1. A

    Two positive series with terms in a fraction

    $$\mathop{\mathrm Σ}_{n=1}^\infty \frac{1+1/2+...+1/n}{n}$$ I have two series in a fraction and I do not understand how to solve this problem.I see that the numerator is a Harmonic series but that doesn't help me a lot.I tried doing the comparison test and I could only compare this series to...
  2. N

    Optimization Problem with Exponential Form (double terms)

    Hello, Could anybody help me with this optimization problem? I want to minimize sum(s=1,S) a_s * exp(b_s*x_s) + c_s * exp(d_s*x_s) subject to the constraint: sum(s=1,S) x_s = A I am supposed to find x_s which makes the statement minimized. a_s, b_s, c_s, d_s, and A values are constants in...
  3. idontknow

    Acceleration in terms of time

    Can anyone help? Find s(t)\; if a(t)=\frac{5}{(1+t)^2 }, \; \; t\in [0,10]. Answer in the pdf is s(t)=5t-5\ln(t+1)+10. (using a=v’=s’’) v(t)=\int a(t) dt =c_1 - \frac{5}{t+1} , how to find c_1 ? Pdf says v(0)=0 then c_1=5. s(t)=\int v(t) dt =5t-5\ln(t+1) + c_2 \; , how to find...
  4. P

    Can someone help me with some accounting terms ?

    I have confusions about vouchers and subsidiary books . Are Accounting Vouchers same as Subsidiary Books ? Thanks
  5. Z

    Please explain to me in simple terms what these circle intersections are all about.

    So, say you got 4 circles intersecting this way: Now, I am looking for two things: A proof that each part of the circle which is in an intersection is 1/4 the size of the whole circle's circumference The exact area of the non-shaded region. Now, in my search for finding the answer to...
  6. B

    How can I solve Logarithmic equations with multiple depented terms?

    I know how to solve this: log_2(x) + log_2(x+2) = 2 But how do I solve this: 8n^2 - 64nlog_2(n) = 0 If I try to get rid of the log: 64nlog_2(n) = 8n^2 \Leftrightarrow 2^{64nlog_2(n)} = 2^{8n^2} \Leftrightarrow 2^{log_2(n^{64n})} = 2^{8n^2} \Leftrightarrow n^{64n} = 2^{8n^2} Dead end...
  7. pmms12585

    Request for help with tricky Riccati DE with exponential terms.

    Hi all, I am developing a model that requires me to derive the solution of a rather tricky Riccati DE, and I am having a devil of a time with it and am beginning to wonder if there is even a closed-form solution. Anyhow, the equation is \frac{dE}{dt} = cB_{t} + bE_{t} + aE_{t}^{2}...
  8. L

    Fermat's Last for >3 terms, n>0

    Fermat's Last Theorem states that no three positive integers a, b, and c satisfy the equation a^n + b^n = c^n for any integer value of n greater than 2. Is there a solution for four or more such terms with an integer n>0?
  9. H

    Variable radius of curvature in terms of sagitta

    How can I express a radius of an arc R in terms of its sagitta H assuming that: (a) the arc follows a locus of a circle with a variable radius, (b) arc length S is constant. I’m interested in the region where the included angle of the arc is between but not equal to 0° and 4°.
  10. L

    Rational terms sequence

    Let $(a_n)$ be a sequence where all rational numbers are terms (and all terms are rational). Then A) no sub sequence of $(a_n)$ converges. B) there are uncountably many convergent sub sequences of $(a_n)$. C) Every limit point of $(a_n)$ is a rational number. D) no limit point of $(a_n)$...
  11. A

    simplification of the integral terms

    Hi, I would like to know whether someone can explain the simplification which follows in the image, thanks!!
  12. J

    Express in terms of a and b

    Hi, Could I possibly ask for a step-by-step solution to the following question, please? a = 3^x b = 3^y Express in terms of a and b, giving your answer in root form where appropriate. a) 3^x+y b) 3^2x-y c) 3^3y-0.5x Thanks in advance.
  13. L

    Series sums' terms choice

    Consider: Sum=1-1+1-1+1-1+1-1...=undefined; Or does Sum=(1-1)+(1-1)+(1-1)+(1-1)...=0 Please give me other simple examples for infinite summation series where choosing the gathering of terms seems to change its ambiguous outcome.
  14. J

    Integrals in terms of I

    Hi guys, can you help me with the following: I=Integral (upper bound: pi/24 lower bound: 0) tan^10(4x)sec(4x)dx Express the value of: Integral (upper bound: pi/24 lower bound: 0) tan^12(4x)sec(4x)dx in terms of I.
  15. L

    Generalized Fermat equation, N+1 terms, power N

    (a1)^N+(a2)^N+...+(aN)^N=(a0)^N Is there at least one solution to this equation for every natural, nonzero N?
  16. M

    Solving for x in terms of y; y = x^5 - x^8

    Hello, I am curious, is there a way to rearrange this in terms of y? Is there a rule for determining when an equation cannot be rearranged if this is not the case. Thank you
  17. H

    Multiplying terms of odd functions

    Hi :) We had to find out whether it's true/or false that multiplying terms of two odd functions will equal to a term of an even function. The solution was f(-x)*g(-x)= -f(x)*(-(g(x)) = f(x)*g(x) I don't understand how f(-x) becomes -f(x) and g(-x) becomes (-(g(x)). Thank you for your help.
  18. S

    A in terms of B in right triangle with perimeter 20

    I have to find the sides of a right triangle so that its area is maximum possible. 20 meter perimeter is given. I have 2 equations A=ab/2 a+b+sqrt{(a^2) +(b^2)} =20 I try to simplify the 2nd equation to get a or b by itself but I can't. I end up with 200 + ab = 20(a+b) I don't know what...
  19. S

    Expressing x in terms of y: y³-xsiny+y²/x=8

    Hello, How do I deal with this here? How do I express in terms of y then x? e^{(x-y)^2}-x\sin(y)+\frac{y^3}x=8 Is this only doable with some form of advanced maths, or this is actually doable with A-levels (pre university) maths? Thank you.
  20. N

    New number of terms in arithmetic series

    Hello, I am given a general arithmetic series: $a_{1}, a_{2}, a_{3},....a_{n}$, and a new arithmetic series is composed of it, where every term is the sum of 3 consecutive numbers of the original series, i.e: $a_{1}+a_{2}+a_{3}, a_{2}+a_{3}+a_{4},...., a_{n-2}+a_{n-1}+a_{n}$ Example: The...