Trigonometry – confusion when looking for solutions to trigonometric problems within a range

I have recently had problems with the solutions proposed for trigonometric problems. For example, there is a case like 2 + 3cos 2x = 0. For all trigonometric problems in any form, I know that I have to use algebra or trigonometric identities to isolate them x or theta or isolating a single trigonometric function with a single angle corresponding to a value on the right before finding all solutions. However, I am confused about the answers to many trigonometric problems. In the above example, it is limited to the range of x is less than or equal to 180 and greater than or equal to 0. Resolve for xI get -20.9 degrees. I see that this is out of range, but if I take the reflection amplitude of that answer (+0.36), I see that a line drawn in the graph of the Sin function intersects the function at two points one is +20.9 degrees and the other is 159.1 (180-20.9) degrees. But in my textbook it says that 110.9 degrees are the answer.

For this reason, I would appreciate any help that helps me understand how to find all solutions to a problem in a limited capacity. I have solved many of these trigonometric problems, but when I come to the point where I have to specify the solutions that will satisfy such problems, I am completely lost. I looked at several videos and read online tutorials on this topic in mathematics, but I can not see their reasons for multiple solutions.

Calculus – Washer method confusion

Calculate the volume of the volume created by rotating the bounded area $ y = sqrt x $, $ y = 0 $ $ x = 1 $, $ x = 4 $around the y-axis.
I understand that I can find the volume by integrating the volume $ A (y) $ from $ 0 $ to $ 2 $ since these are the ones $ y $ Values ​​of the sections of $ x = 1 $ and $ x = 4 $,

My understanding is that I would calculate the range $ (A (y) $by:
$ pi $ $ (R ^ 2) -r ^ 2) $ from where $ R $ is the outer radius and $ r $ is the inner radius. Then I integrate that as $ int_0 ^ 2 A (y) dy $,

So I calculate the outer radius $ R $ by calculating the $ x $ Distance from the rightmost border, in this case $ x = 4 $ and the $ y $ Axis. Thus $ R = 4 $, Is that the way to calculate? $ R $ even if part of the $ R $ $ x $ Distance is not within the limit? Ugh, confused about the definition here.

The inner radius is the $ x $ Distance from the function to the rotation axis (the $ y $ Axis). So, $ r = y ^ 2 $,

But I would think that this distance X is ONLY in the region of $ x = 1 $ and $ x = 4 $, Since I should always calculate from right to left, this radius would not be that way $ y ^ 2-1 $??

I can not seem to understand this washing problem, though I can handle others, and I can see that I do not fully understand the definition of calculating inner and outer radii.

Can someone clarify that? The bottom line is that I can not properly calculate the inner and outer radii of this problem.

Confusion about "unloadwallet"

I do not know how unloaded wallets behave in Bitcoin Core v0.17.0.1.

If I create a new wallet with Createwallet, add with a recipient address import multiand then unload it unload wallet:

  1. Will bitcoind continue to recognize payments to the address (es) of this wallet? (seems yes)
  2. If so, this detection will only be done when used loadwallet once again? (seems yes)
  3. If so, does this require rescanning (last) blocks? (I'm worried how long that might last if I loaded this wallet for the last time months or years ago.)
  4. If so, is that a problem on a cropped knot?
  5. If so, should I avoid this multi-wallet feature on a truncated node, or is there a safe way to use it without risking large downloads? (never unloaded, for example)

Linear algebra – Confusion of the GMRES algorithm

The book Numerical Linear Algebra by Trefethen presents the GMRES algorithm as follows:

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As far as I understand, one should repeat the loop from n = 1 to n = m, where $ m times m $ is the size of the quadratic input matrix $ A $ and $ m $ is the size of the vector $ b $ in the $ Ax = b $, With each step $ n $ Arnoldi enters $ (n + 1) times n $ Hessenberg matrix. In minimization step one $ QR $-Factors $ H_n $ and solves the minimization problem by back-substitution and then checks the norm of the residual for the convergence condition.

What if, after that? $ m $ Steps is the convergence condition not met? What do we do?

Whatever, if the convergence condition is fulfilled in $ n <m $ Steps? Then the last vector $ x $ will have a dimension $ n <m $is not that true? How do I handle this?

And why do we need it eventually? $ x_n $ at every step, if it is not used in a subsequent step?

Please help me to understand what is going on in this algorithm since I have spent many hours and this still seems vague to me.

Confusion about min-cut probabilities

  • There is currently a video on Counting Minimum Cuts by Tim Roughgarden.
  • $ (A_ {i}, B_ {i}) = big ((A_ {1}, B_ {1}), …, (A_ {t}, B_ {t}) big) forall i in Bbb {R} $
  • $ P big ((A_ {i}, B_ {i}) big) geq frac {1} { begin {pmatrix} n \ 2 end {pmatrix}} = p $What I interpret as the lower bound of probability to have at least a minimal cut.
  • In the following problem group, the two answers A and B are marked as correct. I understand why A is right. But I am confused why B is also marked as correct.
  • A: For every diagram $ G $ With $ n $ Knots and every min-cut $ (A, B) $ (I assume that $ (A_ {i}, B_ {i}) $) $ P big ((A, B) big) geq p $,
  • B There is a graphic $ G $ With $ n $ Knots and a min-cut $ (A, B) $ (again the same as $ (A_ {i}, B_ {i}) $) from $ G $ so that $ P big ((A, B) big) leq p $,

Performance – Python Numpy: Confusion – why go through in numpy

I'm programming for 2 years in pure Python.

Now I'm learning Numpy and I'm confused.

Tutorials have shown that Numpy is much more efficient than pure Python. Given examples, but if I try simple iteration for example:

import numpy as np
import time
start = time.time ()
List = Range (1000000)
array = np.arange (1000000)

for item in list:
print (& 39; + str ((time.time () - start) * 1000) + & # 39; n & # 39;)
start = time.time ()
for an element in np.nditer (array, order = & # 39; F & # 39;):
print (& 39; + str ((time.time () - start) * 1000) + & # 39; n & # 39;)

I received an issue:



As you can see above, iteration over Numpy is less efficient than pure Python.

My question is: I do not understand and can not explain why Numpy and Moreso are used: When should I use it?

Callback Pattern – Return Value Confusion

I have a EinschränkungenResolver Class that solves a queue of forces. This happens when a EinschränkungenResolver Property Views meetConstraint () on one force on.

Most of meetConstraint () Implements are returned immediately, so I could just return a Boolean, but there is at least one blocking, which means I need to implement the callback pattern.

Do I have the ability to combine both solutions, or do I just need to implement the callback pattern?

ps: I was not sure if this question had to be asked here or StackOverflow

301 redirect confusion | Web Hosting Talk

I have a client for whom I have created dozens of pages of links to a particular webinar site over the years. This site has just been shut down, so I need to redirect all these old links to a temporary page of the site until we have time to restore things to another service. The problem is that I do not seem to be able to get the htaccess forwarding going, so I hope somebody can help me.

The broken URLs all start with

I'd like to rewrite all the URLs on the site so that this URL will be rewritten anywhere on

I thought of doing something like that

Redirect 301 https: //*

would work, but this will cause the site to issue an error 500 wherever a webinarjam link is displayed. How should I perform this forwarding?