1+(f′(x))^2−f′′(x)=0 Make the substitution u=f′ in equation (B). Solve the resulting first-order equation for u(x).
Integrate your answer for problem 1 to find f(x) solving the original Euler-Lagrange equation.
What is the cheapest path from (−1,0) to (1,0)?
What happens when you try to use the formula you found in problem 2 to write out the cheapest path from (−3,0) to (3,0)?
Explain why the formula doesn't work in problem 4 in terms of the original problem of finding a cheapest path.

Me #1 using vocabulary words, including the word “congruent”, state why the measure of angle d is 120 degrees. #2 what is the measure of angle e and why?

Formulate the indicated conclusion in nontechnical terms. be sure to address the original claim. the foundation chair for a hospital claims that the mean number of filled overnight beds is over 523, and she is therefore justified starting a funding campaign to add a wing to the hospital. assuming that a hypothesis test has been conducted and that the conclusion is failure to reject the null hypothesis, state the conclusion in nontechnical terms.

Which description is represented by a discrete graph? kiley bought a platter for $19 and several matching bowls that were $8 each. what is the total cost before tax? the temperature at 9 a. m. was 83° f and is heating up at an average rate of 6°f per hour. what is the temperature x hours later? juan ate an egg with 78 calories and some cereal with 110 calories per serving for breakfast. what is the total amount of calories he consumed? a bottle contained 2,000 ml of liquid and is being poured out at an average rate of 300 ml per second. how much liquid is left in the bottle after x seconds?