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  1. pka

    Calculus II

    Please post a readable question.
  2. pka

    How do I show the following sequence is bounded above ?

    Do you know about the harmonic numbers H_n~? and the the digamma function. Here are two webpages One & Two. The nth harmonic number is {H_n} = \sum\limits_{k = 1}^n {\frac{1}{k}} and your sequence turns out to be a_n=H_{2n}-H_n On the two references, you can find links to other research do by...
  3. pka

    Still Confused

    Of course I do not speak for Prof. Peterson, but \sqrt{25}=5 is one number. Now twenty has two square roots they are \pm\sqrt{25}=\pm5 For this prof in his complex variables classes this is what we use: "we add(enlargement of the reals) one number \mathit{i} that a solution for the equation...
  4. pka

    The triangle midsegment theorem

    Here completely different way to go. Say the vertices of the triangle are : A:\,(x_A,y_A),\,B:\,(x_B,y_B),~\&~C:\,(x_C,y_C) \begin{cases}\dfrac{x_A+x_B}{2}=-2 &,\quad \dfrac{y_A+y_B}{2}=0 \\\dfrac{x_A+x_C}{2}=0 &,\quad \dfrac{y_A+y_C}{2}=2 \\\dfrac{x_C+x_B}{2}=-4 &,\quad \dfrac{y_C+y_B}{2}=1...
  5. pka

    Arithmetic Laws

    You may find this page interesting.
  6. pka

    How to demonstrate this inequality

    |a-b|=|a+(-b)|=|(a-c)+(c-b)|
  7. pka

    Geometric Sequences

    Have you found the common ratio, r~? That is the terms of the sequence are g_n=60\cdot r^n,~n=0,~1,~2,\cdots. In your study have you learned limits like \mathop {\lim }\limits_{n \to \infty } \,{r^n} = ?
  8. pka

    Area of a trapezoid in triangle.

    Do you know the area of a trapezoid? Look here Now what Prof. Peterson calls "midline" is the upper base equal in length to half the other base. the midline also determines the height. Now post your work.
  9. pka

    Is this right?

    a^5b^{-\tfrac{1}{2}}(a+b)=a^6b^{-\tfrac{1}{2}}+a^5b^{\tfrac{1}{2}}
  10. pka

    Lottery probability question

    I am read this as if one can only one the four possibilities on any the five numbers on one ticket. So that is the sum of the four probabilities. that is winning exactly once.
  11. pka

    Ayan and Naihan are twins. Ayan is the elder by 13 minutes. If Naihan was born on January 1, 2007 at 0005 hours, What is Ayan's date and time of birth

    I hope that you read the posting guidelines. If you post your work it helps us help you. Now I assume that 0005 hours is five minutes after midnight on New Year's day. So work out 13 minutes before.
  12. pka

    Lottery probability question

    Because these events are mutually disjoint and independent the probabilities are additive. So apply that idea to both of these. You must post your work so we are allowed to help you understand.
  13. pka

    What are the polar coordinates of (2√3, 2)?

    This is the most important question: "What does your textbook/instructor say about polar coordinates?" As I said above I use the range -\pi<\theta\le\pi you may find this useful. For any point (x,y) where x\cdot y\ne 0 \arg(x , y) = \left\{ {\begin{array}{{ll}} {\arctan \left( {\frac{y}{x}}...
  14. pka

    What are the polar coordinates of (2√3, 2)?

    There is no hard and fast rule. But it is my preference that yours is the one that I would expect if I were your lecturer. The reason being that the form (r,\theta) where r>0~\&~-\pi<\theta\le \pi. You see r is the absolute value of the number and \theta its identifies location. Note some...
  15. pka

    Some radian cutting circles in parts question, please help!

    But that has absolutely nothing to do with the solution. This does: This image does The answer to the question is the area of the circle minus the area of the circular segment(green area) subtracted from the area of the circle.
  16. pka

    Some radian cutting circles in parts question, please help!

    I wonder if Prof Peterson could tell us about his solution? What did I miss?
  17. pka

    Equality of quantities

    Dear Ryan$, you really need to enroll in a course that may go be many different names but it is philosophical logic. I think that I remember that you are in a area with several higher education units each of which has such a course. At the very least get yourself a copy of Copi's Symbolic Logic...
  18. pka

    Semi-random team assignment

    I would like to help with this. But I simply do not understand the setup. What does "will play in 7 rounds of 6 games" mean? If there are thirty-six players to be placed on teams of three players each then that is twelve teams and there are \dfrac{36!}{(3!)^{12}(12!)}=356765771022012352000000...
  19. pka

    2 proof questions help

    1) Suppose that \begin{align*}\sqrt{m^2-n^2}&=m-n \\m^2-n^2&=m^2-2mn+n^2\\2mn&=0 \end{align*} What does that tell you about m\text{ and }n~? Is that a contradiction? 2) The roots of x^2-2bx+c=0 are x=\dfrac{2b\pm\sqrt{4b^2-4c}}{2}\text{ implies }x=b\pm\sqrt{b^2-c}. To have two real roots we...
  20. pka

    Discrete Mathematics proof question help

    I have wondered if promitheus were thinking of what Copi calls conditional proof? But that is for arguments in which the conclusion is itself a conditional statement. Speaking of Copi, in most of his texts he stresses these two statements. 1. A false statement implies any statement. 2. A true...
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