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34kurt
3 years ago
9

What is the error due to using linear interpolation to estimate the value of sinxsin⁡x 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.)?

Mathematics
1 answer:
Bad White [126]3 years ago
6 0
<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.

___

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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Two objects were lifted by a machine. One object had a mass of 2 kilograms and was lifted at a speed of 2m/sec. the other had a
OLga [1]
Sadly, after giving all the necessary data, you forgot to ask the question.
Here are some general considerations that jump out when we play with
that data:

<em>For the first object:</em>
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The force needed to lift it at a steady speed is 19.6 newtons.
The potential energy it gains every time it rises 1 meter is 19.6 joules.
If it's rising at 2 meters per second, then it's gaining 39.2 joules of
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The machine that's lifting it is providing 39.2 watts of lifting power.
The object's kinetic energy is 1/2 (mass) (speed)² = 1/2(2)(4) = 4 joules.

<em>For the second object:</em>
The object's weight is (mass) x (gravity) = 4 x 9.8 = 39.2 newtons
The force needed to lift it at a steady speed is 39.2 newtons.
The potential energy it gains every time it rises 1 meter is 39.2 joules.
If it's rising at 3 meters per second, then it's gaining 117.6 joules of
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The machine that's lifting it is providing 117.6 watts of lifting power.
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If you go back and find out what the question is, there's a good chance that
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4 0
3 years ago
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1) suppose for purposes of calculation that the cake is inscribed in a square of 8 by 8
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if just 1 carrot cake
then
(9-1)=8 ---------->  coffee cakes and lemon cakes
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the answer part 1) is
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the answer part 2) is
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part 3) distribution of the cakes in the table 24  in x 24 in

answer

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C------->coffee cakes
L------->lemon cakes

Z-C-L    or      C-L-C             
C-L-C             Z-C-L
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Please help with both of these~! Thank you!
Musya8 [376]
Can you please state the questions / problems or attach the image with the questions / problems so that we can answer it for you.
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