The Ferris Wheel has a diameter of 30 meters, the center is 19 meters off the ground and it makes 2 revolutions per min.
1 answer:
The sinusoidal function for the height as a function of time will be h= -15 cos (πt/15)+19 meter
As the Ferris wheel starts with the rider from the bottom position (which is the minimum point in the cycle), we can represent the position of the rider with a negative cosine function.
The general form of the cosine function representing the displacement of the rider is:
f(t) = a cos(bt+c) + d, where:
amplitude = |a| which is the distance that travels above and below the midpoint
period = 2 π/|b| which is the time period i.e. time required to complete one cycle
-c/b is the phase shift.
d = vertical displacement of the function
Given the diameter of the wheel is 30 m, then r = 30/2 = 15 m.
So the distance that travels above and below the midpoint is the radius for which a=15. As we have the negative cosine function, a = -15.
The time period is 0.5min. As it is given the frequency is 2 revolutions per min for which b= 2(2π) rad/min.= 4π/60 rad/sec.= π/15 rad/sec.
The rider starts from the bottom position, so there will be no phase shift, so c=0
Given that the center of the wheel is 19 m above the ground, so d=19m
Therefore the equation will be
height of rider as function of time(t) = h = -15 cos (πt/15)+19 meter
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Answer:
y = 1.
Step-by-step explanation:
f(x) = x^2 + 1
We know that:
replacing the function, we get:
Now we can simplify this to:
and solving the quotient, we get:
then f'(x) = 2*x
And we want the equation for the tangent line at (0, 1)
The slope of that line will be:
f'(0) = 2*0 = 0
So this is a horizontal line, of the type y = a
And we know that this line must pass through the point (0, 1)
so we must have y = 1.
Then the equation of the tangent line to f(x) at the point (0, 1) is:
y = 1.