Step-by-step explanation: 6dsdsnds
By the chain rule, if , then
We have , for which
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•
and and , so that
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Putting everything together, we get
<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
<h3>
Step-by-step explanation:</h3>
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
The answer should be 10, double check though.
Answer:
The new coordinates are (5,7), (10,7), (10,2), (5,2)
Step-by-step explanation:
If we have coordinates (x,y), we can do the following transformations:
- a units up means (x, y+a)
- a units down means (x, y - a)
- b units right means (x + b, y)
- b units left means (x - b, y)
We see that UP/DOWN affects the y coordinate and RIGHT/LEFT affects the x coordinate. When we will have combination of both, we follow the rules with both.
Now,
5 units right will affect x coordinate [add 5]
2 units up will affect y coordinate [add 2]
We do these with 4 coordinates respectively. Shown below:
(0,5) ---------> (5,7)
(5,5) ---------> (10,7)
(5,0) ---------> (10,2)
(0,0) ---------> (5,2)