Recent content by davedave

Homework Statement A bomb is dropped from an airplane at an attitude of 14400 ft. The plane is moving at 600 miles per hour. How far will the bomb move horizontally after it is released from the plane? Homework Equations I use the formula involving the distance traveled by an object with no...

Homework Statement 4 cards are dealt from a 52-card deck. How many hands contain 2 distinct pairs? Homework Equations This is an expression I come up with 13C1x4C2x12C1x4C2. The Attempt at a Solution This is how I approach it. From the 13 ranks, I choose 1. In this rank, I choose 2 cards from...

The speed of car A is 72.2 km/h while the speed of car B is 53 km/h. If car B is now 48 km ahead of car A, how much time is needed for car A to catch up with car B? car A let x = the current position of car A speed = 72.2 km/h time = x/72.2 hours car B let x + 48 = the current...

yes 9cm is a typo. It should be 9m. I've just let my 3rd friend check my solution. He said my answer is wrong. What went wrong in my solution?

At high tide, the average depth of water in a harbour is 25m and at low tide the average depth is 9cm. The tides in the harbour complete one cycle approximately every 12 hours. The first high tide occurs at 5:45am. A cosine function that relates the depth of the water in the harbour to the time...

Here is a very difficult cubic polynomial. x^3 - x - 2 = 0 I am wondering whether it is solvable or not. Please think about it.

A special fastener is used to anchor three cables to an east-facing wall in a factory. One cable applies a load of 300N straight down. The second cable applies a load of 400N, horizontally toward the south. The third cable applies a load of 500N toward the north, but angled at 30 degrees from...

In the game of bridge, four players are dealt 13 cards each from a well-shuffled deck of 52 playing cards. (a)What is the probability that one of the players is dealt all the spades? (b)What is the probability that one of the players holds a hand that is made up of only one suit? (a)...

Because I cannot draw a picture in this problem, I will do my best to describe it in words. This problem is about a circular railway track. The diagram that goes with it shows one of the 15 curved pieces. Its width is MEASURED 1 cm and its arc length of the inner edge is MEASURED 30 cm...

This is not a homework question. I just try it for enjoyment. Let L = log to the base x of (yz) M = log to the base y of (xz) and N = log to the base z of (xy) This is how I do it without much luck. I put all the equations in exponential form yz = x^L xz = y^M xy...

let's consider the following simple example with no ambiguity. To evaluate (-2)^(1/2), we can use simple concepts in applied complex analysis. it is equal to 2^(1/2) * e^((pi/2) i (2k+1)). if k=0, i square root (2) if k=1, -i square root (2) This one is straightforward since we take...

There is a typo in the solution that I write down on the posting. It should be given in terms of x NOT t. sorry about that. ie, y = the square root of 1/(1-e^(2x)) Back to my issue. By setting dy/dx = 0, we should get three steady state solutions. y=0, y=1 or y=-1 Is there a way...

To find the steady state solution, I set dy/dx=0 in the differential equation dy/dx=y(y-1)(y+1) So, y=0, y=1 or y=-1. The book says the only answer is y=0. Why are y=-1 and y=+1 rejected as steady state solutions?

consider and determine the steady state solution of the differential equation below. dy/dx = y(y-1)(y+1) We can separate the variables, break the integrand into partial fractions, and integrate the fractions easily. Solving gives y = the square root of 1 / (1 - e^(2t)). as t goes to...

Here is the question. Find the steady state solution of the differential equation below. dy/dx = tan(x^2) What makes this one difficult is that the tangent has no elementary function. Can anyone explain how to find the steady state solution? Thanks.