.5π(t -0.5))

1 3 5

step-by-step explanation:

i took the test: )

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.