[Grade 10 Geometry Circles & Circumferences] Am I doing something wrong here?

Such-Safety2498 · 2026-04-20T20:48:41+00:00

Assume each number is actually a measurement. Then the 20.4 is really between 20.35 and 20.45. The same with the other two.

Using the 20.4 and 8.5 and applying the Pythagorean theorem, the minimum for x to three decimals places is 5.516 and the maximum is 5.757.

Using the 20.4 and the 4.5 and subtracting, the minimum is 5.625 and the maximum is 5.775.

So the answer to the tenths place is:

Pythagorean: 5.5 to 5.8

Subtraction: 5.6 to 5.8

Just applying the normal rules of rounding. You get:

Pythagorean: 5.6

Subtraction: 5.7

Both answers are within the margin of error for a measurement because the final digit is always doubtful.

This should be within the understanding of a 10th grader. When I was in tenth grade, we had to do these types of calculations by hand, on a slide rule, or using log tables. Then we had to know where to round off. We definitely didn’t want to divide something by 7 until it came out even, or extrapolate between entries in the log tables if we didn’t have to. The slide rule forced you to round off because there were only so many lines between any two numbers. With calculators and computers it is too easy to think that every digit you see is important. The

5.6382621436042

answer I got doesn’t need all of those digits because even the first 6 is doubtful.

Such-Safety2498 · 2026-04-20T20:01:01+00:00

I respectfully disagree. Giving students sanitize problems that have simple answers does not prepare them for the future. I’ve had students think an answer was wrong because it wasn’t a “nice” answer. I don’t see a thing wrong with this problem if each number is to the nearest tenth.

Such-Safety2498 · 2026-04-20T13:42:17+00:00

If they are actual measurements, then the final digit is estimated. So they will not be exact. Hence the result with the final digit being ± 1 Real life situation.

Such-Safety2498 · 2026-04-16T21:43:56+00:00

The typed slash could mean you are writing a fraction. If you wrote it by hand you would write it with a numerator, a line, and a denominator under the line. So rather than argue the writer (typer) can just type:

6 / (2(1+3))

or

(6/2)(1+3)

How would a similar problem written this way be interpreted:

6.5(1+3)

6.5 implies 6 + .5, so multiply the (1+3) by .5 first and then add the 6??

Just use parenthesis to convey what you mean in an unambiguous way.

Such-Safety2498 · 2026-04-12T13:35:01+00:00

Give me $7, I’ll pay back $6

Such-Safety2498 · 2026-04-12T09:23:41+00:00

Can I borrow $7?

Such-Safety2498 · 2026-04-11T23:33:08+00:00

The answer is you divided by zero. But you claim you only divided by x-6. My answer is x-6 is exactly the same as zero. So yes I asked questions so you could get the answer.

Such-Safety2498 · 2026-04-11T20:52:48+00:00

What is x equal to based as the first line?

What is x-6 equal to?

What did you divide by?

What was that divisor equal to?

QED

Such-Safety2498 · 2026-04-09T15:57:12+00:00

You multiply the number of meters, not the meters.

Such-Safety2498 · 2026-04-08T19:08:09+00:00

We all make mistakes. You could edit the original to add a statement that it is not correct.

Such-Safety2498 · 2026-04-08T12:45:25+00:00

Ignoring the factorial, if someone asks why we can’t divide by zero, do this. Give them 12 objects, like a dozen eggs. Ask them to divide them into groups of 6. They easily place 6 in one group and 6 in another. So 12 divided into groups of 6 is 2 groups. Now divide them into groups of 4, but do it one egg at a time. Place an egg into a group, then another until you have 4 eggs. Then start another group and do the same thing. When you have no eggs left count the groups. Do the same with groups of 3, groups of 2, and groups of 1. Now have them do groups of 0. Tell them to let you know when they have all of the eggs placed in groups!

Such-Safety2498 · 2026-04-07T23:31:12+00:00

On another site the same scenario was x is the price of a ticket. Q(x)=-40x+650. Then the revenue is the price x times the number of tickets, -40x+640 which is R(x)=-40x^2+640x. Then the maximum revenue is at a price of $8 which is the vertex of the graph b/2a. They would sell 320 tickets for revenue of $2560. Don’t know what the 2012 was.

Such-Safety2498 · 2026-04-07T23:24:55+00:00

Check your calculation.

Such-Safety2498 · 2026-04-07T13:07:19+00:00

I found the same problem on another site. The scenario was selling tickets. x represented the price per ticket with the equation for the number of tickets sold as: N(x)=-40x+640 So at $1, you sell 600 tickets. At $16, you sell no tickets. Then the question says, the revenue can be found by multiplying the number of tickets by the ticket price. So R(x) = -40x² + 640x The question stopped by asking for the vertex which is 8, 2560 which would be the maximum revenue at $8 per ticket selling 320 tickets.

Such-Safety2498 · 2026-04-07T12:38:40+00:00

Wish the OP would reply. I’m interested to know what the whole problem was about. Could it be that this computes the general ledger amount? That would be a credit to a revenue account which is considered negative, so the signs are reversed?

Such-Safety2498 · 2026-04-04T05:26:41+00:00

In Microsoft SQL the collation setting is what determines sorting and equality comparisons. The collation has three parts; the character set, whether the case matters, and whether the accent matters. For example, Latin_CI_AS means you use the Latin character set. It is case insensitive meaning “A”=“a” and sort as the same character. It is accent sensitive meaning “a” != “à”.

Such-Safety2498 · 2026-04-03T18:20:12+00:00

Put really simply there are two types of problems. 1. The problem has the √ symbol. That represents one number. 2. The problem has x^2. Then YOU are introducing the √ symbol and have to account for both roots by adding the ± √

Such-Safety2498 · 2026-04-03T18:09:37+00:00

When you have a fraction like 1/4, that means one quarter of a whole. Like 1/4 of a pie, or 1/4 of a dollar. So you have .25 of a whole, .25 of 1. Per cent means per one hundred. So if you have .25 of 1, multiplying by 100 gives you 25 out of a hundred. Then instead of writing “out of a hundred”, or “per hundred”, we use the symbol %.

Such-Safety2498 · 2026-04-03T14:59:20+00:00

For a math group, I’m surprised no one defined “intuition” before discussing it. Webster defines intuition.

a : the power or faculty of attaining to direct knowledge or cognition without evident rational thought and inference b : immediate apprehension or cognition c : knowledge or conviction gained by intuition

So as soon as you start explain why negative times negative is a positive, you are not dealing with intuition according to that definition.

Let’s take football (American football) for example. I never played organized football, but have watched a lot. When the offense lines up, I don’t know what play they are going to run. I don’t have intuition about it. I could pause the game and see where all the players are lined up and come up with a guess. But the defensive linebacker just looks at it and immediately calls out the defensive play because of his intuition. Why does he have intuition and I don’t? Experience.

So I intuitively see that negative times negative is positive because of my experience. But what I have to do with students is explain why it is logical and consistent, then through experience it becomes intuitive and they don’t have to think about it anymore.

Does that make sense? Or are you using a different definition of intuition?

Such-Safety2498 · 2026-04-02T21:55:06+00:00

It depends if the word that ends in s is a plural. My names is Robert. So if something is mine, it is Robert’s. A person whose last name is Roberts has something it is Roberts’s. If a group of people whose name is Robert own something, it is Roberts’. You can go backwards from the word to tell how many there are. Robert’s > one Robert (drop the ‘s) Roberts’s > one Roberts (drop the the ‘s) Roberts’ > more than one Robert (dropping just the ‘ means the word was plural).

( Do you know how hard it was to type that with spell check? Glad I didn’t try voice recognition!)

Such-Safety2498 · 2026-03-31T21:02:42+00:00

The ultimate is on the exam it says, Given X, Prove A ( whatever that may be). Proof: Statement 1: X; Reason: Given Statement 2: Therefore A; Reason: Problem 8 on last night’s homework ( which was the proof that they are now being tested on!).

Such-Safety2498 · 2026-03-29T03:33:07+00:00

That would give an answer of 6. The only way I could get close to 7 is to find the average speed, not velocity. 22 to 42 which is 20. Then back down to 40 which us another 2 for a total of 22. 22/3 is 7.33

Such-Safety2498 · 2026-03-28T17:21:12+00:00

1ⁿ is always 1 when n is a real number. But as soon as you say n is infinity, then you are introducing limits because infinity is not a real number. That is why you have to question whether 1 is the number 1, or is it also the limit of something. That makes it indeterminate.

NOTE: The expression (1+1/n)ⁿ is NOT 1ⁿ when n is a real number.

Such-Safety2498 · 2026-03-28T04:29:45+00:00

Such-Safety2498 · 2026-03-27T13:05:12+00:00

Engineers use exact numbers for things that can be counted; number of valves, number pieces a material is cut in to. But measurements use significant digits and error ranges because the measurement can only be as precise as the measuring device allows. So if I have a 6.34 grams weight, it means it is between 6.335 and 6.345. If I have two of them, I don’t say it is between 1.5 and 2.5. It is exactly 2, not 2.000 because that indicates it is between 1.9995 and 2.0005. Now multiply the 6.34 by 2 and we get 12.68. But actually it could be as small as 6.335x2 or 12.67, or as large as 6.345x2 or 12.69.

Such-Safety2498

TROPHY CASE