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  1. K

    Laplace transform of phase-shifted sinusoid

    Homework Statement Find the laplace transform of f(t)=sin(4t+\frac{\pi}{3})u(t). [Broken] Uploaded with Homework Equations Definition of laplace transform, and properties...
  2. K

    Given a 3D vector, how to find the angle it forms with a plane?

    Say I'm given a random 3-dimensional vector, pointing from the origin. How can I find the angle it forms with a plane defined by two other vectors?
  3. K

    Partial sum of n^2

    Is there a nice formula for calculating the partial sum of the series n^2 from 1 to k?
  4. K

    Help! I'm in college and have forgotten everything!

    Hi. I am in college and have forgotten everything about how to solve indefinite integrals. Even very simple problems give me trouble, such as: int( y^3 * sqrt(2y^4 - 1) ) dy So how in the world do you find the answer? The Antiderivative? Please go through this step-by-step, I need a...
  5. K

    Volume of rotated graph

    Mind helping me figure out how you actually do this then?
  6. K

    Volume of rotated graph

    Hi. There are a few problems on my homework that involved the volume of a rotated solid. I do not know how to do these, but I'm trying to devise a method. This is what I figure: \int_{a}^{b} f(x) dx is the area under the graph. \frac {\int_{a}^{b} f(x) dx} {b-a} is the average height. This...
  7. K

    Related rates of change are killing me!

    Hi. I am getting absolutely embarassed by these related rates problems. Here is one that I simply keep getting wrong: The volume of an expanding sphere is increasing at a rate of 12 cubed cm per second. When the volume is 36\pi, how fast is the surface area increasing? V=\frac...
  8. K

    Present value

    No. I am suggesting that the second installment would be $2400 plus interest for one year on the remaining $4800. The big question here is, why is your rate -0.06? Your rate should be positive, a negative amount would indicate the payment 'decreasing continuously'.
  9. K

    Present value

    Is the $2400 really $2400 plus interest? Also double-check the "now" amount, becuase even three payments of $2400 without interest is $7200. The second payment would be 2400 + interest for one year on the remaining 4800: A=4800 \cdot e^{6*2}
  10. K

    Two curves with two shared tangents

    No, I don't think I can. But that seems to make a lot more sense than the L(x) stuff. I still don't see how to solve either of those methods. The first method you described is essentially what I have been trying for. The tangent equation for f(x) (the one you described was actually g(x))...
  11. K

    Two curves with two shared tangents

    Could you go through that approach? I sort of understand your logic, and sort of don't. I don't understand what L(x) is doing when those two equations can be simplified to g(x)-f(x)=0.
  12. K

    Does this negative sign even matter in sin(x)?

    Definitely leave it in there. For the equations you deal with right now, it might be removable, but you don't want to develop bad habits for when it does matter.
  13. K

    Does this negative sign even matter in sin(x)?

    Well, sin(x) is different from sin(-x). There are some problems where it will make a difference and some where it won't.
  14. K

    Two curves with two shared tangents

    I'm stuck on this problem. I am hoping someone can walk me through it or get me past my choking point. The problem states: Two equations have two shared tangent lines between them. Find the equations of these tangent lines analytically. g(x)=x^2 f(x)=-x^2+6x-5 The first step I took was to...