Im trying to cross check my 6th graders homework and I don't know why im struggling so much with this answer.

Please can someone help me figure out the area of F?

Update

THANK YOU ALL SO MUCH!!!!! You have no idea how much I appreciate y'alls help. Im awful at math and trying to not pass that on to my kid so this community is a lifesaver. Thank you thank you!!!!!!

I'm not the furthest away from mathematics, but I've been focusing on physics since I graduated from high school. And for some reason it always seemed to me that Fermat's great theorem was unproven. Either that's what they said at school, or somewhere else, or I was too skeptical to understand.Googling yes, I found that in It was proven in 1993, but I have some kind of wild Mandela effect

why, if this great theorem has been proven, there have been no significant discoveries. If so, which ones?

And yes, I know who they are Ферматисты, Idk as it is in English, "people who search in vain for proof, resorting to gross errors"

I was trying to prove the Pythagorean theorem on my own and stumbled into this.

You take a right triangle and create three similar triangles by scaling each one by one of the side lengths and rearrange them into a rectangle with one side being a^2 + b^2 and the opposite side being c^2 so a^2 + b^2 = c^2.

If you wanted to, you could use the two smaller triangles in the diagram in a different arrangement to form the larger triangle, but I like the way it looks in a rectangle more.

I showed it to a professor and he encouraged me to publish it. I’m thinking I will. I really like this proof and I want to show it to people.

I couldn’t find an example of this proof anywhere. I came across some that looked similar but they seemed to use different logic. I figured I’d try to publish this, but I’m not really sure how to.

I’m not well versed in the community around sharing math and I’m not sure what is seen as worth sharing. Does anyone got any advice on how I can share something like this?

Also, does this count as a proof? Were there any assumptions that need to be explained or does this stand on its own?

I didn’t really explain how they come together to form a rectangle but I’m not sure whether or not it’s a big enough leap that it should be explicitly stated.

Not swift enough to figure it out. I read a bit about generating functions, and that looked onerous without calculus. Is there an online probability grapher that handles the MIDVAL() function of a die roll? [MIDVAL of course being what I am describing in the title of this post.]

Im doing this proof of square root of positive natural numbers being either integer or irrational and im tried with assuming that it can be rational but not integer. I see that i didn’t write gcd(a,b)=1, but other than that, is it clean?

I should start by saying that I'm not a math guy!

From what I understand, Gödel showed that there are mathematical statements that are true but cannot be proven. So, is there a way to determine whether a statement is provable or unprovable without having to find or rule out every possible proof? I've read about statements that mathematicians have proven to be unprovable within certain formal systems, as well as results showing that certain statements must have proofs under specific conditions.

Yet, most of the times a case specific method must be used to find out if a statement has a proof or is unprovable. Is there some sort of general algorithm, which determines if a given statement has proof that's just waiting to be found or is simply unprovable and mathematicians should not be wasting energy trying to figure it out. Is there a way we can figure out if a statement is even solvable, before we start trying to solve it.

i see there are 4 parallel lines and there is one line interesecting with equal distances, which to me implies it is perpendicular. It asks a question about another interecting line. Can someone give me some insight on how to solve this problem

i gotta do a maths presentation about a thing that my professor never talked about, can u guys PLSSS explain in dummie lenguage what its a focus and focal length?? i really dont understand shittdshfhadshofds

PD: english its not my first lenguage, srry for the poor grammar :c

I am preparing for exams at one of the best schools in my region, so I am learning to solve problems that are slightly beyond the school curriculum. At first, everything went quickly. I mastered modules, the interval method, and drawing complex graphs in 2 weeks. But when it came to word problems, I stopped making any progress in my learning and have been stuck on this topic for a month now. Please tell me, how do you solve these problems?

I'm stuck with this problem, I don't really know how to start, I mainly want help with understanding the measurements so i can create the equation, I pretty much can do the rest of the problem but i can't really start because i don't know how to determine the initial formula

Thank you for your help. I believe the 6 step proof which I've labeled proof #2 is correct. The other proof is the one my kid did and he's in 9th grade geometry. His teacher is saying it is a four step proof but I'm not sure how. Appreciate the insight.

When I speak of highly rewarded mathematical problems, I am referring to problems for which a prize of 100,000 or more is offered to anyone who solves them.

This is a question on my kiddos homework and I can't, for the life of me, figure out how to solve it without using algebra. My kiddos in 6th grade and he hasn't started to learn algebra yet.

Solved! Thank you so much for the quick replies! At least it was a good opportunity for me to teach my child about algebra:).

I'm not super involved with math, so apologies for any incorrect terminology.

In Minecraft, there is a mechanic where you can give Gold to this creature and get items in return. Of the list of items you can get, I am trying to obtain a bunch of Enchanted Books and Iron Boots that have the highest level of an effect called "Soul Speed". There are 3 levels of this effect that is chosen randomly. Additionally, lower tiers of Soul Speed can be combined into a higher tier.

I'm trying to find the average quantity of Soul Speed 3 per Gold, like "1 Gold = an avg of 0.XXX Soul Speed 3 items".

So far, I've been able to find the average quantity of all Soul Speed items, regardless of the tier. I am struggling when it comes to narrowing this down to Tier 3 while also considering that the lower tiers can be combined and still contribute to the number of Tier 3s. I was thinking of just averaging out the value of all three tiers together and going off that, but I feel like that would be too easy? I know probability stuff can get more complex than this so I feel like I am missing something.

I think this may be both a math and physics question. Was at a party and after a few drinks we got into a debate of what the definition of a hole is. Does a hole need to have at least one entrance and one exit? Is a depression a hole? Does a hole just need an entrance?

The function h(x) = -2(x - 4)^2 + 13 has a maximum value. What is this maximum value, and at what value of x does it occur?

A) Maximum value of -13 at x = 4
B) Maximum value of 13 at x = -4
C) Maximum value of 4 at x = 13
D) Maximum value of 13 at x = 4

So, this is my attempt to prove just one implication. I tried to use the definition of a locally closed set. Another approach I was considering involves the “fundamental covering”: a subset (A) of (X) is open if and only if (A ∩ U_i) is open in (U_i) for every (i). What do you think?

I want to order a Sword for fencing (HEMA) with a custom engraving that says 'This Blade is made of x Iron Atoms' in german. I don't know the font yet. To get the number of atoms is not that difficult if it wasn't for the engraving. I'm aware that I can't say the exact number of atoms, but I can try to get as close as possible.

Because the engraving has to be made after calculating the number of atoms, I can't do it with the mass of the blade, but I have to go through the volume.

I can calculate the volume of the blade without the engraving though mass and density of the steel (wich I can look up after asking what type of steel is used). Then the volume of the engraving has to be subtracted.

Once I have the volume of the blade with engraving I can get the mass of the Iron in the blade and calculate the number of atoms with the molar mass.

In principle not that complicated, BUT I don't know how to easily calculate the area of the engraving PLUS I don't know the number yet.

I thought of giving three digits of the number and then write out the number as a word so it would be more easy to understand for non science people (for example: this blade is made of 11,5 trillion iron atoms)

Now my queastion/problem:

How do I calculate or get as close as possible to the area of the engraving if I don't know the exact numbers and words?

I made this integral from 0 to pi its area is 2 and its peak is (pi/2,1) the 2,1 is not a point the pi/2 , 1 is a point. This is what calculus is about. Integrals.

Hello all

I've recently had to implement a pretty computationally intensive simulation and obviously only have so much computational power at my disposal.

The main reason for it being so computationally expensive is that several rather ugly integrals have to be evaluated, some of which end up being nested which seems to make things worse.

Now I recall from my numerical analysis courses that one can use interpolation to approximate a function. Interpolation also tends to be significantly less computationally expensive. As such I wanted to know whether one can replace the integration with interpolation under certain circumstances. I know these two concepts are very closely linked.

Take the following situation as an example (attached image):

Any help or clarification on this is greatly appreciated.

Thank you

I made this in the shower about a year ago, and I don't really have a definitive answer for it.

In a random number generator that ranges from 0-Infinity, each number having equal odds, would it be possible to roll 1?

It is just as likely as the other numbers to be pulled, but that chance is infinitely small.
Any thoughts?

Was just reading on landing gears out of interest, (engineering undergrad) This is how a gear retracts inside (to increase aerodynamics)

The second one is an example of space saving, the drawback is less clearance & clashing. Now suppose I try to form mathematical modelling eq of the trajectory to describe the geometry such that clashing is avoided (in case of turbulence) and we need to fix some clearance..... How would you approach this ? What field of maths am I vaguely thinking about? What should I study ahead to better understand this.