Right Triangles
Rotation
Sinusoidal Waves
Transformations
Exponentials
100
The length of side c
10 centimeters
100
London ties a green ribbon to a blade on one of her fans. She then records the fan with a high speed camera. She finds that her fan completes a full rotation in 0.01 seconds. The fan blade is 1 foot long. Assuming that the green ribbon starts in the rightmost position, how could we model the green ribbon's vertical position relative to the center after x seconds? Use radians, and don't turn fractions into decimals.
v(x)=1sin((2pi)/0.01x)
100
The midline, amplitude, period, and phase shift of this graph.
Midline: y = 0
Amplitude: 2
Period: pi
Phase Shift: -(3pi)/4
100
The name of this transformation, including direction
Reflection across the x-axis
OR
Reflection along the y-axis
100
An investment of $75,000 increases at a rate of 12.5% per year. Find the value of the investment after 30 yr to the nearest cent
$2,568,247.87
200
The distance between these two points.
13 units
200
Lilly is going to ride a ferris wheel. She boards the ride at the bottom position of the circle. The ferris wheel completes a rotation in 2 minutes. The wheel has a radius of 20 meters. How could we model the Lilly's vertical position relative to the center after x minutes? Use radians, and don't turn fractions into decimals.
v(x)=20sin((2pi)/2x-pi/2)
OR
v(x)=20sin((2pi)/2x+3pi/2)
200
y=5cos(4x+pi/2)-2
The midline, amplitude, period, and phase shift
Midline: y=-2
Amplitude:5
Period: pi/2
Phase Shift: + +pi/2
200
Modify the solid line function f(x) so that it matches the dashed line.
f(x-6)-3
200
A savings account balance is compounded continuously. If the interest rate is 3.1% per year and the current balance is $1077.00, in how many years (to the nearest tenth) will the balance reach $1486.73?
10.4 years
300
The angle θ in degrees rounded to the nearest tenth
60.9 degrees
300
Hailey is enjoying her rainbow pinwheel and hat. A gust of wind blows her pinwheel so that it takes 0.2 seconds to go at full rotation. The pinwheel has a radius of 3 inches. The red blade of the pinwheel starts on the leftmost position of the circle. Hailey is holding the pinwheel up so that the center is 48 inches in the air. How could we model the horizontal position in inches relative to the ground after x seconds? Use radians, and don't turn fractions into decimals.
h(x)=3cos((2pi)/0.2x+pi)+48
OR
h(x)=3cos((2pi)/0.2x-pi)+48
300
The Midline, Amplitude, Period, and appropriate trig function for this graph.
Midline: y=1
Amplitude: 2
Period: (2pi)/3
Trig Function: cos
300
Modify the solid line function f(x) so that it matches the dashed line.
-f(x+5)+1
300
You buy a new computer for $2100. The computer decreases by 50% annually. When will the computer have a value of $600 (to the nearest hundredth)?
1.81 years
400
The length of side DE to the nearest tenth
16.1 units
400
The center of a wind turbine is 300 meters in the air. The wind turbine completes a rotation in 0.07 minutes. The turbine has a radius of 55 meters. How could we model the topmost blade's horizontal position, in meters, relative to the ground after x minutes? Use radians, and don't turn fractions into decimals.
h(x)=55cos((2pi)/0.07x+pi/2)+300
OR
h(x)=55cos((2pi)/0.07x-3pi/2)+300
400
The equation for this graph
y=sin(4/3x)+1
400
2(x+3)^3+5
400
A radioactive sample of Khouredium-94 has a half-life of 4 years. If the initial mass of the sample is 50g, how long will it take for the sample to reach 23g? We can model this situation with the equation
23=50(2)^-(x/4)
4.48 years
500
5543 kilopascals
500
The center of a water wheel is 3 feet above the awater. The water wheel completes a rotation in 4 seconds. The water wheel has a radius of 10 feet. How could we model the leftmost spoke's vertical position, in feet, relative to the water line after x seconds? Use radians, and don't turn fractions into decimals.
v(x)=10sin((2pi)/4x+pi)+3
OR
v(x)=10sin((2pi)/4x-pi)+3
500
The equation for this graph
y=3sin(1/4x)-1
500
Ibrahim throws a basketball in the air. Its path from the initial throw can be modeled with a parabola. The ball reaches 18 feet into the air and lands 6 feet away from Ibrahim. A graph of the balls path is shown below:
What is the equation of this parabola?
-2(x-3)^2+18
500
The population of Tiki Tiki town halves every 15 years. In how many years will the population decrease by 25%?
6.23 years.