AnswersCommon Core Algebra II - MA3111 B-ICModeling with Periodic Functions

Modeling with Periodic Functions Answers

8 verified answers1 views
1
Free Preview

A rider boards a Ferris wheel 10 feet above ground level. The diameter of the Ferris wheel is 50 feet and the wheel completes one full rotation every 24 seconds. Which graph represents the relationship between time and height off the ground?

A
On a coordinate plane, a curve starts at (0, 10). It has a maximum at y = 60 and a minimum at y = 10. It increases through the y-axis. Its cycle is 0.4 x.
Option A
B
On a coordinate plane, a curve starts at (0, 60). It has a maximum at y = 60 and a minimum at y = 10. It decreases through the y-axis. Its cycle is 0.4 x.
Option B
C
On a coordinate plane, a curve starts at (0, 10). It has a maximum at y = 60 and a minimum at y = 10. It increases through the y-axis. Its cycle is 0.8 x.
Option C
D
On a coordinate plane, a curve starts at (0, 10). It has a maximum at y = 60 and a minimum at y = 10. It decreases through the y-axis. Its cycle is 0.8 x.
Option D
2
Free Preview

A buoy starts at a height of 0 in relation to sea level and then goes up. Its maximum displacement in either direction is 6 feet, and the time it takes to go from its highest point to its lowest point is 4 seconds. Which of the following equations can be used to model h, the height in feet of the buoy in relation to sea level as a function of time, t, in seconds?

A
h = 4 sine (StartFraction pi Over 6 EndFraction t)
Option A
B
h = 4 sine (StartFraction pi Over 3 EndFraction t)
Option B
C
h = 6 sine (StartFraction pi Over 4 EndFraction t)
Option C
D
h = 6 sine (StartFraction pi Over 2 EndFraction t)
Option D
3

The height, h, in feet of a buoy in relation to sea level as a function of time, t, in seconds can be modeled by the graph below. How long does it take for the buoy to go from its highest point to its lowest point and then back to its highest point?

Question illustration
A
1 second
B
2 seconds
C
3 seconds
D
4 seconds
4

The height, h, in feet of a piece of cloth tied to a waterwheel in relation to sea level as a function of time, t, in seconds can be modeled by the equation . What is the period of the function?

Question illustration
A
seconds
Option A
B
seconds
Option B
C
8 seconds
D
20 seconds
5

Throughout the day, the depth of water at the end of a dock varies with the tides. The function represents the height, in feet, of the water t hours after midnight.Which graph shows the height of the water at the dock at any time after midnight?

Question illustration
A
On a coordinate plane, feet is on the x-axis and depth is on the y-axis. A curve starts at (0, 5). It decreases through the y-axis. It has a minimum of y = 2 and a maximum of y =12. It goes through 1 cycle in 13 feet.
Option A
B
On a coordinate plane, feet is on the x-axis and depth is on the y-axis. A curve starts at (0, 5). It increases through the y-axis. It has a minimum of y = 2 and a maximum of y =12. It goes through 1 cycle in 13 feet.
Option B
C
On a coordinate plane, feet is on the x-axis and depth is on the y-axis. A curve starts at (0, 5). It increases through the y-axis. It has a minimum of y = 2 and a maximum of y =12. It goes through 1 cycle in 7 feet.
Option C
D
On a coordinate plane, feet is on the x-axis and depth is on the y-axis. A curve starts at (0, negative 2). It increases through the y-axis. It has a minimum of y = negative 5 and a maximum of y =5. It goes through 1 cycle in 13 feet.
Option D
6

A weight attached to a spring is at its lowest point, 9 inches below equilibrium, at time t = 0 seconds. When the weight it released, it oscillates and returns to its original position at t = 3 seconds. Which of the following equations models the distance, d, of the weight from its equilibrium after t seconds?

A
d = negative 9 cosine (StartFraction pi Over 3 EndFraction t)
Option A
B
d = negative 9 cosine (StartFraction 2 pi Over 3 EndFraction t)
Option B
C
d = negative 3 cosine (StartFraction pi Over 9 EndFraction t)
Option C
D
d = negative 3 cosine (StartFraction 2 pi Over 9 EndFraction t)
Option D
7

Suppose that you want to model the height of a rider on a Ferris wheel as a function of time. The amplitude of the function you use as a model should be equal to which of the following?

A
the area of the Ferris wheel
B
the circumference of the Ferris wheel
C
the diameter of the Ferris wheel
D
the radius of the Ferris wheel
8

Mark sits on a swing that is 2.5 feet off the ground. Swinging as hard as he can, the swing reaches a height of 6 feet. Assuming Mark holds a steady pace, the height of the swing could be represented by a cosine curve.If Mark makes a full swing forward and backward in 3 seconds, which graph below could represent the height of the swing, in feet, for any time, t?

A
On a coordinate plane, seconds is on the x-axis and feet is on the y-axis. A curve starts at (0, 3). It has a maximum of y = 6 and a minimum of y = 3. It goes through 1 cycle in 1.5 seconds.
Option A
B
On a coordinate plane, seconds is on the x-axis and feet is on the y-axis. A curve starts at (0, 3). It has a maximum of y = 8 and a minimum of y = 4. It goes through 1 cycle in 1.5 seconds.
Option B
C
On a coordinate plane, seconds is on the x-axis and feet is on the y-axis. A curve starts at (0, 3). It has a maximum of y = 6 and a minimum of y = 3. It goes through 1 cycle in 3 seconds.
Option C
D
On a coordinate plane, seconds is on the x-axis and feet is on the y-axis. A curve starts at (0, negative 2). It has a maximum of y = 2 and a minimum of y = negative 2. It goes through 1 cycle in 1.5 seconds.
Option D

Did you find these answers helpful?

More from this Course

Quiz
19 verified answers

Modeling with Periodic Functions

Quiz
15 verified answers

Modeling with Periodic Functions

Quiz
14 verified answers

Three-Dimensional Figures and Cross Sections

Modeling with Periodic Functions Answers…