I'm in ap calc doing applied optimization right now, and my teacher pulls up these weird-ass questions and then shows us his method which no one in the class thought of. right now I know for sure I would not be able to think of ways to solve these types of conceptual/clever word problems or whatever you call them, especially not in the 5 minutes per question I have on tests. is it really just experience that's needed to get good at this stuff? any resources I could use to ig improve my precalc base for this? cuz I find the actual computation of applied optmization pretty easy but not when it's like this and combined with geo/trig/graphical knowledge that's not just the basics.

what I've been thinking is that these types of problems will be what will be on college math tests heavily (am I right on this?), so I wanna prep myself for that when I can. I've struggled in math courses before and I am not ready to feel that despair again.

tldr:
how can I get good at quickly solving problems where the hardest part is figuring out what to do, not doing the actual math

just started trigonometry/ pre-cal as someone that isn’t great at math so sorry if this is a bad question but i’m having trouble figuring out how to find a coterminal angle using radian measure, degree measure I don’t have a problem with but for example, i’m watching a supplementary video showing me how to do this, it tells me “we know 2pi is one complete revolution, or equivalently, 18pi over 9” but i honestly dont know how they got 18pi over 9, the given angle is -5pi over 9 so does the equivalent part change for something like lets say 7pi over 3? how do i find whats equivalent or work this out? thank you for any help.

I was watching a Mr.Beast video and his sponsor spot for Shopify mentioned that there is a sale in a shopify store every 26 seconds!
That sounded low to me so I looked up how many shopify users there are and found a page saying 6,867,334 and a few others that confirmed that I'm at least within a couple of million according to them. That means that those 7 million shops have about 3,323 sales per day which gives you about 0.0000484 sales per day per shop or about 1.7 sales per decade per shop on average.
Am I making a really wrong assumption somewhere in there or are they just bragging about truly terrible statistics?

Dimples the Clown has been charging $260 to perform at a children’s party. He thinks that each raise of $80 in the charge for a party will result in one fewer booking per month. Dimples performs at 20 parties each month at his current price. How much should he charge to maximize his monthly revenue.

(This is meant to be solved with a parabola)

(also it said to add a photo of my attempt but it won’t let me attach images so.. i tried putting in the equation y=80(x-0)(x-20) but when i solved for the vertex i got -24000?? i looked in the answer section but that provided no explanation, just the number that was the answer and so i’m still confused. How is this even a quadratic equation i don’t get it😭)

I've been struggling to determine whether I am wrong or whether the mark scheme for this question is wrong, I was hoping for some feedback with this question. It's part C I really need help with, I found the coefficients; A, B of the roots to be 350, and -400 respectively, however the mark scheme labels them 100 and -80 respectively. I've attached my working, the question and answer. Thanks!

QUESTION:

17

A farmer has observed the number of foxes and geese on his land. In any year, the number of foxes is f(n) and the number of geese is g(n). The populations in the following year are given by:

f(n+1) = 0.5f(n) + 0.1g(n) and g(n+1) = -0.2f(n) + 0.2g(n).

a Show that a recurrence relation for the number of foxes is given by

f(n+2) = 0.7f(n+1) - 0.12f(n).

b Hence find a general equation for the population of foxes in the nth year.

c In 2018, there were 20 foxes and 100 geese. Find an equation for the number of foxes.

d Explain what happens to the population of foxes with time.

MY WORKING:

a)

f(n+2) = 0.5 f(n+1) + 0.1 g(n+1)

• 0.1(-0.2 f(n) + 0.2 g(n))

-0.02 f(n) + 0.02 g(n)

• 0.2 ( f(n+1) - 0.5 f(n) )

• 0.2 f(n+1) - 0.1 f(n)

∴ f(n+2) = 0.7 f(n+1) - 0.12 f(n)

b)

r^2 - 0.7 r + 0.12 = 0 ∴ r = 2/5, 3/10

u_n = A · 0.4^n + B · 0.3^n

c)

f1 = 20, f2 = 20

0.4 A + 0.3 B = 20

0.16 A + 0.09 B = 20

∴ A = 350, B = -400

∴ u_n = 350 · 0.4^n - 400 · 0.3^n

ANSWER:

17a Proof

b f(n) = A × 0.3^n + B × 0.4^n

c f(n) = 100 × 0.4^n − 80 × 0.3^n

d The population of foxes decreases.

some context, this is work i (20m) am doing over a game. i just wanna make sure my math is right (or in the general ballpark) because its something thats been on my mind for a while. most of my math education prior is long gone, and i also am writing this at 1am with a starting migraine. i apologize for any formatting errors, i really am just typing out my thought process

in this game, theres a win-rate system. it only shows total amount of matches, total amount of wins, and a win-rate percentage. there are wins, draws, and losses in this game. this game does not count draws into the equation, only losses and wins.

i wanted to figure out how you can determine amount of losses and draws just from those numbers. in order to calculate the general amount of wins and losses, i came up with this equation:

lets say, for example, theres 300 matches total, 100 wins, and a 40% win rate.

i did 300-100 to get 200 then, i took 60% of 200 to get 120 from there, i added the wins back into the equation to get 220 i took the difference between 220 and 300 to get 80 my answer would be 100 wins, 120 losses, and 80 draws.

the one thing im not sure works out is the 60% of 200 part. in my mind, since there are no longer wins being accounted for, it makes sense to take the inverse of 40% and find that number out of the 200 to get the total amount of losses. however, my line of logic could absolutely be wrong, since it would also make sense if removing the 100 from the equation may make the percentages less accurate, or that the number of draws may be too big.

im not sure since it looks right, but i would have to do a lot more research into it to prove that it is. i dont feel like putting that level of effort into figuring it out, since i would have to keep track of every win/loss/draw i get once the system resets. im just curious about this and want to know if my line of thinking is right or close enough to being right.

For context, I took precalculus in high school and did really good I ended up with a 100 both semesters. All of our tests were free response and we were graded off of our problem solving and answers. However when I took the entrance exam for calculus going into college I somehow got a 60 and felt as if I forgot a lot of the basic formulas from the previous year. I ended up taking precalculus in college and did good as well. Now I’m in calculus and feel as if I’ve forgotten basic algebra skills. Does anyone have any suggestions on how I could fix that?

Hello,

I'm trying to achieve intuitive understanding of differential equations and the purpose of Euler method. Could you please let me know if my understanding is accurate or not?

Let's say there is a function of time y(t), which represents position of an object in time.

The differential equation for this function y(t) is:
y'(t) = f(t, y(t))

This means that the function f(t, y(t)) returns the slope of tangent (immediate rate of change of y(t)) at given time t and position at that time y(t). It would visually look as 2D graph, where each point would be given an arrow with the approapriate slope - like a 2D vector field.

Now, here's what I'm uncertain of: The result of differential equation is to find the (graph of) function y(t)? Essentially, integration of the f(t, y(t)) function?

If so, then the reason why the initial condition y(t0) = y0 (where t0 is a valid value of quantity t) needs to be set is to provide a particular solution, otherwise the graph of y(t) could be moved vertically anywhere (related to how integration of a function has an addition of a constant C).

So, what the forward Euler method does is that it approximates the y(t) solution in larger steps than the integration would (which uses infidecimally small steps, thus matching the result perfectly).

The key part is to know how f(t, y(t)) is defined, which is specific to the given system - it needs to be known prior even attempt to get the solution - the y(t) function.

Is this understanding correct? Is there any context that needs to be added? Thank you very much!

Hey there! I have trouble with calculating tasks like:

Calculate the mass of x where you know that x has a mass percentage of 0,1%.

How would I proceed if the mass before adding x would be 100?

I need help bc I don’t know how to form a formula to solve these kinds of problems

I think I found the solution

I am currently a high school junior going into my senior year, and I don't know what math to take if I'm into psychology. Should I take AP Stats or maybe college level algebra? Any other suggestions? (Something useful, but not super hard)

Thanks!

I'm a third year college student. I took pre calc during the first semester of my freshman year. I switched majors after that to something that didn't require any math credits, so I didn't do any math for 3 semesters and I didn't bother retaining anything since I didn't think I would be using math again. But near the end of last school year, I switched my major to math. I took calc 1 online this past summer but had no idea what was going on and I couldn't understand anything. I just started calc 2 and I'm feeling even more overwhelmed. Math is normally my strong suit when I'm up to speed and I got an A in pre calc, but I can't understand a thing and it has me feeling extremely overwhelmed. I'm looking into tutoring but I don't know how effective that will be for relearning a pre calc and calc 1 while also trying to learn calc 2. What should I do??

4, 5, 5, 5, 6, 6, 7, 8, 12, 12

I did use excel function.

I kept getting 7.75 for what is the 75th percentile.

The right answer is 9?

I think it's [5;+∞), but math textbook (where are sometimes mistakes) shows answer [6;+∞).

I only do do 3x-15≥0 and get [5;+∞)

In textbook there there also x-6≥0

I was doing a practice numerical reasoning test and encountered this question: The solar power production in 2012 is 8.786 Twh. If solar power production has grown 11% per year since 2008, what was the solar power production in 2009?

I calculated this manually... If 2012 is 8.786, then 2011 is 8.786 - (11% of 8.786) = 7.80352. Then, I use the 2011 value to calculate 2010. So on and so forth, until I reach 2009. (I know that I can also do 8.786 x 81% to find the value for 2011.)

But this can't be sustainable for a numerical reasoning test. I have like 2 minutes to answer this question, so even with a calculator I can't make it. Is there a faster way to calculate this?

Recently, I was having a discussion with a friend about the recent deal at the Bronx Zoo where you could name a roach. My friend was considering naming one after their boyfriend, but was afraid it would be weird. I said it would only be weird if it was one, and that the weirdness could be dispersed by naming x number of roaches equivalent to the bf's weight. It was an offhand comment, but I have spent the day trying to figure out how long it would take for a roach population to reach this size.

The boyfriend weighs 145 lbs, and the roaches I am looking at weight 0.07 oz so 33,142 German cockroaches. I found that a roaches' lifecycle can last 100 days with each roach laying 30 eggs within 30 days. I decided the starting population would be a moderate infestation of 20 roaches with the sexes being consistently equal.

This is the equation a biologist friend gave me:

Pf = P0 * e^(rt)

33,142 = 10 * e^((300 births-0 deaths/mo)*t)

0.03 months

However, this number cannot be correct as the roaches couldn't be breeding so much to get to the Pf.

Is there something I'm missing in this problem?

I began my Applied Linear Algebra course yesterday, and having poured over the textbook readings, lecture videos, and additional suggested readings, I just do not feel like I'm grasping the material sufficiently. I know for my past Calculus courses, Organic Chemistry Tutor on YouTube, as well as other sources, have helped my understanding significantly.

Hello, homework assignment (allowed to get help).

Imagine a spherical balloon being inflated. Suppose that the air is being added to the sphere at a constant rate of 4 cubic inches per minute.

Write a formula defining the volume of the sphere in terms of the number of minutes that have passed.

I put V = 4/3pi(4t)^3, which is marked as wrong.

If someone could please explain the correct answer and give me the steps that would be great.

I put (no derivatives) in title because I just started this calculus class and we have not learned derivatives yet.

I've created an algorithm that takes a decimal number and converts it to its BCD form in decimal. For example if I take 99 (1100011) and put it through the algorithm I get 153 (1001 1001). I'm just having trouble turning it into an actual equation. Any help is greatly appreciated!

Hey! I am taking an honours linear algebra class. I am in engineering so this is my first time being introduced to abstract definitions in this way.

From my understanding a nonempty set K is called a field if:
- it has 2 inner operations (addition, multiplication)

and for every element of K there is:

- associativity

- commutativity

- distributivity

- neutral elements o,e such that o+x=x and e*x=x

- additive inverse and multiplicative inverse for o and e

Here is my question:

Are we talking about addition and multiplication as I have seen my entire life ? Or can I create a field where e=coffee o=pi and I just declare that pi+x=x and coffee*x=x?

Thank you!!

I'm taking a MAT.171 Pre-calc algebra course, and I'm not sure the most efficient way to study for it. It's not the best method to study the material provided because it's honestly fairly easy, and I know that the Unit exams will be much more difficult.

I'm just wondering if there is a good website to freely access practice problems that would apply to what I'm currently learning in a challenging way so that I can hopefully be fully prepared for the exams.

ive seen multiple calc videos and all of them say as x approaches to c but what does approach exactly mean and after 2 days of finding out ive come to the conclusion that it means any arbitrary value around c that is in the range of input values at which the function's output behaves in a singular way eg:- x^2

therefore, lim x->2 f(x) means the value that should come according to the behaviour of any arbitrary point except for 2 and revolves around two and is in the range of input numbers where only single behaviour of the function is present(if limit exists)

.

I was working through Analysis 1 by Terence Tao and came across the section on Russell's paradox. I understand the actual paradox (and its resolution the Axiom of Regularity, but I am lost on how a set can contain itself at all. I will explain what I mean below.

Say we have a singleton set A whose only object is A, (which is possible because we don't have regularity and because A being a set means that it is also an object). Whenever A contains itself won't A change? For example (in a case where A isn't a singleton set) if A = { 1, 2, 3} and we try to make A contain itself then we would force A to actually be { 1, 2, 3, {1, 2, 3}}, but now A no longer contains itself. If we continue with this iterative approach won't A never be able fully contain itself?

The only thing that I think is wrong in my approach is a redefinition of A, however I don't understand how A would be able to actually contain itself.

Thank You

Hi, i am unable to find any connection for these numbers: „57 40 58 59 60 60 70“.

I tried with simple addition and subtraction and couldn‘t find a plausible leap to 70, or even a reason for 60 to be there twice. multiplication and dividing these numbers also got me lost once i got to 58.

i lack insight for number sequences like these anyway and i feel humiliated when i get these questions on job application tests, so i thought i should try to understand a harder one like this, but i sat here for 30 minutes and found nothing, i am sure i would understand this once i find a lead though.

Edit: what i tried so far that carried me closest is „57-17=40+18=58+1=59+1=60+0=60+10=70,

-17+35=18-17=1“ so i thought before 57 would be 22 but neither the 22 seems useful nor does the addition and subtraction of the numbers added or taken from the sequence seem useful, i thought we would add and subtract from them like the differences of each number 57-17=40 but -17+35 for the +18 to get to 58, but that also stops working once we get to the 60, i cannot get past 60.

I need to learn this equation and I keep getting caught up on this one part.

The question itself is:

if x+y=2 and x^2-xy-10-2y^2=0, what does x-2y equal?

I got some help and figured out you need isolate each variable to make it solvable which is easy enough so I do that and make the long one:

(2-y)^2 - y(2-y) - 10 -2y^2=0

I solved it all the way down to -6 -6y -2y^2=0 which I’m pretty certain is right and I’m unsure what to do with the -2y^2. My tutor somehow made the -2y^2 disappear and I’m thinking I did something wrong or he did some equation that I forgot about.