What is the error due to using linear interpolation to estimate the value of sinxsinx at x = \pi/3? your answer should have at
least three significant figures, accurate to within 0.1%. (e.g., 1.23 and 3.33e-8 both have three significant figures.)?
1 answer:
<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.
___
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
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Answer:
<u>All the four statements are true , which are -</u>
(A) The subset contains contains of all the outfits that have grey slacks .
(B) The subset contains contains of all the outfits that have grey slacks and red tie .
(C) The subset contains contains of all the outfits that have grey slacks and blue shirt .
(D) The subset contains contains of all the outfits that do not have black slacks .
Step-by-step explanation:
<u>We are given with Outfit 2 , 4 and 6</u>
Outfit 2 - Blue grey red
Outfit 4 - White grey red
Outfit 6 - Black grey red
(A) Since only 2,4, and 6 contain grey slacks, and no other outfit contains grey slacks, those are the subsets that contain grey slacks. Thus , this statement is true .
(B) Just outfits 2, 4, and 6 have grey slacks and a red tie, proving the statement. Other clothes do not include grey slacks and a red tie; they may include a red tie but not both grey slacks and a red tie. Hence , the statement is true .
(C) Since the outfit 2 has grey slacks and a blue shirt, the statement is correct; no other outfit has both grey slacks and a blue shirt. Therefore , this statement is also correct .
(D) The argument is correct since all of the subsets contain grey slacks and no black slacks.
Hence , all the options A , B , C , D are correct and describes the subset .
<u>The given question is incomplete , the complete question is attached here - </u>
