Graphing orthogonal trajectories
WebFind the orthogonal trajectories of the family of curves. Use a graphing device to draw several members of eachfamilyonacommonscreen.1 y2 = kx3 First, we find the slopes of the given family. y2 = kx3 2ydy= 3kx2 dx 1 2ydx · dy= 1 2ydx ·3kx2 dx dy dx = 3kx2 2y From y2 = kx3 we get k= y2 x3. Substituting, dy dx = 3· y2 x3 · x2 2y dy dx = 3y 2x WebSince the orthogonal trajectories should have perpendicular tangent lines, their slopes will be negative reciprocals of the above. In other words, the orthogonal trajectories of …
Graphing orthogonal trajectories
Did you know?
WebMay 10, 2024 · Orthogonal Trajectories Consider two families of curves, circles and lines as shown in the figure. If you look at the intersection points, you’ll notice that these … WebJan 12, 2024 · Orthogonal Trajectories The only problem that arises with the previous approach is that non-linear functions have curves and changing slopes. To fight this, we need to shift from a macro perspective to a …
WebPart A. Find the orthogonal trajectories of the family of curves. (Use C for any needed constant.) x2 + 2y2 = 17k2 Part B. Find the orthogonal trajectories of the family of curves. (Use C for any needed constant.) y2 = 7kx3 This problem has been solved! You'll get a detailed solution from a subject matter expert that helps you learn core concepts. WebFind the orthogonal trajectories of the family of curves. Use a graphing device to draw several members of each family on a common screen. x^2+2y^2=k^2 x2 +2y2 = k2 Explanation Verified Reveal next step Reveal all steps Create a free account to see explanations Continue with Google Continue with Facebook Sign up with email Already …
WebQuestion: Find the orthogonal trajectories of the family of curves. (Use C for any needed constant.) x^2 + 2y^2 = 5 k^2 Use a graphing device to draw several members of each family on a common screen. This problem has been solved! See the answer Show transcribed image text Expert Answer 100% (11 ratings) WebNow I have a differential equation, and the orthogonal trajectory should be represented by the negative reciprocal. d y d x = − 5 2 x y ∫ y d y = ∫ − 5 2 x d x y = − 5 4 x 2 + C This …
WebVector Orthogonal Projection Calculator Vector Orthogonal Projection Calculator Find the vector orthogonal projection step-by-step Matrices Vectors full pad » Examples The …
honey drip font freeWebExample 2. Find the orthogonal trajectories to the family of curves y= cxn, where n is a fixed positive integer and can arbitrary constant. Solution. If n= 1, the curves are the family of rays from the origin, so the orthogonal trajectories should be the circles centered at the origin – this will help check our work. honeydrippers rockin at midnight youtubeWebOct 21, 2024 · Find the orthogonal trajectories of the family of curves. y 2 = k x 3 Take the derivative, d d x 2 y = k 3 x 2 d y d x 2 y k 3 x 2 = d y d x Bring in k 2 y y 2 x 3 3 x 2 = d y d x Simplify 2 y x 3 k 3 x 2 y 2 = 2 x 3 y … honey drippingWebFind the orthogonal trajectories of the family of curves. Use a graphing device to draw several members of each family on a common screen. y = k/x Solution Verified 4.5 (9 … honey dripping clipart black and whiteWebAug 28, 2024 · You have eliminated c in the fourth step to get the ODE for the orthogonal trajectories. Finally, in solving the last ODE you cannot use the same constan c. Use spmething else like k. So the x 2 + 2 y 2 = k … honey drip coffeeWebFind the orthogonal trajectories of the family of curves y= cx3 c x 3 Graph some examples of both families of curves. You can use Wolfram Alpha or any other graphing tool to create the... honeydrippers rockin at midnight wikiWebThe common approach for determining orthogonal trajectories is based on solving the partial differential equation: where the symbol means the gradient of the function or and … honey dripping art