I just need help with this then I'm done with my homework
2 answers:
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<h3>Answer:</h3>
- using y = x, the error is about 0.1812
- using y = (x -π/4 +1)/√2, the error is about 0.02620
The actual value of sin(π/3) is (√3)/2 ≈ 0.86602540.
If the sine function is approximated by y=x (no error at x = 0), then the error at x=π/3 is ...
... x -sin(x) @ x=π/3
... π/3 -(√3)/2 ≈ 0.18117215 ≈ 0.1812
You know right away this is a bad approximation, because the approximate value is π/3 ≈ 1.04719755, a value greater than 1. The range of the sine function is [-1, 1] so there will be no values greater than 1.
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If the sine function is approximated by y=(x+1-π/4)/√2 (no error at x=π/4), then the error at x=π/3 is ...
... (x+1-π/4)/√2 -sin(x) @ x=π/3
... (π/12 +1)/√2 -(√3)/2 ≈ 0.026201500 ≈ 0.02620
Answer:
The closest to the output when the input is approximately 12
Step-by-step explanation:
The given (x, y) coordinates are;
The line of best fit is
x, 0, 3, 6, 6, 8, 10, 11
y, -2, 7, 16, 15, 21, 28, 31
The line of best fit can be obtained from the scatter plot of the given data from where a linear pattern is apparent
A linear line of best fit is a trend line that gives an overall cumulative minimum distance of all the points from the line
The method for constructing a line of best fit includes;
1) The least Squares Method
2) The method of linear regression
3) Construction of line of best fit
a) The area method
b) The dividing method
The least squares equation is given as follows;
= a + b·x
From MS Excel, we have;
= 266.8571
= 89.42857
∴ b = 266.8571/89.42857 ≈ 2.984
From MS Excel, with the given data, we get;
= 16.57143
= 6.285714
Therefore;
a = 16.57143 - 2.984 × 6.285714 = -2.185
Therefore, we get the following regression equation;
= -2.185 + 2.9·x
Where;
x = The input
= The output
Therefore, when x = 5, we get;
= -2.185 + 2.9 × 5 = 12.315
Therefore, the closest to the output when the input is 5, y ≈ 12