Question:

Using the method of Laplace transform. Solve the partial differential equation δu(x,t)/δt + u(x,t) = δu(x,t)/δx, u(x,0) = 6e-³x, which is bounded for all x >0; t>0; using the method of Laplace Transf

Using the method of Laplace transform. Solve the partial differential equation δu(x,t)/δt + u(x,t) = δu(x,t)/δx, u(x,0) = 6e-³x, which is bounded for all x >0; t>0; using the method of Laplace Transform.

Using the method of Laplace transform. Solve the partial differential equation δu(x,t)/δt + u(x,t) = δu(x,t)/δx, u(x,0) = 6e-³x, which is bounded for all x >0; t>0; using the method of Laplace Transform.

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5. [0/1 Points] DETAILS PREVIOUS ANSWERS ZILLDIFFEQMODAP11 2.2.010.MI. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Solve the given differential equation by separation of variables. dy 2y + 5)2 6x + dx 1 + c 36x + 42 X Need Help? Read It Master It

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5. [0/1 Points] DETAILS PREVIOUS ANSWERS ZILLDIFFEQMODAP11 2.2.010.MI. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Solve the given differential equation by separation of variables. dy 2y + 5)2 6x + dx 1 + c 36x + 42 X Need Help? Read It Master It

11:19 1 . 5G < III = < > Motion Along a Line Revisited Suppose an object moves along a linear path according to the velocity function v(t) = 3x2 – 2x, where v(t) is in meters per second. = - If the object's position at t = 1 is s = 5, what is the function

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11:19 1 . 5G < III = < > Motion Along a Line Revisited Suppose an object moves along a linear path according to the velocity function v(t) = 3x2 – 2x, where v(t) is in meters per second. = - If the object's position at t = 1 is s = 5, what is the function in terms of t that represents the position at any time t? 5 - si (3u² – 2 u) du 05+5 (3u? – 2u) du Si 01+S (3u² – 2 u) du 05 - Si (3u? – 2 u) du / 5 - 2 Next AA learning.k12.com < >

IR denotes the reaction of the body to some stimulus of strength x the sensitivity S is defined to be the rate of change of the reaction with respect to x. A particular example is that when the brightness x of a light source is increased, the eye reacts by

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IR denotes the reaction of the body to some stimulus of strength x the sensitivity S is defined to be the rate of change of the reaction with respect to x. A particular example is that when the brightness x of a light source is increased, the eye reacts by decreasing the area R (square millimeters) of the pupil. A formula used to model the dependence of Ron x is: R(x) = (40 + 24 x^(2/5))/(1+4 *2/5). The sensitivity can be found by the derivative 5 - dR/dx = R'(x). This derivative can be found by NWU o applying the Quotient Rule on the overall problem and the Power Rule in individual derivatives, such as R'(X) =[(1 +4x^(2/53"(24 (2/5***(-3/5) - (40 + 24 x^(2/5)44 1275) 13/5) / (1+ 4 x 2/5)) ^2, and then simplifying + o dividing the derivative of the denominator by the derivative of the numerator with the use of the Power Rule, such as R b) = (4 (2/5) > ^(-3/5)] / [24 (2/5) X^(-3/5). and then simplifying o dividing the derivative of the numerator by the derivative of the denominator with the use of the Power Rule, such as Rºbx) = [24 (2/5) x^(-3/5)] / [4 (2/5) x^(-3/5), and then simplifying o "cancelling the x^(2/5) in the original function, and then reducing R(x) = (40 +24)/(1 + 4) to 64/5, which is a constant having derivative R'(x) = 0