As Devine rides her bike, she picks up a nail in her front tire. The height, h, of the nail from the ground as she rides her bike over time, t, in seconds, is modelled by the equation below: As Devine rides her bike, she picks up a nail in her front tire. The height, h, of the nail from the ground as she rides her bike over time, t, in seconds, is modelled by the equation below:f(x)=-14 cos(720(t-10))+14 Using the equation, determine the following. Show your work for part marks.
a) What is the diameter of the bike wheel?
b) How long does it take the tire to rotate 3 times?
c) What is the minimum height of the nail? Does this height make sense? Why?

Step-by-step explanation:

a) The diameter of the wheel is the distance between the minimum and maximum.  In other words, it's double the amplitude.

d = 2 × 14 = 28.

b) The period of the wave is:

720 = 2π / T

T = π/360

So the time for 3 revolution is:

3T = π/120

3T = 0.026 seconds

c) The minimum here is when cosine = 1.

h(t) = -14(1) + 14

h(t) = 0

This makes sense, since the minimum height is when the nail is at the bottom of the wheel, or at the ground.

hello from mrbilldoesmath!

answer:

the domain is the set { -2, 0, 2, 3}

discussion:

the domain is the set of x values in the ordered pairs (x,y). taking the x, or first component, of each ordered pair gives   -2, 0, 2, 3.

you,

mrb

80° is the measure of gh

step-by-step explanation:

circle f is congruent to circle j

we have two circle with center f and j.

both circles are congruent. the radius of the circle would be equal.

see the attachment for the circle.

we are given ∠efd ≅ ∠gjh

therefore, arc (ed) = arc (gh)     (∴ circle f is congruent to circle j)

but ∠dfe=80°=arc (ed)

therefore, arc (gh) = 80°

thus, 80° is the measure of gh