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- Hyperbolic sine Function The hyperbolic sine function is defined by sinh(x)=exex2 a Sketch the graph of this function using graphical addition as in Exercise 17. b Use the definition to show that sinh(x)=sinh(x) Hyperbolic Cosine Function The hyperbolic cosine function is defined by cosh(x)=ex+ex2 a Sketch the graphs of the functions y=13ex and y=12ex on the same axes, and use graphical addition see Section 2.7 to sketch the graph of y=cosh(x). b Use the definition to show that cosh(x)=cosh(x).Graphical Reasoning Use the formulas for the area of a circular sector and arc length given in Section 1.1. (a) For =0.8, write the area and arc length as functions of r. What is the domain of each function? Use a graphing utility to graph the functions. Use the graphs to determine which function changes more rapidly as r increases. Explain. (b) For r=10 centimeters, write the area and arc length as functions of . What is the domain of each function? Use the graphing utility to graph the functions.Simple Harmonic Motion A mass suspended from a spring oscillates in simple harmonic motion at a frequency of 4 cycles per second. The distance from the highest to the lowest point of the oscillation is 100 cm. Find an equation that describes the distance of the mass from its rest position as a function of time. Assume that the mass is at its lowest point when t=0.
- Salmon Survival For reasons that are not yet fully understood, the number of fingerling salmon that survive the trip from their riverbed spawning grounds to the open ocean varies approximately sinusoidally from year to year. The table shows the number of salmon that hatch in a certain British Columbia creek and then make their way to the Strait of Georgia. The data are given in thousands of fingerlings, over a period of 16 years. a Make a scatter plot of the data. b Find a sine curve that models the data as in Example 1. c Graph the function you found in part b together with the scatter plot. d Use a graphing calculator to find the sine curve that best fits the data as in Example 2. Compare to your answer from part b. Year Salmon 1000 Year Salmon 1000 1985 43 1993 56 1986 36 1994 63 1987 27 1995 57 1988 23 1996 50 1989 26 1997 44 1990 33 1998 38 1991 43 1999 30 1992 50 2000 2247. A sinusoidal function below is used to model the motion of a pendulum over time, where y is the distance, in centimetres, from its rest position and t is the time, in seconds. Suppose the period of the motion doubles. If all other factors in the equation remain unchanged, what is the new equation?midline: y=0 amplitude of the function f: 3.5 what is The equation of the midline for the function f. Assume y=f(θ):?? what is The period of the function f: ??
- The musical note "A" creates a sound wave that is the graph of the function f(x)=sin(880πx), where x represents the time in seconds. This note completes 440 cycles of the sine wave per second. What is the length of time for one period of this sine wave? What is the number of x-intercepts of f(x) in the interval (0, 1]?Create and sketch (by hand) a sinusoidal function that fits the following criteria: Amplitude greater than 5 Midline value greater than 5 Max greater than 20 Minimum lower than 10 A non-zero phase shift Period of either 43 or 116 explain how you are graphing it and how the equation you created satisfies all the criteria above. Part 2: Using that function you created, model after a real-life application and create a word problem. Then use the function to solve the problem. Examples of real-life application include tide, ferris wheel, weight on a spring, etc. No graphing technology may be used for this assignment. You must graph the function by hand. A well-drawn sketch of the function is also acceptable. Think: What is necessary when graphing? What do you need to include?Create and sketch (by hand) a sinusoidal function that fits the following criteria: Amplitude greater than 5 Midline value greater than 5 Max greater than 20 Minimum lower than 10 A non-zero phase shift Period of either 4pi/3 or 11pi/6 explain how you are graphing it and how the equation you created satisfies all the criteria above. Part 2: Using that function you created, model after a real-life application and create a word problem. Then use the function to solve the problem. Examples of real-life application include tide, ferris wheel, weight on a spring, etc. Show a hand drawn graph
- Analyzing the functions below, compare and contrast the two functions in each problem situation. Be sure to use complete sentences in your comparison. Be sure to include a discussion of similarities and differences for the periods, amplitudes, y-minimums, y-maximums, and any phase shift between the two graphs. Use the rubric below as a guideline for your solutions. y= 4sin(2x-π) and y=cos(3x- π/2)Next question Get a similar question You can retry this question below Without graphing the function y=−5sin(9x), determine its amplitude, period, and the distance between its critical points. Leave answers in exact form; type pi for π.1be Sine Function The sine function sin x has the property that the square of itself plus the square of its derivative is identically equal to one. Find the most general function that has this property.