Homework Statement
I need to write a Matlab program that solves the following:
Use the Runge-Kutta Fehlberg Algorithm with tolerance TOL= 10^(-4) to approximate the solution to the initial-value problem:
y'=(y/t)^2 + y/t, 1<=t<=1.2, y(1)=1, with hmax=0.05 and hmin=0.02.
Homework...
Homework Statement
Let R and S be rings. Show that \pi:RxS->R given by \pi(r,s)=r is a surjective homomorphism whose kernel is isomorphic to S.
Homework Equations
The Attempt at a Solution
To show that \pi is a homomorphism map, I need to show that it's closed under addition and...
Homework Statement
Let J be the set of all polynomials with zero constant term in Z[x]. (Z=integers)
a.) Show that J is the principal ideal (x) in Z[x].
b.) Show that Z[x]/J consists of an infinite number of distinct cosets, one for each n\inZ.
Homework Equations
The Attempt at...
Homework Statement
Show that for any natural number K, there is an n large enough so that (2^n) > K.
Homework Equations
The Attempt at a Solution
K is a natural number -> the smallest possible K would be 0 (lower bound?) and the smallest 2^n is 1 when n = 0, and the upper bound...
Homework Statement
Prove that for any two integers a and b, a+b=b+a. You may use the face that this holds for natural numbers.
Homework Equations
The Attempt at a Solution
a=(x,y), b=(u,v)
x,y,u,v are natural numbers
a+b = (x,y)+(u,v) = (u,v)+ (x,y) = b+a
I'm not sure if my...
Homework Statement
Let S be a nonempty set and F a field. Prove that for any s_0 \in S, {f \in
K(S,F): f(s_0) = 0}, is a subspace of K(S,F).
K here is supposed to be a scripted F.
Homework Equations
The Attempt at a Solution
I don't know how to approach this problem. I know the three...
Homework Statement
Let V = {(a1,a2,...an): ai \in C for i = 1,2,...n}; Is V a vector space over the field of real numbers with the operations of coordinatewise addition and multiplication?
Homework Equations
I know that V is a vector space over C.
The Attempt at a Solution
I...
Homework Statement
A 5.00-m, 0.732-kg wire is used to support two uniform 235-N posts of equal length (see figure). Assume that the wire is essentially horizontal and that the speed of sound is 344 m/s. A strong wind is blowing, causing the wire to vibrate in its 7th overtone. What are the...
Homework Statement
While on a visit to Minnesota, you sign up to take an excursion around one of the larger lakes. When you go to the dock where the 1500-kg boat is tied, you find that the boat is bobbing up and down in the waves, executing simple harmonic motion with amplitude 20cm. The boat...
Homework Statement
A rocket is accelerating upward at 4.00 m/s^2 from the launchpad on the earth. Inside a small 1.50-kg ball hangs from the ceiling by a light 1.10-m wire. If the ball is displaced 8.50 degrees from the vertical and released, find the amplitude and period of the resulting...
Homework Statement
A 1.50-kg, horizontal, uniform tray is attached to a vertical ideal spring of force constant 185 N/m and a 275-g metal ball is in the tray. The spring is below the tray, so it can oscillate up-and-down. The tray is then pushed down 15.0 cm below its equilibrium point (call...
[SOLVED] Simple Harmonic Motion
Homework Statement
A cheerleader waves her pom-pom in simple harmonic motion with an amplitude of 18.0 cm and a frequency of 0.850 Hz. Find (a) the maximum magnitude of the acceleration and of the velocity; (b) the acceleration and speed when the pom-pom's...
Homework Statement
A box of negligible mass rests at the left end of a 2.00-m, 25.0-kg plank (see image). The width of the box is 75.0 cm, and sand is to be distributed uniformly throughout it. The center of gravity of the nonuniform plank is 50.0 cm from the right end. What mass of sand...
A wheel is rotating about an axis that is in the z-direction. The angular velocity w_z is -6.00 rad/s at t=0, increases linearly with time, and is +8.00 rad/s at t =7.00s. We have taken counterclockwise rotation to be positive.
a.) Is the angular acceleration during this time interval...
Your job is to lift 30-kg crates a vertical distance of 0.90 m from the ground onto the bed of a truck. How many crates would you have to load onto the truck in one minute for the average power output you use to lift the crates to equal 0.50 hp?
The equation that I used is: P_av = (delta W)/...
Homework Statement
A fireworks rocket is fired vertically upward At its maximum height of 80.0 m, it explodes and breaks into two pieces, one with mass 1.40 kg and the other with mass 0.28 kg. In the explosion, 860 J of chemical energy is converted to kinetic energy of the two fragments.
(a)...
An old oaken bucket of mass 6.75 kg hangs in a well at the end of a rope. The rope passes over a frictionless pulley at the top of the well, and you pull horizontally on the end of the rope to raise the bucket slowly a distance of 4.00 m.
So far, I have:
F = force exerted by me
s =...
James and Ramon are standing 20.0 m apart on the slippery surface of a frozen pond. Ramon has mass 60.0 kg and James has mass 90.0 kg. Ramon pulls on the rope to give himself a speed of 0.70 m/s. What is James's speed?
From what I understand, since there is an external force due to Ramon's...
A small marble rolls horizontally with speed v0 off the top of a platform 2.75 m tall and feels no appreciable air resistance. On the level ground 2.00 m from the base of the platform, there is a gaping hole in the ground. The hole is 1.50 m wide. For what range of marble speeds v0 will the...
According to a Scientific American article, current freeways can sustain about 2400 vehicles per lane per hour in smooth traffic flow at 96 km/h (60 mi/h). With more vehicles the traffic flow becomes "turbulent" (stop-and-go).
a) If a vehicle is 4.6 m (15ft) long on the average, what is the...