Precalculus in a Nutshell, Geometry, Question 11

“An equilateral triangle and a square are inscribed in a circle, with a side of the triangle being parallel to a side of the square. The entire figure is revolved about that altitude of the triangle which is perpendicular to a side of the square. Find the ratio of the area of the sphere to the total area of the cylinder, and the ratio of the total are of the cylinder to the total are of the cone”.

I seem to get the right result for the ratio sphere / cylinder, but not the second one. In this problem the cylinder has height = diameter, therefore we can get the sphere’s diameter (cylinder’s diagonal) using the Pythagorean theorem and then working through the rest.

When I deal with the cone, I would be tempted to use the same logic, as the diameter of the cone should be the same as the cylynder’s.

Any hints?

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What is the point of showing publicy a new user’s question vote count more than -1?

Mostly I am on where new/experienced programmers share their knowledge. When a new user asks his first question, the question can be downvoted because the user’s question is a bad question. They do not read the document which helps users to ask a good question.

Now what is the point of the possibility of downvoting a new user’s question if it is already -1? Example: A question which has now -8.

Of course, there are a few things about the user’s question that make it a bad question. But why can users downvote a question if it is already -1? What is the point of showing -8? The point that the question is bad is already indicated by the -1 (note: only people with 125 reputation can publicly downvote a question).

I feel -8 does not have any added value to the user itself. I think when he sees the -8 he just leaves the website or anything other than positive. It is now like: “Hey man! Bad question! Here, have a downvote!” times eight

Especially for new users, I think it is important that a review should be made when the question received a downvote. The question should be on hold and “normal” people should not be able to downvote/see the question. When the review is made, the mod can decide that the user should rewrite his question to make sure people see it again. I already thought this was possible, but I think it is a great idea to not bash away the new user, by simply spam downvoting his question.

What do you think about this? Is it okay there is no limit on downvoting a new user’s question?

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Conceptual question about log-linear analysis

I have measured the binary occurrence of three types of events on multiple days. Theory suggests that these events are not independent and should occur on the same days more than would be expected based on their marginal probabilities alone. To test this hypothesis, I believe I can use log-linear modeling to predict the count of each combination of events.

Question 1: Is log-linear modeling the correct approach here?

# Example data
df <- data.frame(
    Y = c(911, 44, 538, 456, 3, 2, 43, 279)

If the four events are A, B, and C, and my count variable is Y then I think I can specify the independence and saturated models with the following formulas:

mod0 <- glm(Y ~ A + B + C, data = df, family = poisson)
mod3 <- glm(Y ~ (A + B + C)^3, data = df, family = poisson)

Question 2: To test my hypothesis, am I correct in comparing the saturated model to a homogeneous associations model without the three-way interaction?

mod2 <- glm(Y ~ (A + B + C)^2, data = df, family = poisson)
aod <- anova(mod2, mod3)
#> Analysis of Deviance Table
#> Model 1: Y ~ (A + B + C)^2
#> Model 2: Y ~ (A + B + C)^3
#>   Resid. Df Resid. Dev Df Deviance
#> 1         1    0.37399            
#> 2         0    0.00000  1  0.37399
pchisq(0.37399, df = 1, lower.tail = FALSE)
#> [1] 0.5408374

Question 3: To extend this to more than three types of events, would I just increase the exponent (e.g., compare mod4 to mod3 for four event types)?

Thank you in advance!

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DB maintenance question

We have a very large database (4.5 terabyte). When maintenance jobs are run, application users experience slowness. How do you solve the slowness problem? We have 4 Active-Active SQL servers, with one primary. Should I do the maintenance offline?

Thank you in advance for your help.

  • Dutch.

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How can I focus attention on the intent of a question rather than details?

I asked what seemed a reasonable, understandable question on an SE site and got two good answers so far. Commenters focused on details that were not the point of the question. Please help me know how I can write Questions so as to avoid causing a debate about irrelevant details.

I am asking here because I have seen this on most other SE sites where I have posed questions so I think it applies generally.

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Why does $deg p(x)=2$ in this older question about finite extension of $Bbb R$

I was reading this older question and at some point the OP says “Surely $deg (p(x))=2$ since otherwise it would be reducible.”

Why is that true?

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Can a shopping question be made viable on Stack Overflow (and similar sites)?

Jaydles asked about how to improve Off Topic closings yesterday. I suggested a new explanatory paragraph to display on closed shopping questions, but hit a snag when it came to the “what can I do to improve the question” section. What can an OP do on Stack Overflow to make a shopping question viable?

In his canonical blog post on Shopping questions, Jeff describes how you can modify your “what is the best x?” shopping questions so it becomes viable on Stack Exchange (emphasis mine):

However, there is a way to ask these questions that avoids the inherent problems with shopping recommendations. For example, let’s say you wanted — as I did — to buy a point-and-shoot camera that takes good low light photos. So we’re going to ask on, naturally!


The former question provides the path of least resistance: a laundry list of products I can buy without thinking about it too much. […] The latter question may take some thinking, but its answer will be valid forever … or at least until camera technology somehow shifts beyond lenses and sensors as we know them today. Thus, when it comes to shopping questions, don’t ask us what you should buy — ask us what you need to learn to tell what you should buy.

That’s great advice, but is it really valid on today’s Stack Overflow? I’m not sure. I expect questions about how to tell a great framework or plugin would be closed as quickly as simple requests for the “Best framework” or “best plugin”.

Is this true? What should OPs do to improve their shopping question on Stack Overflow (and similar sites)?

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Need help on solving this maths question

I need help on this question please
27 multiplied by 9 to the power of 3x (x is variable) can be written in the form 3 to the power of k (variable) . where k is an expression in terms of x (variable).
find k (variable)

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The Final Question: is P = NP?

I heard my teacher say that many theorists tend to be inclined to P!=NP. Why it is that and what is your personal intuition about this topic?


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Arduino serial question

just a quick question on an oddity I noticed while playing with serial on my Arduino.

I’m using the serial monitor to test an interface I plan to adapt to Bluetooth later. Except I’m noticing if I only read fixed sizes with readBytes I can only ever input data of that exact byte length or my serial connection gets broken.

Example pseudocode:

if(Serial.available() >= NUM_BYTES){
/* Do stuff */

If I input something of length NUM_BYTES + 1, it reads the first NUM_BYTES. But then I can never send more data over the serial monitor. Why is this? Is it part of the serial implementation?

A fix I had was just to clear the buffer by calling until nothing else was available. As a matter of curiosity too… If anyone cares to answer or give me a link to some reading – is there a way to check before I write to serial to make sure there’s buffer space for my message on an Arduino? I read that they have a 64 byte buffer for data but I’m unsure how the protocol caters to sending larger sets of data if the buffer ever overflowed. Perhaps the serial library is using some form of ack behind the scenes?

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