H1. Consider the scalar differential equation d Define the potential V(x) by Use the chain rule to show that x(t) = f(x). dt dV (x) dx = -f(x). dV(x) dx dV(x(1)) ≤ 0. H2. Let x* be an equilibrium solution of Eq (2). First, show that x* is an extrema of V by calculating (2) -||x=x* = 0. Next, if x* maximizes V, is x* locally stable or unstable? Finally, if x* minimizes V, is x* locally stable or unstable?

How do I find the relative extrema of x3 - 27x?

Please answer number 3, please show work. Show the formula used, etc etc.

An important advance in ecological research is the Theory of Island Blogeography, which demonstrates a relationship between the size of islands and the number of species of different amphibians that can be found in the islands, The scatterplot of number of species versus island area (in thousands of square miles) is nonlinear. The graphs below show the results of two different transformations of the data. Model I plots the square of the number of species against area. Model II plots the square root of the number of species against area. Linear regression analyses are provided below. Model II: VNumber of species vs. Area Model I: (Number of Species)? vs. Area 10 8000 9. ecies)

Flying twice as farA flight from Los Angeles to ABQ is about 2 hours but is 670.2 miles.A flight from San Jose to Chicago is 4 hours but is 1859.0 miles.Can anyone explain why the travel time from San Jose to Chicago is notlonger and closer to 5.75 hours?If the distance increase by 2, shouldnt the time increase by a factorof 2 as well?1. Write a linear model for this question. Takeoff and landing will take a fixed amount of time. Actualtravel in the air will take time proportional to the distance traveled. Think about which of thevariables (time and distance) is the independent variable, and identify the slope and intercept withtheir units.2. Use the data in the quotation to estimate the two constants in your linear model.

Please answer this question and show all work and steps to how the answer was found.

Table of results Variable Intercept Revenue Efficiency Coefficients 11.680464 0.6999226 0.8029396 Print Standard Error 7.132097 0.321328 0.077201 T Statistic 1.64 2.18 10.40 Done p-Value 0.1048 0.0319 <0.0001 X ons of dollars, as a measure of nonp sure of nonprofit fundraising efficienc haritable services. Both variables X₂ d in the accompanying table. Comple

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Can you guys help me on this? Thank you!

Home | bartleby c.edu/med/ti/view.php?id=3173015 A = (71) Ex: Identify the initial Library MyESC Faculty & Staff Policies & Resources Help ▼ 22SU1-MATH-1005-A01) Contemporary Mathematics / Module 6: Growth Modules / Quiz: Module 6 Growth Models 204 1+11e-0.65t deer A herd of 17 white-tailed deer is introduced to a coastal island where there had been no deer before. Their population is predicted to increase according to (b) What is the carrying capacity for this model? years. Operoo where A is the number of deer expected in the herd after t years. (a) How many deer will be present after 6 years? Round your answer to the nearest whole number. Orection Holn X - Video 1 in 2022SU1-MATH-1005-A0 X (c) How many years will it take for the herd to grow to 50 deer? Round your answer to the nearest whole number. Video 2 Sy 24600(1.01