Ok. I think I'm over thinking this. v^2/2=2/3*s^3+c, so v^2=4/3*s^3+2c, and then v(s)=sqrt(4/3*s^3+2c), and since v(0)=1, sqrt(2c)=1, therefore 2c must=1. Is that the right way to think about this?
Again sorry, I know these are really easy concepts we're dealing with here. Just want to make...
Homework Statement
Okay I've basically solved this problem... but I need some clarification.
The problem is "The acceleration of an object is given as a function of its position in feet by a=2*s^2 ft/s^2. When s=0, it's veloctiy is 1 ft/s. What is the velocity of the object when s=2 ft...
Wanted to brush up on my diff equations a bit. I have kind of forgotten how to determine phase plane stability in systems of differential equations.
Homework Statement
Solve linear systems. Determine whether the critical point (0,0) is stable, asymptotically stable, or unstable.
dx/dt=2x...
Working on some DE homework and need a tad bit of guidance. I got fairly far, I'm just wondering what the next step is.
Homework Statement
The rate of change of an alligator population P is proportional to the square of P. The swamp contained a dozen alligators in 1988, two dozen in 1998...
I don't know why I'm so hung up on this question.
For the x component for instance,
it the curve is t^3-1, the slope of the tangent is 3t^2. If we're talking about the slope of the tangent at 26 in the curve, why wouldn't we plug in 26 for t in dx/dt?
What is the next step I should...
I substituted x and y into my derivatives to find the slope of the that component of the line at that point. I then multiply it by t, and add x and y for intercepts or to start from the origin.
Homework Statement
Find the parametric equation for the line tangent to the curve:
x=t^3-1, y=t^4+1, z=t
at the point (26, 82, 3).
Use the variable t for your parameter.
Homework Equations
The Attempt at a Solution
dx/dt=3t^2, dy/dt=4t^3, dz/dt=1
I got then that...