Hi there can anyone help me out with this please please please
1 answer:
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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:
The dimensions of the larger cylinder are 3 times the dimensions of the smaller cylinder
The surface area of the larger cylinder is 3^2. or 9 times the surface area of the smaller cylinder
If proportional dimensional changes are made to a solid figure, then the surface area will change by the square of the scale factor of similar solids
Step-by-step explanation:
we know that
If two figures are similar, then the ratio of its areas is equal to the scale factor squared
Let
z ----> the scale factor
x ----> the area of the base of larger cylinder
y ---> the area of the base of smaller cylinder
so
we have
substitute
solve for z
<u><em>Verify each statement</em></u>
1) The dimensions of the larger cylinder are 3 times the dimensions of the smaller cylinder
The statement is true
Because the scale factor is equal to 3 ( see the explanation)
2) The surface area of the larger cylinder is 3^2. or 9 times the surface area of the smaller cylinder
The statement is true
Because, the surface area of the larger cylinder is equal to the surface area of the smaller cylinder multiplied by the scale factor squared
3) If proportional dimensional changes are made to a solid figure, then the surface area will change by the square of the scale factor of similar solids
The statement is true
because
If two figures are similar, then the ratio of its areas is equal to the scale factor squared