How can you use rates to determine wheather a situation is a proportional relationship
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Answer:
Step-by-step explanation:
Solution:-
- We are to model a sinusoidal function for the number of hours of daylight measured in one year in Ellenville.
- We will express a general form of a sinusoidal function [ f ( t ) ] as follows:
Where,
A: The amplitude of the hours of daylight
w: The angular frequency of occurring event
c: The mean hours of daylight
t: The time taken from reference ( days )
- We are given that the longest day [ ] occurred on June 21st and the shortest day [
] on December 21st.
- The mean hours of daylight ( c ) is the average of the maximum and minimum hours of daylight as follows:
- The amplitude ( A ) of the sinusoidal function is given by the difference of either maximum or minimum value of the function from the mean value ( c ):
- The frequency of occurrence ( w ) is defined by the periodicity of the function. In other words how frequently does two maximum hours of daylight occur or how frequently does two minimum hours of daylight occur.
- The time period ( T ) is the time taken between two successive maximum duration of daylight hours. We were given the longest day occurred on June 21st and the shortest day occurred on December 21st. The number of days between the longest and shortest day will correspond to half of the time period ( 0.5*T ):
- The angular frequency ( w ) is then defined as:
- We will now express the model for the duration of daylight each day as function of each day:
..........................
Answer:
Step-by-step explanation:
To write the quadratic equation, begin by writing it in vertex form
Where (h,k) is the vertex of the parabola.
Here the vertex is (-2,-20). Substitute and write:
To find a, substitute one point (x,y) from the parabola into the equation and solve for a. Plug in (0,-12) the y-intercept of the parabola.
The vertex form of the equation is .
You can convert this into standard form by using the distributive property.