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:
1.5
Step-by-step explanation:
1. Create a graph of the pH function. Locate on your graph where the pH value is 0 and where it is 1. You may need to zoom in on your graph.
<span>The pH value is 1 at the orange dot, and is 1 at the red dot. </span>
<span>The transformation p(t+1) results in a y-intercept. </span>
<span>In this graph, the blue line is the original and first parent function p(t) = –log10 t. The pink line represent p(t) + 1, the transformation shifts up the y-axis by 1, but the p(t) + 1 transformation does not result in a y-intercept like the ones prior. The gold line represents p(t +1), which shifts horizontally by 1 to the left. This does result in a y-intercept, because the graph doesn't completely flip over the line to the other side, and the green line represents -1*p(t), which causes the graph to flip upside down, and doesn't end up as a y- intercept.</span>
Well a decameter is 10 meters so if she has 250 meters then she has 25 decameters Hope this helps!
