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Kitty [74]
3 years ago
8

Find the arc length function for the curve with starting point (0,1). y=sin−1x+√1−x2

Mathematics
1 answer:
Ilya [14]3 years ago
8 0

dy/dx = 1/√(1 - x^2) - x/√(1 - x^2) = (1 - x)/√(1 - x^2) 

1 + (dy/dx)^2 = 1 + (1 - x)^2/(1 - x^2) = [(1 - x^2) + (1 - x)^2]/(1 - x^2) = (1 - x^2 + 1 - 2x + x^2)/(1 - x^2) = (2 - 2x)/(1 - x^2) = 2(1 - x)/[(1 + x)(1 - x)] = 2/(1 + x) 

ds = √(1 + (dy/dx)^2 = √(2/(1 + x)) = √2/√(1 + x) dx 

<span>L = √2 ∫ dx/√(1 + x) {0, 1} = √2 ∫ (1 + x)^(-1/2) dx = 2√2 √(1 + x) {0, 1} = 2√2 (√2 - 1) = 4 - 2√2 ≈ 1.1716

The arc length would be </span><span>1.1716 units.</span><span>

I hope my answer has come to your help. Thank you for posting your question here in Brainly.
</span>
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The mean is the average value of the given data set. When the outlier is removed the mean and the median of the data set are changed.

<h3>What are mean, median, and mode?</h3>
  • The mean is the average value of the given data set.
  • The median is the middle value of a given data set when the data is arranged in increasing order.
  • The mode is the number that is repeated the most number of times in a given data set.

The data set can be arranged as 12, 19, 19, 20, 21, 22, 22, 23, 24, 26, 27, 28, 29, 30, 32, 35, 48. Now, The means, median and mode for the data set is,

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Hence, when the outlier is removed the mean and the median of the data set are changed.

Learn more about Mean, Median, and Mode:

brainly.com/question/15323584

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