Recent content by johnsholto

So the integral must be √3 *arctan(√3 *(x+3))+C. Which would give us y=-1/√3 *arctan(√3 *(x+3))+C

I did try that, but I don't know how to integrate 1/x^2+6x+12 easily.

Homework Statement I need to solve for a general solution of the following equation: (x^2+6x+12)dy=y^2dx 2. The attempt at a solution I tried using the method for seperable ODEs and got the following: ∫(x^2+6x+12)dy=∫(y^2)dx (x^2+6x+12)y=(y^2)x+C (x^2+6x+12-C)/x=y

A spring catapult consists of a massless spring and a massless cup. An object of a certain mass is loaded into the cup, the spring is extended to a length L, and the object is launched horizontally. What is the speed of the object? s is the natural length of the spring, L is the length...

Punishment. Alas, I just remembered small angle approximation. cosA = 1-(A^2/2) cosA = R/R+100 R ≈ 8000000 I did not enjoy this problem.

I tried it with: AB^2 + R^2 = (R+100)^2 AB = (R+100)sinA But i can't solve the equation without the calculator.

A person stands on a cliff overlooking the sea. He is 100m above the sea level and he observes the horizon to be 5mrad below the local horizontal. How do you calculate the radius from this information without using a calculator? Trigonometry I am guessing, but I need a better hint.

What about angular momentum? mvr=mVR 50*4*10^10=x*10*10^10 x=20

A comet orbits a star. At its closest approach (r=4*10^10 km) it has a speed of v=50 km/s. How fast is the comet at its maximum distance (R=10*10^10 km)? Could someone verify my results? F=GMm/r^2=mv^2/r f=GMm/R^2=mV^2/R F/f = R^2/r^2 = Rv^2/rV^2 -> R/r = v^2/V^2 R=2.5r -> 2.5r/r...