Find the length of the curve. y = 2 x 3 / 2 ,  from …

Find the length of the curve. y = 2 x 3 / 2 ,  from  x = 0  to  x = 5 4 {“version”:”1.1″,”math”:”y=2x^{3/2}, \text{ from } x=0 \text{ to } x=\frac{5}{4}”} Note:  L = ∫ a b ( 1 + ( f ′ ( x ) ) 2 ) d x {“version”:”1.1″,”math”:”L=\int_a^b\left(\sqrt{1+(f'(x))^2}\right)dx”}

Consider the initial value problem (IVP) with initial condi…

Consider the initial value problem (IVP) with initial conditions y(0) = y'(0) = 1 and y”(0) = y”'(0) = 0. (a) Write this as a system of four 1st order ordinary differential equations (ODEs). [9 points] (b) Change (any) one feature of the ODE to convert it into a nonlinear ODE. [2 points] (c) Change the initial conditions to (any) boundary conditions and convert the IVP to a boundary value problem (BVP). [4 points]

The slope fields f(t, y) for two IVPs y’ = f(t, y) are shown…

The slope fields f(t, y) for two IVPs y’ = f(t, y) are shown below.   (a) Trace (approximately) the solution on both figures if the initial condition is y(t = 0) = 0.1 (indicated by the star). If you are taking the quiz online, then write down the approximate values of y(t) at four different points in the domain 0 < t < 10 [9 points] (b) For which one of the two problems would a method like RK4 (classical explicit 4th order Runge-Kutta) be more appropriate? Why? [3 points] (c) What method would you recommend for the other problem? Why? [3 points]

Modern societies are thought to create a toxic, “obesogenic”…

Modern societies are thought to create a toxic, “obesogenic” environment for eating. Unfortunately, the rise of this obesogenic environment has been paralleled by a significant decline in physical activity (Corsica & Perri, 2012).(Source: Psychology. Themes and variations. By Wayne Weiten. 10th edition. 2017. Boston, USA. Cengage Learning.Chapter 9 Motivation and emotion. Page 311)The term obesogenic has been formed by combining forms, namely OBESO+GENIC. What does this mean?

What is the main idea in the Extract below?  As always, acro…

What is the main idea in the Extract below?  As always, across the world, the most vulnerable have borne the brunt of this latest health crisis. COVID-19 has simply further highlighted and exacerbated existing inequalities. Redressing health disparities cannot be effectively achieved during times of crisis, but instead requires longer-term sustained action: through policies and interventions that tackle key social determinants. (Taken from an article titled “A stronger and more united Africa?” Written by Marisa Casale, in Africa in Fact, page 17. Issue 55, October-December 2020.)