Question

In: Advanced Math

Let a be a positive constant number. Draw the graph of a catenary y=acosh(x/a). Calculate the...

Let a be a positive constant number. Draw the graph of a catenary y=acosh(x/a). Calculate the arc length s from the point (0,a) to the point (x,acosh(x/a)), and find the expression of the curve in terms of the parameter s.

Solutions

Expert Solution

Given questions solution are complete.


Related Solutions

Let X be the number of heads and let Y be the number of tails in...
Let X be the number of heads and let Y be the number of tails in 6 flips of a fair coin. Show that E(X · Y ) 6= E(X)E(Y ).
Let x be the number of different research programs, and let y be the mean number...
Let x be the number of different research programs, and let y be the mean number of patents per program. As in any business, a company can spread itself too thin. For example, too many research programs might lead to a decline in overall research productivity. The following data are for a collection of pharmaceutical companies and their research programs. x 10 12 14 16 18 20 y 1.9 1.4 1.6 1.4 1.0 0.7 Complete parts (a) through (e), given...
Let x be a fixed positive integer. Is it possible to have a graph G with...
Let x be a fixed positive integer. Is it possible to have a graph G with 4x + 1 vertices such that G has a vertex of degree d for all d = 1, 2, ..., 4x + 1? Justify your answer. (Note: The graph G does not need to be simple.)
Let X and Y be independent positive random variables. Let Z=X/Y. In what follows, all occurrences...
Let X and Y be independent positive random variables. Let Z=X/Y. In what follows, all occurrences of x, y, z are assumed to be positive numbers. Suppose that X and Y are discrete, with known PMFs, pX and pY. Then, pZ|Y(z|y)=pX(?). What is the argument in the place of the question mark?    Suppose that X and Y are continuous, with known PDFs, fX and fY. Provide a formula, analogous to the one in part (a), for fZ|Y(z|y) in terms...
Let X be the event that the first number is even. Let Y be the event...
Let X be the event that the first number is even. Let Y be the event that the second number is even. Let Z be the event that the sum of the two numbers is even. Are the events X and Z independent? ( Are the events X ∩ Y and Z independent?
Let f(x, y) = x^ 2 + kxy + 4y^ 2 , k a constant. The...
Let f(x, y) = x^ 2 + kxy + 4y^ 2 , k a constant. The point (0, 0) is a stationary point of f. For what values of k will f have a local minimum at (0, 0)? (a) |k| > 4 (b) k ≥ −4 (c) k ≤ 4 (d) |k| < 4 (e) none of the above The point P : (2, 2) is a stationary point of the function f(x, y) = 6xy − x ^3...
Let x be per capita income in thousands of dollars. Let y be the number of...
Let x be per capita income in thousands of dollars. Let y be the number of medical doctors per 10,000 residents. Six small cities in Oregon gave the following information about x and y. x 8.6 9.7 10.3 8.0 8.3 8.7 y 9.7 19.0 22.0 10.2 11.4 13.1 Complete parts (a) through (e), given Σx = 53.6, Σy = 85.4, Σx2 = 482.72, Σy2 = 1344.7, Σxy = 784.51, and r ≈ 0.963. (b) Verify the given sums Σx, Σy,...
Let x be per capita income in thousands of dollars. Let y be the number of...
Let x be per capita income in thousands of dollars. Let y be the number of medical doctors per 10,000 residents. Six small cities in Oregon gave the following information about x and y. x 9.0 9.4 10.2 8.0 8.3 8.7 y 9.5 18.0 21.2 10.2 11.4 13.1 Complete parts (a) through (e), given Σx = 53.6, Σy = 83.4, Σx2 = 481.98, Σy2 = 1269.3, Σxy = 761.13, and r ≈ 0.864. (b) Verify the given sums Σx, Σy,...
Let x be per capita income in thousands of dollars. Let y be the number of...
Let x be per capita income in thousands of dollars. Let y be the number of medical doctors per 10,000 residents. Six small cities in Oregon gave the following information about x and y. x 8.4 9.1 9.8 8.0 8.3 8.7 y 9.8 18.4 21.2 10.2 11.4 13.1 Complete parts (a) through (e), given Σx = 52.3, Σy = 84.1, Σx2 = 457.99, Σy2 = 1289.65, Σxy = 747.71, and r ≈ 0.958. (a) Draw a scatter diagram displaying the...
Let x be per capita income in thousands of dollars. Let y be the number of...
Let x be per capita income in thousands of dollars. Let y be the number of medical doctors per 10,000 residents. Six small cities in Oregon gave the following information about x and y. x 8.3 9.3 10.2 8.0 8.3 8.7 y 9.9 18.1 20.6 10.2 11.4 13.1 Complete parts (a) through (e), given Σx = 52.8, Σy = 83.3, Σx2 = 468, Σy2 = 1255.59, Σxy = 750.81, and r ≈ 0.974. (a) Draw a scatter diagram displaying the...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT