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.
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Answer:
78% as a fraction in simplest form would be 39/50.
78% as a decimal is 0.78
Answer: 8.49
This is the answer I did show the work how I did in the paper but I can’t take a picture of it sorry
The coefficient of correlation is independent of change of scale and origin of the variable X and Y. Change of origin means some value has been added or subtracted in the observation. If we divide all observations with x then new mean =initial mean/x.
For this case we are going to define the following variable:
x: time in minutes
We write the linear function that represents the problem:
t (x) = (14/4) x + 7
For x = 6 we have:
t (6) = (14/4) * (6) + 7
t (6) = 28 ° C
For x = 11 we have:
t (11) = (14/4) * (11) + 7
t (11) = 45.5 ° C
Answer:
t (6) = 28 ° C
t (11) = 45.5 ° C
