Mathematics: if the period is a sine function is 24 what is the frequency of the function

if the period is a sine function is 24 what is, №13154504, 07.09.2021 00:47

Mathematics

1. what is the period of the function f(x) shown in the graph? 2. (picture) 3. graph the function. f(x)=sin(πx/4) use the sine tool to graph the function. the first point must be on the midline and the second point must be a maximum or minimum value on the graph closest to the first point. 4. in the function f(x), x is replaced with 2x and 1 is added to the function. f(x)= −3sinx what effect does this have on the graph of the function? 5. over a 24-hour period, the tide in a harbor can be modeled by one period of a sinusoidal function. the tide

Step-by-step answer

P Answered by Master

Problem 1)

pi/2

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Place your pencil at (0,3) which is a good starting point, since x = 0 is often a good starting point. Trace along the curve until you reach back up at y = 3 again. So you'll go down and then back up until you reach (pi/2, 3). The difference in x values is pi/2-0 = pi/2. Every pi/2 units, the graph curve repeats itself over and over infinitely.

Note: this is not the only way to determine the period. You can start at any point really. It helps to start at a min or max value, or at x = 0. In this case, it happened to be both.

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Problem 2)

See figure 2 (attached image)

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Point A is at (0,0)
Point B is at approximately (1.57,-2) which is exactly (pi/2,-2)

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Problem 3)

See figure 3 (attached image)

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Problem 4)

Choice B
The graph is horizontally compressed by a factor of 2 and shifts up 1 unit

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The jump from x to 2x will have the period go from 2pi to pi. The graph curve repeats itself more and more often (twice as often). Therefore we have an accordion squeeze effect going on, or think of it like a spring being pressed down. We have horizontal compression along the x axis.

Adding 1 to the end shifts every point upward 1 unit. Overall, this gives the visual the entire curve itself is shifted up 1 unit.

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Problem 5)

f(x) = 5.05*sin((pi/12)x)+5.15

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max = 10.2
min = 0.1
difference = 10.2-0.1 = 10.1
Divide this difference in half: 10.1 = 5.05
So a = 5.05 is the amplitude

The period is T = 24 hrs since the height is 5.15 at midnight of one day, it rises and then falls and rises back to 5.15 by the next midnight
b = 2pi/T = 2pi/24 = pi/12
c = 0 since there is no phase shift in this sine function

d = 5.15 is the midline, which is the starting height at x = 0

f(x) = a*sin(bx-c)+d
f(x) = 5.05*sin((pi/12)x-0)+5.15
f(x) = 5.05*sin((pi/12)x)+5.15

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Problem 6)

Answers are:
A) The max height of the Ferris wheel is 64 ft
B) The radius of the Ferris wheel is 30 ft

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The largest height of the table is 64, so 64 is the max height. This is why A is true.

B is true since the max is 64 and the min is 4, so 64-4 = 60 is the diameter, making the radius r = d/2 = 60/2 = 30

C is false because the height at t = 0 is 34 ft, but the lowest point is at height h = 4

D is false because the period is actually 10 seconds. Eg: going from t = 7.5 to t = 17.5 is a time of 10 seconds. During this time, the heights are 4, 34, 64, 34, 4 telling us that a full cycle has taken place.

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1. what is the period of the function f(x) shown in the graph? 2. (picture) 3. graph the function.

1. what is the period of the function f(x) shown in the graph? 2. (picture) 3. graph the function.

Mathematics

1. what is the period of the function f(x) shown in the graph? 2. (picture) 3. graph the function. f(x)=sin(πx/4) use the sine tool to graph the function. the first point must be on the midline and the second point must be a maximum or minimum value on the graph closest to the first point. 4. in the function f(x), x is replaced with 2x and 1 is added to the function. f(x)= −3sinx what effect does this have on the graph of the function? 5. over a 24-hour period, the tide in a harbor can be modeled by one period of a sinusoidal function. the tide

Step-by-step answer

P Answered by Specialist

Problem 1)

pi/2

-------------------------------

Place your pencil at (0,3) which is a good starting point, since x = 0 is often a good starting point. Trace along the curve until you reach back up at y = 3 again. So you'll go down and then back up until you reach (pi/2, 3). The difference in x values is pi/2-0 = pi/2. Every pi/2 units, the graph curve repeats itself over and over infinitely.

Note: this is not the only way to determine the period. You can start at any point really. It helps to start at a min or max value, or at x = 0. In this case, it happened to be both.

===========================================================
Problem 2)

See figure 2 (attached image)

-------------------------------

Point A is at (0,0)
Point B is at approximately (1.57,-2) which is exactly (pi/2,-2)

===========================================================
Problem 3)

See figure 3 (attached image)

===========================================================
Problem 4)

Choice B
The graph is horizontally compressed by a factor of 2 and shifts up 1 unit

-------------------------------

The jump from x to 2x will have the period go from 2pi to pi. The graph curve repeats itself more and more often (twice as often). Therefore we have an accordion squeeze effect going on, or think of it like a spring being pressed down. We have horizontal compression along the x axis.

Adding 1 to the end shifts every point upward 1 unit. Overall, this gives the visual the entire curve itself is shifted up 1 unit.

===========================================================
Problem 5)

f(x) = 5.05*sin((pi/12)x)+5.15

-------------------------------

max = 10.2
min = 0.1
difference = 10.2-0.1 = 10.1
Divide this difference in half: 10.1 = 5.05
So a = 5.05 is the amplitude

The period is T = 24 hrs since the height is 5.15 at midnight of one day, it rises and then falls and rises back to 5.15 by the next midnight
b = 2pi/T = 2pi/24 = pi/12
c = 0 since there is no phase shift in this sine function

d = 5.15 is the midline, which is the starting height at x = 0

f(x) = a*sin(bx-c)+d
f(x) = 5.05*sin((pi/12)x-0)+5.15
f(x) = 5.05*sin((pi/12)x)+5.15

===========================================================
Problem 6)

Answers are:
A) The max height of the Ferris wheel is 64 ft
B) The radius of the Ferris wheel is 30 ft

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The largest height of the table is 64, so 64 is the max height. This is why A is true.

B is true since the max is 64 and the min is 4, so 64-4 = 60 is the diameter, making the radius r = d/2 = 60/2 = 30

C is false because the height at t = 0 is 34 ft, but the lowest point is at height h = 4

D is false because the period is actually 10 seconds. Eg: going from t = 7.5 to t = 17.5 is a time of 10 seconds. During this time, the heights are 4, 34, 64, 34, 4 telling us that a full cycle has taken place.

===========================================================

1. what is the period of the function f(x) shown in the graph? 2. (picture) 3. graph the function.

Mathematics

Over a 24-hour period, the tide in a harbor can be modeled by one period of a sinusoidal function. The tide measures 4.35 ft at midnight, rises to a high of 8.3 ft, falls to a low of 0.4 ft, and then rises to 4.35 ft by the next midnight. What is the equation for the sine function f(x), where x represents time in hours since the beginning of the 24-hour period, that models the situation? f(x) =

Step-by-step answer

P Answered by Master

f(x)=4.35+3.95*sin( $\pi /12\\$ )

Step-by-step explanation:

Mathematics

Iver a 24-hour period, the tide in a harbor can be modeled by one period of a sinusoidal function. The tide measures 4.35 ft at midnight, rises to a high of 8.3 ft, falls to a low of 0.4 ft, and then rises to 4.35 ft by the next midnight. What is the equation for the sine function f(x), where x represents time in hours since the beginning of the 24-hour period, that models the situation?

Step-by-step answer

P Answered by Specialist

$f(x)=3.95sin(\frac{\pi}{12}x)+4.35$

Step-by-step explanation:

Recall:

Sinusoidal Function -> f(x)=a*sin(bx+c)+d

Amplitude ->

Period -> $\frac{2\pi}{|b|}$ Phase Shift -> $-\frac{c}{b}$ Vertical Shift/Midline ->

Given:

Amplitude -> a=8.3-4.35=3.95

Period -> $\frac{2\pi}{|b|}=\frac{2\pi}{|24|}=\frac{2\pi}{24}=\frac{\pi}{12}$ Phase Shift -> $-\frac{c}{b}=-\frac{0}{24}=0$ Vertical Shift/Midline -> $d=\frac{8.3+0.4}{2}=\frac{8.7}{2}=4.35$

Conclusion:

The equation that models the situation is $f(x)=3.95sin(\frac{\pi}{12}x)+4.35$

Hope this helped! I've attached a graph of the function so you can understand it better!

Iver a 24-hour period, the tide in a harbor can be modeled by one period of a sinusoidal function. T

Mathematics

Over a 24-hour period, the tide in a harbor can be modeled by one period of a sinusoidal function. The tide measures 5.15 ft at midnight, rises to a high of 10.2 ft falls to a low of 0.1 ft, and then rises to 5.15 ft by the next midnight What is the equation for the sine function f(x), where x represents time in hours since the beginning of the 24-hour period, that models the situation? Enter your answer in the box

Step-by-step answer

P Answered by Master

f(x)=5.05 sin((pi/12)x) + 5.15

Step-by-step explanation:

Over a 24-hour period, the tide in a harbor can be modeled by one period of a sinusoidal function. T

Mathematics

A cosine function is a reflection of its parent function over the x-axis. The amplitude of the function is 11, the vertical shift is 9 units down, and the period of the function is 7pi/12. The graph of the function does not show a phase shift. What is the equation of the cosine function described? Fill in the blanks using values from this list: -20, -11, -9, -2, 2, 9, 11, 20, 7pi/12,12pi/7,7/24,24/7 f(x)=___cos(x)

Step-by-step answer

P Answered by PhD

7

We have been given that a cosine function is a reflection of its parent function over the x-axis. The amplitude of the function is 11, the vertical shift is 9 units down, and the period of the function is $\frac{7\pi}{12}$ . The graph of the function does not show a phase shift. We are asked to write the equation of our function.

We know that general form a cosine function is $y=A\cos(b(x-c))-d$ , where,

A = Amplitude,

$\frac{2\pi}{b}$ = Period,

c = Horizontal shift,

d = Vertical shift.

The equation of parent cosine function is $y=\cos(x)$ . Since function is reflected about x-axis, so our function will be $y=-\cos(x)$ .

Let us find the value of b.

$\frac{2\pi}{b}=\frac{7\pi}{12}$

$7\pi\cdot b=24\pi$

$\frac{7\pi\cdot b}{7\pi}=\frac{24\pi}{7\pi}$

$b=\frac{24}{7}$

Upon substituting our given values in general cosine function, we will get:

$f(x)=-11\cos(\frac{24}{7}x)-9$

Therefore, our required function would be $f(x)=-11\cos(\frac{24}{7}x)-9$ .

Mathematics

Design a sine function with the given properties: it has a period of 24 hr with a minimum value of 10 at t=4 hr and a maximum value of 16 at t=16 hr. show all the steps

Step-by-step answer

P Answered by PhD

$f(x)=3\sin\left(\frac{\pi}{12}\left(x-10\right)\right)+13$ .

Step-by-step explanation:

Given information:

Period = 24 hr

Maximum = 16 at t=16 hr.

Minimum = 10 at t=4 hr.

The general sin function is

$y=A+\sin(B(x-C))+D$ .... (1)

where, |A| is altitude, $\frac{2\pi}{B}$ is period, C is phase shift and D is midline.

Period is 24 hr.

$24=\dfrac{2\pi}{B}\Rightarrow B=\dfrac{\pi}{12}$

Altitude is

$A=\dfrac{Maximum-Minimum}{2}=\dfrac{16-10}{2}=3$

$D=\dfrac{Maximum+Minimum}{2}=\dfrac{16+10}{2}=13$

The function is minimum at t=4 and maximum at t=16,phase shift is

$C=\dfrac{16+4}{2}=10$

Substitute these values in equation (1).

$y=3\sin\left(\frac{\pi}{12}\left(x-10\right)\right)+13$

Therefore, the required function is $f(x)=3\sin\left(\frac{\pi}{12}\left(x-10\right)\right)+13$ .

Mathematics

A cosine function is a reflection of its parent function over the x-axis. The amplitude of the function is 11, the vertical shift is 9 units down, and the period of the function is 7pi/12. The graph of the function does not show a phase shift. What is the equation of the cosine function described? Fill in the blanks using values from this list: -20, -11, -9, -2, 2, 9, 11, 20, 7pi/12,12pi/7,7/24,24/7 f(x)=___cos(x)

Step-by-step answer

P Answered by PhD

7

We have been given that a cosine function is a reflection of its parent function over the x-axis. The amplitude of the function is 11, the vertical shift is 9 units down, and the period of the function is $\frac{7\pi}{12}$ . The graph of the function does not show a phase shift. We are asked to write the equation of our function.

We know that general form a cosine function is $y=A\cos(b(x-c))-d$ , where,

A = Amplitude,

$\frac{2\pi}{b}$ = Period,

c = Horizontal shift,

d = Vertical shift.

The equation of parent cosine function is $y=\cos(x)$ . Since function is reflected about x-axis, so our function will be $y=-\cos(x)$ .

Let us find the value of b.

$\frac{2\pi}{b}=\frac{7\pi}{12}$

$7\pi\cdot b=24\pi$

$\frac{7\pi\cdot b}{7\pi}=\frac{24\pi}{7\pi}$

$b=\frac{24}{7}$

Upon substituting our given values in general cosine function, we will get:

$f(x)=-11\cos(\frac{24}{7}x)-9$

Therefore, our required function would be $f(x)=-11\cos(\frac{24}{7}x)-9$ .

Mathematics

Design a sine function with the given properties: it has a period of 24 hr with a minimum value of 10 at t=4 hr and a maximum value of 16 at t=16 hr. show all the steps

Step-by-step answer

P Answered by PhD

$f(x)=3\sin\left(\frac{\pi}{12}\left(x-10\right)\right)+13$ .

Step-by-step explanation:

Given information:

Period = 24 hr

Maximum = 16 at t=16 hr.

Minimum = 10 at t=4 hr.

The general sin function is

$y=A+\sin(B(x-C))+D$ .... (1)

where, |A| is altitude, $\frac{2\pi}{B}$ is period, C is phase shift and D is midline.

Period is 24 hr.

$24=\dfrac{2\pi}{B}\Rightarrow B=\dfrac{\pi}{12}$

Altitude is

$A=\dfrac{Maximum-Minimum}{2}=\dfrac{16-10}{2}=3$

$D=\dfrac{Maximum+Minimum}{2}=\dfrac{16+10}{2}=13$

The function is minimum at t=4 and maximum at t=16,phase shift is

$C=\dfrac{16+4}{2}=10$

Substitute these values in equation (1).

$y=3\sin\left(\frac{\pi}{12}\left(x-10\right)\right)+13$

Therefore, the required function is $f(x)=3\sin\left(\frac{\pi}{12}\left(x-10\right)\right)+13$ .

Mathematics

INFORMATION TO HELP FILL OUT GRAPH: I need the exact graph so I know exactly what to put on the paper The function will be h(t) = -197cos (pi/15 t) +246 (NOTE: pi/15 is being multiplied with t) The maximum height of the Ferris wheel is 443 ft and its diameter is 394 ft. The distance between the top-most point and the bottom-most point is 394 ft. Therefore, the amplitude will be 394 = 197ft 2 Suppose you start at the bottom-most point it means that the equation should be an inverted cosine function because it also starts at the bottom-most point.

Step-by-step answer

P Answered by Master

1

Answer:

See below

Step-by-step explanation:

To sketch the graph, you can follow these steps:

1. Choose a scale for the x-axis that ranges from 0 to 30. This represents the time in minutes for one complete rotation of the Ferris wheel.

2. Choose a scale for the y-axis that ranges from 0 to 500. This will allow you to plot the maximum height of the Ferris wheel, which is 443 feet, and the height of the Elizabeth Tower, which is 320 feet.

3. Plot the center of the Ferris wheel at (15, 246) feet.

4. Plot the highest point of the Ferris wheel at (15.66, 443) feet.

5. Plot the lowest point of the Ferris wheel at (0, 49) feet.

6. Plot the two points where the height of the Ferris wheel is equal to the height of the Elizabeth Tower, which are approximately (3.685, 320) and (8.318, 320) feet. Note that these points are obtained by solving the equation h(t) = -197cos(pi/15 t) + 246 for h(t) = 320.

7. Sketch the graph of the function h(t) = -197cos(pi/15 t) + 246 by plotting points at various times t and their corresponding heights h(t), using the equation and the values for A, B, C, and D given in the problem.

Remember to label the x-axis as "Time (minutes)" and the y-axis as "Height (feet)" and to provide a title for the graph. I hope this helps!

if the period is a sine function is 24 what is the frequency of the function

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