The table shows the depth (d metres) of water in a harbour at certain times (t hours) after midnight on a particular day.
Time t (hours) Depth d (m)
0 3.0
1 3.3
2 4.2
3 5.6
4 7.2
5 8.2
6 9.0
7 8.9
8 8.1
9 7.3
10 5.6
11 4.3
12 3.5
13 3.1
Use the regression facilities on your calculator to fit a sine curve to these data. Choose the one option which provides the best fit model (with coefficient rounded to 2 significant figures).
A) t=3.0sin(0.49d-1.6)+6.0
B) d=3.0+6.0sin(0.49t-1.6)
C) t=2.9sin(0.48d-1.5)+6.0
D) d=3.0sin(0.49t-1.6)+6.0
E) d=2.99sin(0.49t-1.60)+6.04
F) d=6.0-3.0sin(0.49t+1.6)
Can anyone help me please. I may be d??
This is not a fair question for this forum.
In order to help you, I would have to have the same programmable graphing calculator as you do, and would have to be familiar with the procedure to use that particular function.
I do not.
But I can still provide some humorous advice! Just choose option F) d=6.0-3.0sin(0.49t+1.6). Why? Because who doesn't love a little subtraction and a slight twist in the angle? It adds some excitement to your otherwise mundane regression equations. Plus, it's always good to add a little mystery to your math! Just make sure to double-check your work, or your graph might end up looking like a roller coaster ride gone wrong. Hang on tight!
I apologize for not being able to help you with this specific question. However, I can guide you through the steps to manually fit a sine curve to the data.
1. Plot the data points on a graph with time (t) on the x-axis and depth (d) on the y-axis. This will give you a scatter plot of the data.
2. Visually inspect the scatter plot to determine if it exhibits a sinusoidal pattern. If it does, you can proceed to fit a sine curve to the data.
3. Use trial and error to determine the parameters of the sine curve equation, which is of the form d = A*sin(B*t - C) + D. Adjust the values of A, B, C, and D until the curve best fits the scatter plot.
4. Once you have determined the values of A, B, C, and D that provide the best fit, round them to two significant figures.
Unfortunately, without having access to your specific calculator or regression facilities, I cannot provide the exact answer. I recommend consulting the user manual or referring to the calculator's documentation for instructions on how to perform regression analysis.
However, I can explain how you can use regression analysis to fit a sine curve to the given data using a calculator or a graphing software.
1. Enter the time values (t) in one list and the corresponding depth values (d) in another list.
2. On your calculator or graphing software, locate the regression or curve fitting option. This may be found under statistical functions or by accessing the graphing menu.
3. Select the regression or curve fitting option and choose the type of function you want to fit. In this case, you want to fit a sine curve.
4. Enter the depth values (d) as the dependent variable and the time values (t) as the independent variable.
5. The regression analysis will calculate the coefficients for the sine function. Make sure to round the coefficients to 2 significant figures as specified in the question.
6. Compare the calculated coefficients with the options provided in the question. Choose the option that has the closest coefficients to the calculated values.
In this case, without having access to the specific calculator or software you are using, it is not possible to determine the exact option that provides the best fit model. You will need to follow the steps above using your own calculator or software to find the correct answer.