Question

1. Check that a curve x=cosht, y=sinht becomes a hyperbola. Draw its graph, and calculate its...

1. Check that a curve x=cosht, y=sinht becomes a hyperbola. Draw its graph, and calculate its curvature.

2. 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.

Math   Advanced-Math   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Find the center, foci, vertices, and eccentricity of the hyperbola, and sketch its graph y^2 -...
Find the center, foci, vertices, and eccentricity of the hyperbola, and sketch its graph y^2 - 16 x^2 + 64 x - 208 = 0 Please solve all the following needs.
Let y = x 2 + 3 be a curve in the plane. (a) Give a...
Let y = x 2 + 3 be a curve in the plane. (a) Give a vector-valued function ~r(t) for the curve y = x 2 + 3. (b) Find the curvature (κ) of ~r(t) at the point (0, 3). [Hint: do not try to find the entire function for κ and then plug in t = 0. Instead, find |~v(0)| and dT~ dt (0) so that κ(0) = 1 |~v(0)| dT~ dt (0) .] (c) Find the center and...
find the vertices,foci and asymptotes of the hyperbola and sketch its graph y^2/25-x^2/9=1 show all work...
find the vertices,foci and asymptotes of the hyperbola and sketch its graph y^2/25-x^2/9=1 show all work and step
An equation of a hyperbola is given. x^2/ 9 - y^2//49=1 (a) Find the vertices, foci,...
An equation of a hyperbola is given. x^2/ 9 - y^2//49=1 (a) Find the vertices, foci, and asymptotes of the hyperbola. (Enter your asymptotes as a comma-separated list of equations.) vertex (x, y) = (smaller x-value) vertex (x, y) = (larger x-value) focus (x, y) = (smaller x-value) focus (x, y) = (larger x-value) asymptotes     (b) Determine the length of the transverse axis. (c) Sketch a graph of the hyperbola.
a) Find the arc length parametrization of the line x=-2+4t, y=3t, z=2+t that has the same...
a) Find the arc length parametrization of the line x=-2+4t, y=3t, z=2+t that has the same direction as the given line and has reference point (-2,0,2). Use an arc length S as a parameter. x= y= z= b) Use the parametric equations obtained in part (a) to find the point on the line that is 20 units from the reference point in the direction of increasing parameter. x= y= z= b) Use the parametric equations obtained in part (a) to...
Find the exact length of the curve. x = 8 + 9t2, y = 3 +...
Find the exact length of the curve. x = 8 + 9t2, y = 3 + 6t3, 0 ≤ t ≤ 5 Find an equation of the tangent to the curve at the given point by both eliminating the parameter and without eliminating the parameter. x = 6 + ln(t), y = t2 + 1, (6, 2) y = Find dy/dx. x = t 3 + t , y = 3 + t Find the distance traveled by a particle...
A) Use the arc length formula to find the length of the curve y = 2x...
A) Use the arc length formula to find the length of the curve y = 2x − 1, −2 ≤ x ≤ 1. Check your answer by noting that the curve is a line segment and calculating its length by the distance formula. B) Find the average value fave of the function f on the given interval. fave = C) Find the average value have of the function h on the given interval. h(x) = 9 cos4 x sin x,    [0,...
1.) Let f ( x , y , z ) = x ^3 + y +...
1.) Let f ( x , y , z ) = x ^3 + y + z + sin ⁡ ( x + z ) + e^( x − y). Determine the line integral of f ( x , y , z ) with respect to arc length over the line segment from (1, 0, 1) to (2, -1, 0) 2.) Letf ( x , y , z ) = x ^3 * y ^2 + y ^3 * z^...
1. Graph the curve given in parametric form by x = e t sin(t) and y...
1. Graph the curve given in parametric form by x = e t sin(t) and y = e t cos(t) on the interval 0 ≤ t ≤ π2. 2. Find the length of the curve in the previous problem. 3. In the polar curve defined by r = 1 − sin(θ) find the points where the tangent line is vertical.
1.) Let f(x,y) =x^2+y^3+sin(x^2+y^3). Determine the line integral of f(x,y) with respect to arc length over...
1.) Let f(x,y) =x^2+y^3+sin(x^2+y^3). Determine the line integral of f(x,y) with respect to arc length over the unit circle centered at the origin (0, 0). 2.) Let f ( x,y)=x^3+y+cos( x )+e^(x − y). Determine the line integral of f(x,y) with respect to arc length over the line segment from (-1, 0) to (1, -2)
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT