Trigonometry sums. How can I solve this task?

How can I solve this task with formulas? (3-4 * cos (10) + cos (20)) / (4 * sin ^ 4 (5)) – 4

Is there an example of using Bring radicals to solve a quantum equation?

It says here on Wikipedia that the general quantum equation can be solved by reducing it to the main quantum form, then the Bring-Jerrard normal form. It gives a good overview and after reading it several times, I feel like I understand the general concept. However, he doesn't really give details on how a quintique would be solved on his own. Is there an online example of how to solve this?

How to solve these equations without errors?

I am a new user of Mathica 12. I have to plot real and imaginary solutions of two equations, eq1 and eq2, which contain the Dawson function, here is my program:

f(a_) := - 2 DawsonF(a)+I Exp(-a^2) Sqrt((Pi)) 

eq1(x1_, y_, z_) := 1 - (z y^2/x1^2) - (1/(Sqrt(2) x1 y)) f(x1/(Sqrt(2) y))
eq2(x2_, y_) := 1 - (1/(2 y^2)) f'(x2/(Sqrt(2) y))

slo1(y_, z_) := Re(x1 /. FindRoot(eq1(x1, y, z), {x1, Sqrt(1 + z y^2)}));
slo2(y_) := Re(x2 /. FindRoot(eq2(x2, y), {x2, Sqrt(1 + y^2)}));

Plot({slo1(y, 5000), slo2(y)}, {y, 0.0001, 0.5},PlotRange -> {{0.0001, 0.5}, {0, 4}}, PlotRangePadding -> 0)

When I plot the charts I get these errors

General::munfl: Exp(-4.11658*10^7) is too small to represent as a normalized machine number; precision may be lost.

General::munfl: Exp(-4.11658*10^7) is too small to represent as a normalized machine number; precision may be lost.

FindRoot::lstol: The line search decreased the step size to within tolerance specified by AccuracyGoal and PrecisionGoal but was unable to find a sufficient decrease in the merit function. You may need more than MachinePrecision digits of working precision to meet these tolerances.

General::munfl: Exp(-4.11633*10^7) is too small to represent as a normalized machine number; precision may be lost.

General::stop: Further output of General::munfl will be suppressed during this calculation.

FindRoot::lstol: The line search decreased the step size to within tolerance specified by AccuracyGoal and PrecisionGoal but was unable to find a sufficient decrease in the merit function. You may need more than MachinePrecision digits of working precision to meet these tolerances.

This means that the solutions plotted are incorrect. How to eliminate these errors to get the exact solutions?

How to draw imaginary solutions also without errors?

Thank you.

differential equations: how to solve the natural frequency of the cantilever beam by mathematical method

I want to calculate the natural frequency of the cantilever beam according to the theoretical method.

enter the image description here

I find a post on how to solve the free vibration frequency of a cantilever beam with the finite element method.

(*https://mathematica.stackexchange.com/questions/99724/finite-
element-boundary-breaking*)
ps = {Inactive(
      Div)({{0, -((Y*ν)/(1 - ν^2))}, {-(Y*(1 - ν))/(2*(1 
- ν^2)), 0}}.Inactive(Grad)(v(x, y), {x, y}), {x, y}) + 
    Inactive(
      Div)({{-(Y/(1 - ν^2)), 
        0}, {0, -(Y*(1 - ν))/(2*(1 - ν^2))}}.Inactive(Grad)(
       u(x, y), {x, y}), {x, y}), 
   Inactive(
      Div)({{0, -(Y*(1 - ν))/(2*(1 - ν^2))}, {-((Y*ν)/(1 
- ν^2)), 0}}.Inactive(Grad)(u(x, y), {x, y}), {x, y}) + 
    Inactive(
      Div)({{-(Y*(1 - ν))/(2*(1 - ν^2)), 
        0}, {0, -(Y/(1 - ν^2))}}.Inactive(Grad)(
       v(x, y), {x, y}), {x, y})} /. {Y -> 10^3, ν -> 33/100}

{vals, funs} = 
 NDEigensystem({ps}, {u, v}, {x, y} ∈ 
   Rectangle({0, 0}, {5, 0.25}), 8)
theory = {0, 0, 0, 22/L^2 Sqrt((Y d^2)/(12 1)), 
   61.7/L^2 Sqrt((Y d^2)/(12 1)), 121/L^2 Sqrt((Y d^2)/(12 1)), 
   200/L^2 Sqrt((Y d^2)/(12 1)), π/L Sqrt(Y/1.)} /. {Y -> 10^3, 
   d -> 0.25, L -> 5}
TableForm(Transpose({Sqrt(Abs(vals)), theory}), 
 TableHeadings -> {Automatic, {"Calculated", "Theory"}})
bcs = DirichletCondition({u(x, y) == 0, v(x, y) == 0}, x == 0);

{vals, funs} = 
  NDEigensystem({ps, bcs}, {u, v}, {x, y} ∈ 
    Rectangle({0, 0}, {5, 0.25}), 5);
theory = {3.52 Sqrt((Y d^2)/(12 L^4)), 22 Sqrt((Y d^2)/(12 L^4)), 
    61.7 Sqrt((Y d^2)/(12 L^4)), π/2 Sqrt(Y/L^2), 
    121 Sqrt((Y d^2)/(12 L^4))} /. {Y -> 10^3, d -> 0.25, L -> 5.};
TableForm(Transpose({Sqrt(Abs(vals)), theory}), 
 TableHeadings -> {Automatic, {"Calculated", "Theory"}})
Needs("NDSolve`FEM`")
mesh = funs((1, 1))("ElementMesh");
Column(Table(uif = funs((n, 1));
  vif = funs((n, 2));
  dmesh = 
   ElementMeshDeformation(mesh, {uif, vif}, "ScalingFactor" -> 0.1);
  Show({mesh("Wireframe"), 
    dmesh("Wireframe"(
      "ElementMeshDirective" -> 
       Directive(EdgeForm(Red), FaceForm())))}), {n, 5}))

But I would like to know how to solve the natural frequency of the model in the previous post according to the partial differential equation solving method.

enter the image description here

Other related links:

How do you find the eigenvalues ​​of a PDE (Euler-Bernoulli dynamic beam)?

Euler-Bernoulli non-homogeneous dynamic beam equation with discontinuous parameters

Analytical solution of the Euler-Bernoulli dynamic beam equation with compatibility condition

systems of equations: solve for x and y reals: $ x (x ^ 2-3y ^ 2) = 2, y (3x ^ 2-y ^ 2) = 11 $

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azure sql database – How to solve parameter detection problem in query with operator & # 39; in & # 39;

I have a parameter detection problem in this Azure SQL Server consult with in operator:

    Select Col1, Col2, ..., Coln from T1 Join T2 
    On T1.Id = T2.T1Id
    Where T2.Col2 in ('uniqueIdentifier_1','uniqueIdentifier_2',..., 'uniqueIdentifier_m')

I have around 30-40 unique identifiers in the where clause. And I can't replace them because they are primary keys of another table in another Azure SQL Database. As you can see there are a variety of different unique identifiers and it is difficult to adjust.
Could you guide me to solve a parameter sniffing problem?

probability – Please help, how could I solve it?

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  • Please make sure answer the question. Please provide details and share your research!

But avoid

  • Ask for help, clarification or respond to other answers.
  • Make statements based on opinion; back them up with references or personal experience.

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Networks: Why do I sometimes get a trace route that performs four internal LAN hops before reaching the WAN? And this is a problem that I should solve?

Why could I get 10 … and 192.168 .. internal IPs every time I perform a concert?

If I do a concert I will get something like:

  1    20 ms    10 ms    11 ms  10.118.60.1
  2    11 ms    11 ms    10 ms  10.118.60.1
  3     9 ms     9 ms    18 ms  192.168.62.105
  4    10 ms    11 ms    10 ms  10.224.253.153
  5     *        *        *     Request timed out.
  6    21 ms    23 ms    22 ms  ae-1-3513.edge1.Seattle3.Level3.net [4.69.160.69]
  7    22 ms    22 ms    21 ms  4.68.70.162
  8    23 ms    26 ms    22 ms  74.125.243.177
  9    22 ms    21 ms    22 ms  209.85.254.171
 10    20 ms    21 ms    19 ms  dns.google [8.8.8.8]

or:

  1     2 ms     1 ms     1 ms  192.168.0.1
  2    11 ms    10 ms    10 ms  10.118.60.1
  3     9 ms     9 ms    22 ms  192.168.62.105
  4    10 ms    14 ms    12 ms  10.224.253.153
  5     *        *        *     Request timed out.
  6    22 ms    31 ms    26 ms  4.69.137.205
  7    25 ms    29 ms    26 ms  4.59.234.98
  8    25 ms    25 ms    24 ms  one.one.one.one [1.1.1.1]

The first concert is rare. Most of the time 192.168.0.1 goes first instead of an address 10 … * first.

Is it possible that my ISP is creating a double NAT? If so, is there any workaround other than using a VPN?

I tried that my best effort could not solve

If f (x) is a differentiable function and g (x) is a doubly differentiable function such that | f (x) | ≤1 and f & # 39; (x) = g (x). If f2 (0) + g2 (0) = 9. Show that there is something of c∈ (–3.3) such that g (c) .g & # 39; & # 39; (c) <0.

dnd 5e: players get frustrated when they can't solve a difficult diplomatic problem, how to make them think outside the box

Issue:

The players got into a diplomatic problem that they know is probably above their salary level in terms of difficulty. They spent a session trying to solve this problem by talking to people and doing different charisma checks to try to persuade people that they probably didn't have to persuade (the reels were average, the arguments weren't extremely convincing). The party planned no grand scheme, no extraordinary strategy, no clever idea on the ground, but attempted a very basic basic dialogue.

This has happened in the past when it comes to combat, and the part with a recent deadly encounter had to think more out of the box (one player even said, "Guys, we have to plan more and think less about hacking and cutting sometimes. "). Now it's a more diplomatic problem that doesn't seem as easy as writing a single charisma check and hoping it works.

In the end, the party failed to resolve the diplomatic problem (although there is room in the future for them to try the advantage again), and one of the players said he did not enjoy the session. Player enjoyment is my top priority. But I also think dnd is better when there is risk, when you can miss spins, when PCs don't always win (although it's not that I actively seek it out).

How can I get the party to perform less linearly on dialogue related issues?

An example problem:

P: If he tries to be smart, a bad person with a lot of influence in the city

A: There are options to incriminate the person, bribe people, look for dirt on this person to find his weakness, stain his reputation, try to prove his mistake by looking for evidence, and many other possibilities.

I tried to have a short session-0 to talk again about if they want problems related to disabled dialogue, and they didn't seem to accept it, instead they felt like they tried everything and didn't know what else to do. I also did an autopsy on this issue and tried to give different options that they could have tried, but I have a feeling that the players feel that they still tried everything and failed and that the session was "a waste" (even though they still had exp , I still got loot and got more plot).

Something like a waste of how to tackle this problem isn't just: "Go check out some podcasts dnd for ideas, or go read the X, Y, and Z resources on the subject."