From looking at a periodic function, we had to decide on the equation for it. I got:
y = 1.05 sin x2pi/11.72 + 1.55
1.05 is the 'a' value of the equation
2pi/11.72 is the 'b' value for the equation
1.55 is the 'd' value of the equation
we were told not to take into consideration the 'c' value at all.
the minimum of the graph is 0.5, the maximum is 2.6 and 11.72 is the period
the function showed the depth of water on the 16 January and displayed the times of 6am to 11pm (where 6am = 0x, 7am = 1x ....... 11pm = 17x)
The question is asking what time periods will the water be 1.7 and over on the 19 January.
Should I make y = 1.7 and work out the x values that way? Will it matter even though the equation is for the 16 January data, even though I'm using it to find out what time it will be above 1.7 on the 19 January?
Clearly Steve answered this for you in great detail here
http://www.jiskha.com/display.cgi?id=1432801604
ahhhh. I did the solution, but I failed to notice the three-day time difference. So you'll have to analyze the graph several periods later.
To determine the time periods when the water will be above 1.7 on the 19th of January, you can indeed set the function equal to 1.7 and solve for x. The fact that the equation was derived from data on the 16th of January should not be a problem, as long as the periodic patterns observed in the data are consistent.
Let's start by taking your earlier equation:
y = 1.05 sin((2π/11.72)x) + 1.55
To find when the water level is 1.7 or higher, we can set y equal to 1.7:
1.7 = 1.05 sin((2π/11.72)x) + 1.55
Next, we can manipulate the equation to isolate the sine term:
1.7 - 1.55 = 1.05 sin((2π/11.72)x)
0.15 = 1.05 sin((2π/11.72)x)
Now, divide both sides by 1.05:
0.15/1.05 = sin((2π/11.72)x)
0.143 = sin((2π/11.72)x)
To solve for x, we need to take the inverse sine (also known as arcsine) of both sides. However, keep in mind that the inverse sine function will return multiple values. So, you'll need to consider all possible solutions within the given range.
Using the inverse sine function:
((2π/11.72)x) = arcsin(0.143)
Now, divide both sides by (2π/11.72):
x = (11.72/2π) * arcsin(0.143)
To find the values of x, you can plug this equation into a calculator or use computer software to solve for x.
Remember that the values of x will correspond to time periods, where 6am is represented by 0x, 7am by 1x, and so on until 11pm, which is represented by 17x.