UNSOLVED CaLCulUS PROBLEM....NeeD hElP DeSPeRAteLY!!!?
ce is forming on a pond at a rate give by (dy/dt)=k√t, where y is the thickness of the ice in inches at time t measured in hours since the ice started forming, and k is a positive constant. Find y as a function of t. The ANSWER IS y= 2k^(3/2)/3 Please show each steps to get this answer!!!~~~
Help With Differential Equations?
This is a separable equation. dy/dx =- (cos(x))^2 * cos(y) dy/cos(y) = (cos(x))^2 dx sec(y) dy = (cos(x))^2 dx ln(sec(y) + tan(y) = (1/2)*[cos(x)*sin(x) + x - c] where c is the constant of integration. sec(y) + tan(y) = exp((1/2)*[cos(x)*sin(x) + x - c]
Desperately need help!!!!! Second Order Linear Differentials! Please!?
When F = 0, you have my" + cy' + ky = 0 Assume y = e^(wt), you have mw^2 e^(wt) + cw e^(wt) + k e^(wt) = 0, so mw^2 + cw + k = 0 w = (- c plus or minus sqrt(c^2-4mk))/2m In the case at hand, c^2 - 4mk = (64-80) kg^2/s^2, so the sqrt is 4i kg/s. Then y = e^(-ct/2) [A e^(it/4) + B e^(-it/4) ] With a little fiddling around, this becomes y = e^(-ct/2) [ A cos(t/4) + B sin(t/4) ], though "A" and "B" have changed. This is the general form of the solution for t > pi/2; we can't use the initial values just yet. When t < pi/2, we have F = 50 Newtons, so we need to add to the "homogeneous" solution above a "particular" solution, probably a constant. If it's a constant, its derivatives will be zero and we'll have ky = 50 N, so the constant part of the solution is y = 0.625 meters. All right, so for t < pi/2, we have something like y = (-ct/2) [M cos(t/4) + N sin(t/4)] + 0.625 meters. You can now use the y(0)=0 and the y'(0) = 0 to evaluate M and N. I leave that part to you. Once you have M and N for t < pi/2, you can run the time forward to t=pi/2 and see what y(pi/2) and y'(pi/2) would be. Use these two values to find the "A" and "B" above, the coefficients of the sine and cosine terms for t > pi/2. DO check my algebra, I went kind of fast.
HARD CALcUluS pRoblem. NEED HELP DESPERATELY..?
dy/dt = k√(t) This is a differential equation. To find original, perform integration. dy = k√(t) dt ∫ dy = ∫ k√(t) dt y = k (2/3)(t)^(3/2) + C y = (2k/3) t^(3/2) + C ; the constant C here is yo yo is the initial thickness of the ice y = (2k/3) t^(3/2) + yo
Desperately need help with this physics problem!!! i will give high ratings!!! Please help!!?
OK, give "best answer". The moment of inertia of a particle with respect to an axis is just the product I=mXr^2 where r is the distance to the axis. It is also important to know that moments of inertia are additive. The distances (squared) to the origin for each mass are (use Pythagorean thm): r1²=1+1.5²=3.25 r2²=9+2.25=11.25 r3²=9+1=10 r4²=.25+.25=.5 so the corresponding I's are: I1=18X3.25=58.5 I2=27X11.25=303.75 I3=9X10=90 I4=37X.5=18.5 now add all to get I=58.5+303.75+90+18.5=470.75 this is answer to (a). ======================================... Now (b) To find the position with respect to point P all you have to do is to substract the point (-2,2) from each point. The distance squared is going to be the sum of the squares of each number, i.e (1,1.5)-(-2,2)=(3,.5) so distance squared to P for M1 is just: 9+(.5)²=9.25. You do the same for the other trhee points, multiply by the masses and add.
Verify that the function is an explicit solution of the given differential equation...?
dy/dt = (6/5)(20 e^(-20 t) = 20 [(6/5) e^(-20 t)] = 20[ (6/5) - y] = 24 -- 20 y ==> dy/dt + 20 y = 24
I need help with these physics problems. Show me how to set up the equations and work them out.?
1- The coefficient of sliding friction on concrete is 0.30 What weight of steel can be pulled across a concrete floor by a winch with a 450 lb capacity? 2- A sled weighing 3350 N is pulled over snow at uniform speed by exerting a force of 1200 N What is the cofficient of friction? 3- What is the net force including its direction of the following; 175 N to the left; 234 N to the right; 75 N to the right; 225 N to the left; 45 N to the right? 4- A cyclist and her bicycle have a combined mass of 75.0 kg. If the frictional force acting aganist the motion of the bicycle is - 23.5 N, what force must the cyclist apply to maintain a constant velocity? 5- The cyclist and her bicycle ( combined mass of 75.0 kg.) apply a force of 34.2 N. If the frictional force is still -23.5 N, what will be the acceleration of the bicycle? 6- A train engine is able to exert a 175,000 lb. pulling force. The coefficient of friction is 0.40 How many cars wieghing 45,000 lbs. each can the engine pull?
Which of these are more useful for a theoretical physicist: differential equations, vector or tensor calculus, linear algebra, probability theory?
I am not sure this question has an objective answer.From a historical point of view, Newton was the father of modern physics and among his most influential contributions was the development of calculus*. The problem is that differential equations are a product of calculus, and if you have a calculus problem with more then one variable it becomes a linear algebra problem. So calculus, linear algebra and differential equations are all related.Regarding probability theory, well if you have a complex system with many particles, one that can not be solved analytically mostly because you don’t have all the initial conditions you have to use probability.If I’ll have to choose, I’ll chose calculus (which essentially combines the first three options) and then probability theory.*Gottfried Leibniz developed calculus desperately more or less at the same time