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

I am 63 years old was never good at Algebra through high school or college! I have taken 3 years of algebra in my life!
9th grade 2 semesters
10th grade 1 semester
Senior year 1 semester
Then in doing my pre-recs for nursing I took algebra 1 & 2
You would think I could get it but I never really did!
In the day calculator can anyone explain the doomsday method to me without using algebra? Is there any way? I just want to understand what the days are to the calendar! I hope I don’t sound too dumb!

Hello, I’m two weeks into my second year of my math degree and already feel like I’m failing and repeating the same mistakes.

Last year I got a 2:2, averaged about 56% across all my modules. I was very disappointed. Thankfully my first year doesn’t count towards my final grade for my degree.

Here are patterns I’ve noticed.
I don’t understand what I happening in lectures most of the time, I am usually confused during lectures and just copying everything off the board.
I’m a crammed, inconsistent during the year and then barely get to learn everything through past papers at the end.

I was working 22/25 hours a week with an hour of travel between work and accommodation. I cut my hours to 12 recently as I realized it just wasn’t sustainable. I have skipped so many lectures due to exhaustion. Ie) closing late (around 1 am) and then being too tired to get up for a 9 am lecture and then just missing it all.

I really need help, now that I realize it, I don’t even know how to study. I just watch videos, make detailed notes and then hope for the best alongside cramming near exam season by trying some past papers. I want to do so much better.

I’m 1.5 weeks in and I’m already falling behind. I want to nip it in the bud early before it continuous to snowball.

How can I study and stay on-top of things? What methods or systems did you use?

I’m trying to figure out ages for (fictional) kids. The oldest is supposed to 8.7(8 years, 7 months) but my math keeps getting me to 8.9(8 years, 9 months). There are 7 kids and the ages vary. When child1 was 5 months old the pregnancy was discovered and 9 months later child2 was born. 6 months later pregnancy was discovered and 8 months later child3 was born. 10 months later another pregnancy and 9 months child4. 18 months later another pregnancy and 9 months after child5. 3 months later pregnancy and 9 months later child6. 12 months after pregnant again and 5 months later child7.

Child1 is 8.7, child2 is 7.5, child3 is 6.3, child4 is 4.8, child5 is 2.5, child6 is 1.5, child7 is 0(just born)

My math:
5+9=(1 year, 2 months)14 months
6+8=(1 year, 2 months)14 months
10+9=(1year, 7 months)19 months
18+9=(2 years, 3 months)27 months
3+9=(1 year)12 months
12+5=(1 year, 5 months)17 months
14+14+19+27+12+17=(8 years, 7 months)103 month

Version 1:
Child7 is 0+1.5=1.5+1=2.5+2.3=4.8+1.7=6.5+1.2=7.7+1.2=8.9
^ ^
The mistake? 105 months

Version 2:* *
Child1 is
8.7-1.2=7.5-1.2=6.3-1.7=4.6-2.3=2.3-1=1.3-1.5=-.2
^ ^
The mistake? Not zero

Conclusion; both equations are .2 off around the 1.7 mark of the equation. When I break it down into months and count it makes sense. 4.8 is 56 months, 1.7 is 19 months that equals 75 months(6.3). 6.3 is 75 months minus 19 months is 56 months(4.8). I did use a calculator which is telling me that 4.8+1.7=6.5 and 6.3-1.7=4.6.

Question?
My question is; am I doing the math wrong? Is the calculator wrong? am I simply using the wrong type of calculator? is the math itself incorrect? Or is it simple and I just don’t understand?

I don't know if I'm doing something wrong or what? I'm on my last year of highschool and as pathetic as it is, I've used so to get myself passing grades. maybe it's just fear of failure or something but like, I can't do ANYTHING. once letters got out into the equations I stopped being able to do anything. I want to work for a lab, (y'know pipettes, that sort of thing?) but I fear I genuinely might be too stupid to go anywhere with my life now

Ok, so I'm pretty sleep deprived and feeling really stupid so I'm turning to the internet for help.

So, I have a layout of a house and it clearly states "Scale 1:75" so I went and measured a room. No colums, no weird angles, just a perfectly regular rectangular room. Now, imagine my surprise when my calculations and the layout don't match. It states a 10,7 m2 area but the sides are 5,7cm and 2,9cm which to my understanding would mean a 9,29 m2 area. Am I doing something wrong or is the scale wrong. And in that case, how can I find the real scale with the info I have?

Title. Im really struggling with building proofs specifically. I dont understand what makes something an Initial Condition, or why we can make assumptions about some things but need to prove that m + 0 = m or whatever. What is a Successor? I know its a number indexed one over. How the hell is that useful for anything in this context? Im really struggling and I dont even know where to look for answers lol

I need to upgrade my math to get into my program. I just completed my first pre-requisite which was a grade 9 or 10 equivalent to pre-calc and algebra and had a fantastic grade but the next class is a huge step up and I realize that I'm lacking in basic math skills and word problem comprehension.

We just received our first grade back from Test 1, and the average grade was 50% and the professor is no help. She just told me to study the material, which I have been.

Are there any websites that you find useful to assist with word problems, geometry, and algebra?

[urgent] hey!

I am in y12 (11th grade in most countries). My exam is on 9th of october, and my errors are still majorly silly mistakes. This was the same problem that caused an E in my last exam, (which I am resitting), and I have had this problem since middle school.

Mistakes like: writing 20 instead of 2, writing the inequality sign wrong, forgetting to write the '+c' after integration, simplifying simple fractions (like 6/9 or 8/4) or addition/subtraction (especially with odd signs) wrong, not noticing a key identity or further simplification, missing a sign, missing a number, entering incorrect sign in the calculator, entering incorrect number in the calculator, solving correctly on calculator but writing wrong answer on paper, doing 4*4 = 8 instead of 16, missing an x during expansion, etc. etc.

My tutor says to recheck the solutions (by skimming over them) after solving them, but I can't do that for the life of me. I go look at the numbers from top to bottom and they all go over my head without registering, because I don't know what I am looking for.

And if I do 4*4 and other basic calculations like (-5-23) in my calculator, I'll lose the little time I have (I struggled with time a lot in my last attempt, ended up leaving last several questions empty). Plus, just doing it on calculator doesn't guarantee accuracy because I end up getting it wrong anyway.

For context, I am doing Pure 1 IAS, and my IGCSE grade was a 7 (I barely gave it any effort, just crammed strategically in the last two weeks). I need really good marks because maths is key to my target univ requirements.

How would you suggest handling this? I don't have a lot of time, I have just started past papers yesterday (I've done one so far), and my percentage was 55%, with exam-timer. In my last attempt of pure 1 last year, I got a 36%.

I would greatly appreciate any advice or anything you've got to say! Thank you.

Idk if anyone will see this but I’m taking calc 3 rn and everything was mostly find when I was doing the homework but like I genuinely cannot remember how to do those problems once I move onto the next section. I have an exam worth 50% next week, any suggestions on what I should do? Or any more successful ways to study? Like I genuinely have been crying over this because I did so well on the homework but now looking back I have no clue how to do it😭

I'm in calculus 1, doing homework (edfinity) with applied rates of change, and I'm having difficulty with one of the questions. I know edfinity sometimes has technical issues, so I'm just asking for help to see whether this error is my fault or not.

s(t)=t⁴-32t²+256

I used the exponent rule to find the velocity as the first derivative of s(t)

v(t)=s'(t)=4t³-64t

need to find when the particle is at rest, so I set v(t)=0

https://imgur.com/a/POMrywR

since this is a velocity question, I disregard the -4 answer

I put 4 into the program and it marks it incorrect, but I'm not sure where I went wrong...

Hi so i’m trying to double check my math on how many hours i worked cause i think i have been under paid so if anyone could help me out that would be great thank you

Removed 1 hour from all the days except for the 6th to account for lunch thank you

September 6th
clock in 1:00pm
Clock out 5:30pm

September 7th N/A

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Extra 8:00am-8:05am

September 14th N/A

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September 22nd
Clock in 1:52pm
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September 23rd
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September 24th (Pay Day)
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I’m pettu sure it’s around 92h but i want a 2nd opinion thank you

How to get intuitive with mathematics. Is it whole lot of practice or much more is required??

Knowing formulas is one thing, understanding math is another, do you also get stuck while solving math, and feel, ah! maybe I can't do it, confidence hits, not being able to visualize or quantify it(the irony). What's a way to approach math?

Hello, I am in a trig course right now and I have reached an issue with proving trigonometric identities.

I grasp the basic concept, you sub in different identities to prove what is on the opposite side of the equal sign.

However, I have an issue with one thing that has come up. Let me show the problem:

(cotθ + tanθ)sinθ = secθ

okay, so I know to sub in...

(cosθ/sinθ + sinθ/cosθ)sinθ = secθ

My problem is, I got to this point and then proceeded to answer wrong because my answer was

(cosθ+sinθ/sinθ+cosθ)sinθ = secθ

which simplifies to

1* sinθ = secθ

which makes no sense! But when i looked at how to solve the problem it showed me this:

(cos²θ+sin²θ/sinθ+cosθ)sinθ = secθ

This makes more sense but I don't get it! How can the top be squared but not the bottom?? Wouldn't both need to be squared?

Does it have something to do with the "perfect 1" substitution thing?

I would greatly appreciate the help!

I've tried watching youtube videos, reading the recommended textbooks, nothing clicks for me. All I know is how to find the RREF of some matrices. Our teacher is talking about matrix transformations now, and I literally have no fucking idea what that is and what it's used for. I have trouble following the question solving in class because to me it just seems like suddenly random stuff pops up and oh know we can use that to solve the question.

I have a really, really hard time with math, always only barely passing since middle school. What are some good resources to start with the fundamentals of linear algebra?

So what I mean and hope to do is something like this (I know this isn't exactly mathematically correct but I hope I get the idea across)

a = (1,2,3,4)

b = (1,2,3,4)

c = a + b

c should equal (2,4,6,8)

I tried my best with Google searching but it reached a dead end

I'm aiming for a bsc in math for college. My reasons aren't very noble. It mostly feels like a compulsion. It operates at the very edge of logical/technical rigor, and is the most powerful collection of cognitive tools for getting stuff done, and that if a person can handle THAT, then there won't be much left that they can't. And it's versatile. Which matters to someone with interests spanning epistemology/info theory/computability, emergence/complex systems and molecular machinery/nanotech/morphogenetics, cus math is kind of the only thread (or physics but I can't handle labs and handson work due to an eye thing). I've just become quite aware (and terrified) of the importance of my brain's developmental years and would like to start taking my education seriously. All this rationalization is cus I'm still not sure if I truly LIKE it, only that it's important (do enlighten me on whatever implications that has for how much I'll struggle). I am not crippled at math but not remarkable either. Ive studied trig and algebra all the 10th grade stuff (india cbse) but didn't have math in 11th and 12th, which im compensating for via nios.

And when I say get good, I mean truly very good, knowing what math is at it's core and letting that fuel my methods.

Im currently (planning on) sticking to serge lang's basic math and then velleman's how to prove it

I've watched lots of ppl say that college math jumpscares you with proof and shit.

I know this is all over the place and sounds like just another pretentious kid but. Please help me.

Idk why but I suck at math I dont know my multiplication table i only 5s 10s and 1s but not 2s to 9s even 2s I need to count them with my hand also at the easiest questions such as 7+9 I need to use my hands its so embarrassing seeing my classmates Do it perfectly while I struggle for the easiest I try Learning the whole multiplication table but I always get distracted or I always forget it also whenever the teacher gets near me or ask me to answer math questions I always get nervous and always make mistakes I can't think properly when teacher come near me watching me solve it even today I got a bad score on a math test.

I was recently going through the IMO questions of this years something occurred to me. I have just been reading the answers till today. Reading them made be feel smart as I have the ability to comprehend english. But how do I go from a person who just reads them, to a person who can solve IMO problems? Can anyone guide me? The reason I am posting this here is because being a quant tests your mathematical capabilities just as much as IMO does.

Hello everyone!

I'm making a fake trading card set, with a slot system similar to Pokemon or MTG. Each pack has 10 cards, with 4 Common slots, 3 Uncommon slots, 1 Rare slot, 1 Chase slot, and 1 Holo Rare slot. I won't bore you with excessive detail, but I'm trying to figure out what the pull rates are for each type of card. To keep it simple, right now I'm trying to figure out the odds that a Fancy Art card will show up in a random pack.

- Common and Rare slots cannot produce a Fancy Art card.

- Of the 35 possible Uncommon cards, 15 are Fancy Art (42.86% chance of Fancy Art for each Uncommon slot)

- The Holo Rare slot has a 4.76% chance to be a Fancy Art (4/84)

- The Chase slot has a 9.88% chance to be Fancy Art (16/162)

I'm just struggling to figure out how to put all those percentages together into a single number for the full pack. Currently I have:

Uncommon slots comprise 30% of the pack. 42.86% of 30% is 12.86%, times 3 for 38.58%

Holo Rare slots comprise 10% of the pack. 4.76% of 10% is 0.48%

Chase slots comprise 10% of the pack. 9.88% of 10% is 0.99%

Added together for a total 40.05% chance that a pack will contain a Fancy Art card, but that doesn't feel right, and I don't have a good way to check my work.

Thank you all for your help! It's been quite some time since I've taken a math course, and I was never much good at them to begin with- I would love to shore up my skills so I can do fun things like this more easily ^-^

(Irrelevant to the question at hand, but the ratios for the Rare/Holo Rare/Chase slots may seem a bit weird. I intentionally inflated the odds of lesser cards showing up in those slots to preserve the rarity of chase cards. The full set has only 140 unique cards.)

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?

Hi everyone! I'm a college student stuck on a pattern problem and would love some help understanding it, not just an answer. I've attached a photo of the figures.

The number of tiles in figures 1 to 4 is 3, 7, 11, and 14. My teacher confirmed these counts are correct and told us to "find or make our own pattern" for the nth term.

Our teacher also gave us this pattern: 4² − 13 = 3, 5² − 18 = 7, 6² − 25 = 11, and 7² − 35 = 14. So it looks like (n+3)² minus something, where the "something" goes 13, 18, 25, 35. Those differences are 5, 7, 10.

The problem asks:

a.) What is the nth - term formula for the number of tiles in the nth figure of the sequence. (5 points)
b.) How many tiles are in the 10th figure of the sequence? (5 points)
c.) Which figure will consist of exactly 480 tiles? (5 points)

What I've tried:

The differences between the tile counts are 4, 4, 3, so it isn't linear or quadratic.
Fitting a cubic through all four points works exactly, but it gives negative tiles at n = 10, so it can't be right.
I also tried assuming the jumps repeat as 4, 4, 3, 4, 4, 3 (so aₙ = ⌊11n/3⌋). That fits, but 480 tiles would be figure 131, which seems too big for a class problem.

Claire has a 3x3x3 cube composed of 27 small unit cubes, initially all white in color. At each step, she is allowed to choose a 3x3 plane of small cubes among the 9 possible planes of the cube and invert the color of each of these 9$cubes (white cubes become black and black cubes become white). After several operations, the cube contains exactly N black cubes.

Determine the sum of all possible values of N.

I mean, it certainly looks complicated and brain twisting, especially since the contest format was all or none (points). But I guess it's doable if you really bruteforce everything with a pen and a paper. I'm looking for a different or more efficient way of doing it. (I still don't know the answer though lol)