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- In a city the number of hours of sunlight on the summer solstice of 2015 was 18.42, and the number if hours of sunlight on the winter solstice was 5.44. (Hint: the summer solstice occurs on the 172nd day of the year and there are 365 days until the next one.) Find a sinusoidal function of the form y = Asin that models the data. y = ___sin (___x - ___) + ___According to the Old Farmer’s Almanac, in Anchorage, Alaska, the number of hours of sunlight on the summer solstice of 2010 was 19.42 and the number of hours of sunlight on the winter solstice was 5.48. (a) Find a sinusoidal function of the form y=Asin(ωx- ϕ)+B that models the data. (b) Use the function found in part (a) to predict the number of hours of sunlight on April 1,the 91st day of the year. (c) Draw a graph of the function found in part (a). *(d) Look up the number of hours of sunlight for April 1 in the Old Farmer’s Almanac,and compare the actual hours of daylight to the results found in part (c).Did you know that out from the rotation of a Ferris wheel a graph of either sine or cosine function is formed? Amazing right?! This is due to the shape of the said ride as compared to a unit circle. Assume that you were riding on the biggest Ferris wheel in the Philippines – known as the Pampanga eye. As you enter on its gondola at the base, the minimum point of the graph of the said functions above is already represented and the maximum point of the graph is located when you have reached the top of the wheel. Whereas, the period or one complete cycle of the graph is attained when you reach at the base again. Your task this time is to sketch the graph of a circular function based on the movement of a Ferris wheel, determine its amplitude and period, and illustrate its domain and range. Now, let’s get started! From riding the Ferris wheel, you observe the following: (1) The gondola is 2 meters off the ground; (2) The top portion of the wheel is 60 meters from the gondola at the base (3)…
- suppose that the length of time between consecutive high tides is 12 hours and 26 mins. on a particular day the high tide occurred at 12:26 am (0.43 hours) and the low tide occurred at 7:07 (7.12 hours). Water heights are measured as the amounts above or below the mean lower low water. The height of the water at high tide was 5.94 feet and the height of the water at low tide was 0.04 feet. The next high tide will occur at 12:52pm. Find the sinusoidal function of the form of sinplot the curve x^3+y^3=6xy together with the tangent to the curve at the point(4/3,8/3). Show all the work as well as identify the numpoint(n) of the implicit graph.Find the slope of the line tangent to the curve y = cos2 x at the point(−π/3 , 1/4)
- Determine the DE of the family curves. Sketch some of its representative members. - Circles tangent to the y-axis.If the normal to the curve y-f(x) at the point(3,4) makes an angle of Pi with the positive x-axis .What is the value of f'(3) ?Match the velocity graph (blue) to its postion graph (red).
- The pedals on a bicycle have a maximum height of 30 cm above the ground and a minimum height of 8 cm above the ground. Out for a ride, a cyclist pedals at a constant rate of 20 cycles per minute. Write an equation for this periodic function in the form y=asin(bt)+d AND explain in details how you got there.Find the length of the arc of the function x^2 = 4y fromx = -3 to x = 3Find the equation of a cosine wave that is obtained by shifting the graph of y = cos x to the left 9 units and upward 3 units and that is horizontally compressed by a factor of 10 when compared to y = cos x.