I'm running a programming class for python and I was doing a class quiz. This question popped up. I believed the answer should be 64 but it's actually 512. Even the calculator gave me 512.

However if you go from left to right, 2 ^ 3 = 8 ^ 2 = 64

For some reason, the caluclator is and quiz is doing it like: 2 ^ 3 ^ 2 = 2 ^ 9 = 512

I guess my question is: why is the 3^2 portion being calculated first over the 2^3 portion?

I genuinely dont understand how algebra works. I get that a + b = c. Thats pretty understandable.

What i dont understand is where they want me to get numbers from. Am i supposed to pull them out of my ass?

"Find the center and radius of the circle. x² + y² = 25"

I have the equation (x - h)² + (y - k)² = r² as the formula to find the radius where (h,k) is the center. Then it tells me to, "Write x² in the form of (x - h)².

x² = (x - ?)² "

I dont understand how to find "?". Did i miss something? Where the hell am i supposed to find that information. If i knew how it works and why it works this would be so much easier to work.

I'm trying to graph the distance traveled by a projectile with constants for v0 and g, and x as the angle of the launch and y as the total distance traveled when it hits the ground. I am using the equation y=v^2 sin(2x)/g. The graphs are just end up looking like sines with large coefficients though. I get why its there, its so that you can get the amount of vertical vs horizontal velocity, but my graph can't be correct because a projectile launched at 45 degrees should be going the farthest, and projectiles can't have negative distance traveled.

As far as I'm aware anytime you multiply it's going to end up in the numerator so I'm not sure how to accomplish this. Even x(1)^-1, the ¹ happens before multiplying due to operational order.
With any luck it's something obvious I'm missing.

First time I tried posting this got deleted and the mod mail doesn't work so I'm guessing it's because it doesn't think that I posted the things that I already tried but I don't really know what to try besides but I already mentioned. I don't know of any way really to approach this problem. My best effort was to try to invoke reciprocation but like I mentioned, that gets executed before the multiplication does. I'm happy to engage in discussion with anybody about with us or to work it out if there isn't an easy solution or something.

I just ran it through a couple of online factoring calculators to see if they could figure it out but they can't. Maybe there's just not an answer? I don't know what more to do to make this like a valid post for this subreddit so hopefully this is enough this time

f(x)= kx^4 + 8x^2
Function has 3 turning points and global max at 8, zero at 2
Find k

I asked gpt, but it gave a method about using derivative or something which we haven’t learned yet since my teacher said our course (we are taking grade 12 advanced functions) need a lot of calculus and the graphs we draw aren’t exactly 100% accurate.

I knew this function is going to be even since both powers are even numbers, I also knew that it is going from quadrant 3 to 4 since we have a global max. I also knew that there will be 2 global max both at the height of 8 since there are 3 turning points.

I drew the graph which probably secured me a bit of points, but have no idea what the equation was let alone the k value.

My friend told me he just plugged in the x intercept (2,0) and got k which is -2, which turned out to be the correct answer. I thought about that at first but I remember my teacher said that you can’t use the x intercepts as a point and plug it in since you will get 0=0 when the polynomial is in factored form.

But this one is in standard form, so I don’t know if being in standard form let me plug in the x intercepts to find a or something…

Please help me out

Ok, so I am an adult. I graduated highschool almost 10 years ago, and... I don't remember squat from maths class. Trouble is, I'm a tutor. I've been tutoring these two kids for years, and at first it was chill. Basics, foundations, I could do it. But now, the oldest is at the point where he's supposed to do long division in his head, apparently. I haven't used it since *before* I graduated (senior years we used calculators) so I'm trying to relearn it for him.

Trouble is, I can't explain what he's meant to do when you're trying to solve it, and the numbers are still too big.

Take this one question we got:

42,028 Divided by 79.

79 doesn't fit into 4 or 42, so you have to divide 420 by 79!

Even when you get past that point, the next part you have to divide is 79 and 252! That's not any easier!

Is there a trick to dividing these? I'm not very good at maths, and he's not naturally gifted either, though determined to be good at it (wish I had the dedication he has when I was a kid. Maybe I'd remember this shit if I did). But when we get to these parts, all I can do is either sit there with him trying to figure it out through brute force and scribbles on the page, or just pass him the calculator because we only have an hour for all of his subjects, and can't waste it on a small part of one question! I don't know how to get an answer to 420 divided by 79 in any semblance of efficiently or decency.

Is there any trick, method, strategy? It's not like either of us have our 79 times tables memorised.

Sorry if this is long winded, but I've been trying to figure this out all morning, and I feel so incredibly stupid. What kind of tutor can't figure out long division? Maths always makes me wonder how the hell I finished highschool to begin with. If anyone has something that can help, it would be greatly appreciated. I don't want him to be past what I can help with already.

Thank you. I look forward to finally being able to explain this to him.

I'm taking algebra 2 and we're reviewing factoring right now. Since polynomials live in the real numbers, it's not clear to me why we limit ourselves to integers when factoring.

If I was factoring 6, why isn't 1.5 * 4 just as valid as 2 * 3? I realize factoring beyond integers would mean there are an infinite number of factors...but I'm not sure that alone is justification.

Ok, so here's my thesis: A perfectly round circle can't exist in the real world, because a curve cannot exist in the subatomical level. The plank length proves it: all shapes are polygons, even if it's in the subatomical level. So the most perfect circle is just a polygon. So it is possible to calculate the most perfect circle possible, but I don't know how. If all the polygon's sides are exactly 1.616255(18)×10−35  meters long, all the angles from one side to another are equal and the hight of the polygon is exactly 1 centimeter, is it possible to calculate how many sides there are?

If it can be done, we can calculate pi to the smallest scale possible

I really doubt anyone could help, but I don't know anywhere else that could

I’m 24m and came to the US 4 years ago from a 3rd-world country with no real education background (1.8 GPA). I decided to attend college but I was told I couldn’t be accepted at the college level unless I pass the placement test in Math and English. I had only one month to prepare so I started studying Math from grade 4 to 11 and worked my ass off. I finally passed the test, took a few ESL college classes and got into the business major. I’m currently a freshman with six A’s (one in statistics) and dreaming about transferring to a ivy League university. But almost all ivy League schools require having completed at least calculus 1.

Here’s my pain point: at my community college, I have to complete these prerequisites; algebra 2 → college algebra & trigonometry → precalculus before I can take the calculus. That means I have three classes ahead, which will take three semesters. For that reason I’m thinking about taking the CLEP test for precalculus. If I can pass it, I’ll go directly into Calculus.

Here’s my question for you: realistically, can I prepare and pass the precalculus CLEP test if I start learning again from geometry and algebra 1 all the way to precalculus in a few months?

I’m also seeking mentors (who know the US school curriculum) to guide me on where to start and what to do first and next.

Q: IF 6 PATIENTS HAD OPERATION LAST MONTH WHAT IS THE PROBABILITY THAT THE 4TH PATIENT WAS THE THIRD PATIENT THAT RECOVERED FROM OPERATION?

So I tried using the negative distribution where i got the equation of 3C2 x 0.5³ x 0.5¹ = 0.1875. And my answer is wrong. Is there a mistake in my formula or process? Thx!

For example: I simplified the square root of 72 down to the square root of 9x8. Of course 9 is a perfect square and becomes 3, but why can I not also simplify 8 down to 2x4 since 4 is also a perfect square? At least my workbook is telling me this is not the way to do it. Please help <3 thanks

If you have for example y = 2 or x = 9 this would be considered a function.

But why?

If in either of these you don’t get a value of x or y when you plug in a value for x or y. You don’t get any output for any input and if you put an input you would be getting false statements. Such as for y = 2 when you plug in 1 for y you get 1= 2 which is untrue.

Can someone please explain this to me?

I'm taking a Robotics and Automation course and I don't understand the math the professor is putting up on the board and without explaining it, he's asked us to solve it. I think its calculous? Or the first bits of Calculous.

Q1. The total charge entering a terminal is q = (10-10e^-2t) mC. Determine the current at t =1s.
Formulae: i=dq/dt, q=i*t, vdrop= Energy/Charge =w/q

I straight up don't understand. I have a TI-84 and I get the answer 8.6466. I don't understand similar problems online either. Somehow I'm supposed to get 20 out of 10-10? like what? I don't understand e^x power either.

Is it just q/t=i? if thats the case, .11565 would be the answer but with nothing to compare it to, idk if thats right.

I'm going into college soon, and my college requires you to take a math placement assessment to decide what math level you're going into. I took precalc in my sophmore year of highschool, and then stats & discrete mathematics and later finance, so I don't remember a lot of the material they're testing on. I've been using the college's provided study module for a while, and came across a problem where I don't understand the provided correct answer explanation (the module lets you enter your answer/s twice before it gives you the correct answer and explanation).

tl;dr studying and came across an answer explanation I don't understand the reasoning behind

The Problem:

solve for x, where x is a real number

x-5=sqrt(-5x+61)

Problem explanation:

(x-5)²=(sqrt(-5x+61))²

x²-10x+25=-5x+61

The rest of the thing makes sense, I know how to solve these kinds of problems, but I don't know where/why the -10x+25 is coming from- the 25 is obviously from 5 squared, I get that, but the way I was going about it, I was left with x²-25 on that side. I can tell it's an issue with how I'm dealing with the exponent (I even felt that I wasn't doing it right before I got it wrong), I just don't know what the correct method is.

Did mathematicians just arbitrarily decide to label one solution to x+1=0 "i" and the other solution "-i"?

Also in the real numbers "1" is positive, i.e. it is more than 0 where "-1" is negative i.e. it is less than 0, but this doesn't really make sense for imaginary numbers, so what does the negative sign truly symbolize?

Ramanujan states that sum of natural numbers till infinity is -1/12, which is counter intuitive.

And in the proof, very first step turned me off.

How can 1+1-1+1-1+1-1+1-...... Be 1/2? It can either be 1 or 0. Two possible values.

Is it really logical to take the average of 2 possible values, and conclude that this single value is answer.

If so, (x-2)(x-5)=0 will give the value of x=3.5.

Disclaimer: I am student of commerce and i dont know that much about mathematics. But i enjoy to learn mathematics logically.

So, mathematical proof wont work for me. Can someone justify me how 1+1-1+1-1+1-..... Is 1/2?

Question

Polonium-210 decomposes at a rate proportional to the quantity of polonium present. Suppose that it is found that in 95 days approximately 38% of a certain quantity of polonium has decomposed. Determine approximately how long it will take for one-half of the original amount of polonium to decompose

Note the assignment does not specify rounding amount, nor has their been given precedent for it.

Doing the calculations I get a result of 140 days with 2 significant figures.
My professor marks it wrong saying the correct answer is 137.8 days or 138 days.

I ask him about this, is response via email is

Dear student

Why do you have to round to 2 ? on what basis?

You have to work with precise values not the one you assume

Even if we said "approximately" 38%, you have to use that precise value. 

The final answer given by calculations is 137.8 days rounded to 138 days and not 140. 

Note that 140 does not satisfy our equations.

I bring it up to him, saying that the equation uses the word approximately, so 38% could range from 37.5% to 38.5%, with results 135.1 days to 140.1 days, and that is equation still holds if you round to significant figures. His response

Dear student

No I don’t agree with your proposition.

You work with the  value we give you, that is 38% and it will give you 137.8, you can round to 138 days.

I don’t understand. I don’t want to argue with a professor, but I’ve substantiated my claim for 2 digits rather than just rounding to a whole number. When I ask him for a matting he responds

Because in this specific problem, the only reasonable rounded value is 138 days, since the calculated answer is 137.8 days and we are dealing with whole days.A value of 137 days is incorrect because 137.8 days has already passed 137 days and lies within the 138th day. Likewise, 139 days, 140 days, or any other value would also be incorrect. Therefore, 138 days is the only appropriate rounded answer.

I know! But I’m using significant figures, there is no reason to round to whole numbers. What should I do? Am I wrong?

Edit: I’m not querying further with the professor as they have threatened to lower my mark.

I need the divisibility rules and factoring a binomial this is my 2nd day of middle school HELP

Hi hi! I have a test in physics coming up and im embarrassed to realize I have no idea how to convert units using given powers of ten factors. I cant post a picture, but basically the chart he gives us is like 10^9 Giga G, 10^6 Mega M. I cant for the life of me figure out how to convert using the scientific notations, instead of converting into whole numbers.

He said for the test we will only ever have to go to kilo, so basically how would i convert like 5cm to k using 10^-2 and 10^3. I know i can just divide by 100000, but I also know i wont be able to memorize that for all of them.

(p -> q) ٨ (q -> p) logically equal to (p <-> q)

Solved: it’s a law

-(2 x (-1))² +1-3² = -12

I got the answer of 6 after attempting to solve multiple times and after this failed attempts the site gave me a break down where it ended up coming down to -3-3² where it simplified to -3-9 to get -12

lim = x²-6X+9/x²-9

x=>3

(why cant i scrape the x² to get the function -6x+9/-9)

i tried it and had this=

−6(3)+9​/-9=−18+9/-9​=−9−9​=1

Im a high school student and I really need math hack like a real one im not kidding for example

“When a limit is indeterminate, you can take the derivative of the top and bottom and then substitute to find the answer"

Idk smt like that i wanna expend more about math and know better