Date Jan 16 Feb 16 Mar 16 Apr 16 May 16 Jun 16 Hours light 8.95 10.18 11.62 13.27 14.65 15.40 Date Jul 16 Aug 16 Sep 16 Oct 16 Nov 16 Dec 16 Hours light 15.10 13.90 12.30 10.71 9.30 8.60 a. Determine a sinusoidal function which models the daylight hours with respect to date in the year. Graph your function.
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| Date | Jan 16 | Feb 16 | Mar 16 | Apr 16 | May 16 | Jun 16 |
| Hours light | 8.95 | 10.18 | 11.62 |
13.27 |
14.65 | 15.40 |
| Date | Jul 16 | Aug 16 | Sep 16 | Oct 16 | Nov 16 | Dec 16 |
| Hours light | 15.10 | 13.90 | 12.30 |
10.71 |
9.30 | 8.60 |
a. Determine a sinusoidal function which models the daylight hours with respect to date in the year. Graph your function.
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- 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).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 - ___) + ___Consider the following scenario: The population of fish in a pond can be modeled with the sinusoidal function (e.g., p=3000cos(π10t)+37000p=3000cos(π10t)+37000), where tt is the number of years after 2005. Create your own function based on the scenario above and address the following: Draw a graph or figure to represent this situation. To the nearest whole number, what was the population in the year 2012? Provide another example of a scenario that involves the same concept.
- 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 sinConsider the following scenario: The population of fish in a pond can be modeled with the sinusoidal function (e.g., p=3000cos(π10t)+37000p=3000cos(π10t)+37000), where tt is the number of years after 2005. Create your own function based on the scenario above and address the following: Draw a graph or figure to represent this situation. Describe how the concepts from this module can be applied in this case. To the nearest whole number, what was the population in the year 2012? Provide another example of a scenario that involves the same concept.Some of the highest tides in the world occur in the Bay ofFundy on the Atlantic Coast of Canada. At Hopewell Capethe water depth at low tide is about 2.0 m and at high tideit is about 12.0 m. The natural period of oscillation is alittle more than 12 hours and on June 30, 2009, high tideoccurred at 6:45 AM. This helps explain the following modelfor the water depth D (in meters) as a function of the time(in hours after midnight) on that day: D(t) = 7+ 5cos [0.503(t -6.75)])How fast was the tide rising (or falling) at the followingtimes?(a) 3:00 AM (b) 6:00 AM(c) 9:00 AM (d) Noon
- A rocket will carry a communications satellite into low Earth orbit. Suppose that the thrust during the first 200 sec of flight is provided by solid rocket boosters at different points during liftoff. The graph shows the acceleration in G–forces (that is, acceleration in 9.8 – /msec2 increments) versus time after launch.. Some of the highest tides in the world occur in the Bay ofFundy on the Atlantic Coast of Canada. At Hopewell Capethe water depth at low tide is about 2.0 m and at high tideit is about 12.0 m. The natural period of oscillation is alittle more than 12 hours and on June 30, 2009, high tideoccurred at 6:45 AM. This helps explain the following modelfor the water depth (in meters) as a function of the time t , (in hours after midnight) on that day: D (t ) = 7 + 5 cos [ 0.503 (t - 6.75)] How fast was the tide rising (or falling) at the following times?(a) 3:00 AM (b) 6:00 AM(c) 9:00 AM (d) NoonThe San Francisco Bay tides vary between 1 foot and 7 feet. The tide is at its lowest point when time (t) is 0 and completes a full cycle in 8 hours. What is the amplitude, period, and midline of a function that would model this periodic phenomenon? A. Amplitude = 6 feet; period = 8 hours; midline: y = 4 B. Amplitude = 6 feet; period = 4 hours; midline: y = 3 C. Amplitude = 3 feet; period = 8 hours; midline: y = 4 D. Amplitude = 3 feet; period = 4 hours; midline: y = 3
- Need solve of Beta function. At wind speeds above 1000 cm/sec, significant sand–moving events begin to occur. Wind speeds below 1000 cm/sec deposit sand and wind speeds above 1000 cm/sec move sand to new locations. The cyclic nature of wind and moving sand determines the shape and location of large dunes. At a test site, the prevailing direction of the wind did not change noticeably. However, the velocity did change. 75 wind speed readings gave an average velocity of x =1045 cm/sec. Based on long–term experience, can be assumed to be 240 cm/sec Find a 99% confidence interval for the population mean wind speed at this site. (Round your answers to the nearest whole number) (DO A MANUAL CALCULATION, SHOWING ALL WORK INCLUDING THE EQUATION USED AND THEN WITH ALL VALUES PLUGGED INTO THE EQUATION)(SHOW WORK ABOVE) [final answer] Margin of Error: E = (value with units)[final answer] Confidence Interval : _________________ < __________________ < __________________ (value with units) (correct symbol) (value with…Describe your understanding of the meaning of a periodicfunction