Katniss

I came across this while doing homework. The final answer I got was ln(1/2), while the quoted correct answer was -ln(2). Since my answer was marked as correct, it seems to imply that ln(1/2) = -ln(2). Can someone prove that they equal?

Thanks.

http://i.imgur.com/SEB2FF9.png

A 0.20 kg object, attached to a spring with spring constant k = 10 N/m, is moving on a horizontal

frictionless surface in simple harmonic motion with the speed 56.6 cm/s at equilibrium position. What is its speed at the instant when its displacement is 0.020 m?

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I'm not sure how to approach this problem. Obviously the variables are m = 0.20 kg, k = 10 N/m, v = 0.566 m/s, and x = 0.020 m. There's formulas for finding displacement, velocity, and acceleration for something in simple harmonic motion as a function of time, but I can't substitute the position formula into the velocity one because that leaves the amplitude and frequency variables unsolved.

There's conservation of energy, but that too would need to know the amplitude (max displacement).

I think I'm approaching this wrong. Help?

How would we represent the period of an object in simple harmonic motion (formula: T = 2 * pi * sqrt(m / k) ) as a function of mass so that there is a linear relationship?

This is a lab question where we have a vertical spring with an attached mass, causing simple harmonic motion. The only forces acting on the spring are the forces of gravity and the spring force. Thus, F = mg = -kx.

Either way, I'm at a loss for how I'd write a LINEAR equation for a function of mass that is plotted against the period.

Suppose a pipe's radius is decreased by 2 percent. How much will the flow rate be decreased by?

I figured that since the radius is to the fourth power in the flow rate formula, the answer would be 16 percent, but it's actually 8 percent. How is this obtained?

The question is: http://i.imgur.com/xX5Nhn5.png

Alternatively, for those who don't like links, the question is:

|> Find the derivative of the function:

|> y = ∫{5}{1 - 3x} u^3/(1 + u^2)

The answer is provided in these few lines of work: http://i.imgur.com/zvZjDtC.png

However, I can't figure out what they did. Can someone explain the steps they did in getting that answer?

For those who don't like links, the final answer is: (3(1 - 3x)^3)/(1 + (1 - 3x)^2)

Thanks in advance.

As the title says, Mr. Wickham tried to elope Miss Darcy in hopes of attaining her fortune. However, I'm under the impression that eloping her wouldn't allow him to acquire her dowry, unless I am mistaken? So why does he try and run off with her instead of legitimately proposing? He doesn't seem to have an qualms against marriage, since he weds Lydia once offered enough money.

Can you please explain in depth how that works? I'm assuming that e is Euler's number and i is the same imaginary number where i^2 = -1?

My textbook shows in an example without explanation that the derivative of log_a(e^-x) is -log_a(e). I tried to replicate that myself (my math linked below), but get the answer of -1/lna instead. Can someone show me step by step how the textbook arrived at -log_a(e) instead?

Thanks.

And my math:

http://latex.codecogs.com/png.latex?\dpi{150}%20{[...

(a) Find the magnitude and direction of the electric field at the position of the 2.00µC charge (in attached image). The charges are at the corners of an equilateral triangle. (b) How would the electric field at that point be affected if the charge there were doubled (i.e. if the 2.00 µC charge were replaced with a 4.00 µC charge)? Would the magnitude of the electric force on the charge at that position be affected?

And the image: http://i.imgur.com/YoHhr.png

I can't seem to figure out how I calculate the electric field at that position. Thanks for any help.

A proton is released from rest in a uniform electric field of 500 N/C. Calculate the speed of the proton after it has moved a distance of 0.500 m.

A rock is thrown up at such an angle that the maximum height is equal to the horizontal range. What angle was the rock thrown?

Please explain the process.

Thanks.

The record distance in the sport of throwing cowpats is 81.1m. Assuming the initial launch angle was 45 degrees and neglecting air resistance, determine the total time the projectile was in flight.

I can't seem to figure out the answer from the only two variables given (horizontal distance and angle). I'm more interested in the process than the answer. Thanks in advance.

Hi, I need to know how to find the inverse of a particular function. I know how to find the inverse of a function, but this particular question confuses me, and I'm not sure how to isolate the variable.

y = (e^x) / (1 + 2e^x)

It's a given that I'd have to multiply both sides by the denominator, which gives me

y(1 + 2e^x) = e^x

And that can be simplified to

y + 2ye^x = e^x

However, this is where I'm stuck. I'm not sure how to proceed from here. I'm looking more for how this is done than the answer to the equation.

Thanks in advance.

Back in high school, I was really good at trigonometric identities. Unfortunately, it's been two years since I've used them (nothing on the grade twelve level used trig identities) and now in university, I'm frankly stumped. While I remember the basics, I've run into a question I can't figure out. Please note that I'm more interested in the process, and will happily absorb any additional info about trigonometric identities (gotta bring the mind back up to snuff).

At any rate, the question is:

If sin(x) = 1/3 and sec(y) = 25/24, where x and y lie between 0 and π/2, evaluate the expression using trigonometric identities.

sin(x − y)

Thanks.