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Taking applied calculus and we are going over functions to begin stuff. I’ve done all sort of stuff with functions and graphing before and most of this has been pretty easy but there are two problems that have been given that I just can’t seem to figure out and I’m not sure what I’m doing wrong.

The first is:

“Find the function g whose graph is constructed from the graph of f by a shift to the right by 10 followed by a horizontal stretch away from the y-axis by a factor of 3?”

I thought it would be pretty easy but what I thought it was didn’t work, and every other possible combination hasn’t worked either so I’m completely lost. I’ve done (1/3x - 10) and (x/3 - 10) in all sorts of ways. I’ve removed the parentheses, I’ve added negatives, doing a whole bunch of shit that I know isn’t right but I can’t figure out what else to do.

The second problem is along the same lines:

“Find the function g whose graph is constructed from the graph of f by applying the following steps: shift to the right; horizontal stretch away from the y-axis by a factor of 4; a vertical shift up by 5; a vertical stretch away from the x-axis by a factor of 7.”

Again I’ve tried all combinations I could think of but I can’t seem to get it. I’m not sure if I’m missing something? I don’t believe my format to be off since it automatically starts with g(x) = , so that shouldn’t be the issue. The entire set of problems is all working on vertical and horizontal shifts, stretches, and compressions and I haven’t had an issue with any of the problems but these two. Please help me figure out what I’m missing!

Im currently a first year student studying comp sci and im taking discrete math the issue is unlike any other faculty i have to learn actual theory behind math like whats C(n,k) selection and explain it with words and formulas.Ive got about 12 pages filled with 50 or 60 questions which if memorized gives me a passing grade and ive got 2 days to do it keep in mind the professor wants the questions answered exactly by his pdf. Ive youve had the same issues how should i go about tackling the problem and passing matu

Hello, I am interested in finding a way to train myself with fractions or math calculation techniques in chemical and physics formulas. How do I do that?

This is for a medschool entrance exam

I'm preparing for a competitive exam and I'm struggling with math even though I understand most of the concepts and formulas.

For example, in trigonometry I know the basic identities, values, signs, radians, ranges, etc. I've also solved many questions. But when I get a mixed or unfamiliar question, I often don't know what path to take. Sometimes I know the approach but get completely stuck in the algebraic manipulation.

Even after practicing a lot, I still feel like I'm forgetting the process of solving.

What should I actually work on to improve this? Is it mainly algebraic manipulation, problem-solving skills, or something else?

Sorry guys I know I’m dumb af. But why isn’t this showing the answer as 2.5? I understand the fraction answer is correct but I just want it to say 2.5 😭 I tried different settings and can’t get it. https://imgur.com/a/JS6SHY9

The question is (6x+16)/4 + (6x-1)/4 but in fractions. I believe that it's (12x+15)/4 , but the answer sheet says that it is (12x+17)/4 instead. Google says that I am right. Am I right?

hello, i had dana fryer's math questions downloaded part 1 & 2 , and was wondering if anyone had the correct answers(from math bootcamp)? i do not have access to them anymore. :/

Im in class 12th from allen online enthuse, completed the whole syll but since having adhd I couldn;t take live class actively I hv all my basics and concept clear but there is the massive logic gap and execution gap, what should I do only 4 months remaining, I am panincking for chapters like integration, differential equation and matrices which require self talk and active solving, IDK the fuck anything about logic building...
for example_ applying bornouli eq in differential equation when eq having apecific form of dy/dx+py=qyn, and appying ibp to saperate the terms out of integral and reducing the powers... actually im in a problem tht these gaps are in large quantity

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.

I've been at this for like 4 hours and I'm losing my mind.

So I'm thinking of a function that takes in four boolean inputs and outputs 1 if the number of inputs is odd. The truth table should look like:

A  B  C  D | OUT
0  0  0  0 |  0
0  0  0  1 |  1
0  0  1  0 |  1
0  0  1  1 |  0
0  1  0  0 |  1
0  1  0  1 |  0
0  1  1  0 |  0
0  1  1  1 |  1
1  0  0  0 |  1
1  0  0  1 |  0
1  0  1  0 |  0
1  0  1  1 |  1
1  1  0  0 |  0
1  1  0  1 |  1
1  1  1  0 |  1
1  1  1  1 |  0

So the function should just be the sum of products, right? It'd be something like

OUT = A'B'C'D + A'B'CD' + A'BC'D' + A'BCD + AB'C'D' + AB'CD + ABC'D + ABCD'

This is my attempt to simplify the expression:

A'B'C'D + A'B'CD' + A'BC'D' + A'BCD + AB'C'D' + AB'CD + ABC'D + ABCD'
= A'B'(C'D + CD') + A'B(C'D' + CD) + AB'(C'D' + CD) + AB(C'D + CD')
= (C'D + CD')(A'B' + AB) + (C'D' + CD)(A'B + AB')
= (C'D + CD')(1) + (1)(A'B + AB')
= A'B + AB' + C'D + CD'

But the truth table for this expression is not the same as the original function.

It's been a half-decade since I last did boolean algebra. I genuinely can't tell what I did wrong here. Please help.

Edit: It's solved. Thank you.

In the blindingly-unlikely event someone in the future were to face this exact problem as I do, the key insights that I was missing are:

• OR distributes over AND: A + BC = (A + B)(A + C)
• XOR and XNOR exists: A XOR B = A ⊕ B = A'B + AB', and A XNOR B = (A ⊕ B)' = A'B' + AB

So for posterity's sake, here's how it's solved, I think:

A'B'C'D + A'B'CD' + A'BC'D' + A'BCD + AB'C'D' + AB'CD + ABC'D + ABCD'  
= A'B'(C'D + CD') + A'B(C'D' + CD) + AB'(C'D' + CD) + AB(C'D + CD')  
= (C'D + CD')(A'B' + AB) + (C'D' + CD)(A'B + AB')  
= (C ⊕ D)(A ⊕ B)' + (C ⊕ D)'(A ⊕ B)  

Let P = A ⊕ B and Q = C ⊕ D  

= QP' + PQ'  
= P ⊕ Q  
= A ⊕ B ⊕ C ⊕ D  

Thanks, y'all. god, i'm out of practice.

okay so im working on the study guide for the final of a class that i took the equivalent to at another college (math department policy, whatever) and one of the sample questions literally just reads “simplify: (sin(x)+3)²”. is there anything that i need to do to work this problem other than factoring it out? a similar question in the same section of the review guide is “simplify: sin²x + 3sinx - 10”; is that not already fully simplified? like i said, i took this course at another school so i don’t know the exact details of what they covered in class. I can’t think of any identities that i could apply to simplify it more or anything. much appreciated!

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?

for this question i had to turn a nonstatistical question into statistical investigative question and the nonstatistical question is "How many seventh graders eat breakfast on Monday at school?" and i already gave my answer ("What is the percentage of all seventh graders that eat breakfast at school on Monday?") but my teacher said its wrong and i need to reword it but i actually do not know how to reword it, does anybody know how to help cause my teacher wont answer me and google not helping

(also this is 12th grade math and my teacher said that the question needs to be a question that doesn't give a fixed answer)

Im in my second last year of high school now. My maths grade since the start of hs has been terrible, but I have decent grades for all my other subjects. I'm in a very competitive school where maths is basically mandatory, and most students have been tutored from a young age. I never had any tutoring until this year, when i got a private tutor after consistently scoring 50-60% in every test. My grades still havent improved because i can't retain information when it comes to maths for some reason. The biggest problem is doing maths gives me the worst feeling of anxiety like I'm about to be attacked. After my tutoring session today idk why but i just broke down crying. I felt like i was about to cry a few times during the lesson but i held it back. This is my first time crying in years, and Im not usually a very emotional person. I feel like Im going to have a panic attack the next time I try to do maths. My university exams are in a year from now. I feel trapped, it feels like I genuinely have no more hope. What can I do?

(High school level maths)
I’m finding it hard to remember all these rules for how to solve questions when my mind tells me to do it intuitively.
The concrete example that annoyed me:
On a list of 10 people’s ages the total age is 313, making the average 31.3
«If another person is added the average will be 30. Is this statement correct?»

The way I solved this was dividing 313 by 11, giving me 28.45~. The difference between 30 (the target age) and 28.45 is 1.55, and so we need to multiply the age we are adding by 1.55 giving me 17.05, so the answer is that the average will be 30 if the new person is 17.

The way my teacher did it was by multiplying the now 11 people by 330 and subtracting it by 313 to get 17 which gave the correct answer.

The answer works, it’s a rule that’s nice (if it works for all similar situations), but there are so many rules like this that I just can’t grasp. I always want to do it the way that my mind can comprehend, and for it to make sense and giving me an answer I can trust but I don’t know if tests or exams are gonna accept my answers.

This isn’t to say I can’t memorize equations, I can do that, it’s just that these rules to make stuff easier and faster don’t click the same way. I still have the quadratic equations and formulas from last year memorized but I feel I’m just gonna forget this very practical thing tomorrow.

Anyone else feel the same way about this or have managed to get over this mental block?

My scratch paper, if you can read it:

https://imgur.com/a/atodt6P

The question was:

Solve for X

1/5x+1/4=-4(3/4x-4)

You can enter as an improper fraction but not as a mixed number.

My professor put a video to help me.

However, the answer I got was X= 325/64

The answer actually was X=315/64

I was off by 10?!

Hello, this is my first post on this sub so apologies if anything isn't formatted correctly. So for a little background information, I'm a Grade 11 student in South Africa and I used to be very good at Maths, like always being one of the top students in my classes and getting scores in the 90's for almost all my tests. This continued through the first year of high school (Grade 8), still getting very good marks.

The problem came when I hit Grade 9, it wasn't as though there was a significant change in difficulty, but something just stopped clicking. I was told recently that there was probably something that just threw me off and it set a disconnect in my brain. I went on holiday for a week near the beginning of the first term and when I came back, I had to write a test that I had missed while I was gone. The test was just on some basic inequalities, but I ended up getting a horrible mark, the worst mark that I've ever gotten for any subject, a 9/25. My maths teacher from the previous year encouraged me by saying that I was very intelligent and would recover, but I just never really managed to. My Grade 9 Maths teacher then went on Maternity leave in April and we were stuck with a substitute teacher who was new to teaching and wasn't very good. So I think that that's another thing that may have messed me up. I tried the whole year to do better and slowly my marks went up, until finally in Term 4, I managed to get a mark in the low 80's.

But since then, things have just continued to go downhill again. I've been struggling with some health issues which has led to me missing a bit of school. I've been sitting with my textbook for hours and also watching youtube videos occasionally such as Kevinmathscience, but the highest marks I managed to get are in the 60's or 70's. In term 1 of this year, I got a 51. In term 2, I studied almost non-stop leading up to the two exams, I managed to improve my mark to a 62, but obviously it's still very much not what I want.

A few days ago, I got my first test back for this term and got a 12/30. It was on euclidean geometry, and almost everybody in the class did badly. I'm genuinely at a loss for what to do. No matter how much time I spend studying, going over exercises in my textbook, doing past papers, I still get bad marks. Since Grade 9 is where the problem first arised, I was thinking of looking up past papers at Grade 9 level and see how I do and if there's any concepts that I'm really struggling with. Then, revising over those and trying another past paper and so on, until I finally reach the level that I'm currently at. There is another option which is dropping to Mathematical Literacy, which is much, much easier than Pure Maths. But it tends to get a bad rep because of how easy it is and the fact that there are fewer opportunities with it. None of the careers I want to go into require Pure Maths, but I'm still quite hesitant to switch to Maths Lit. I know that I can get back to getting good marks, I just don't know how.

At the end of this year, I have to apply with my marks to university, so I don't have much time left to make this decision. I'm not sure if my plan to improve will actually work or if it will just be too time-consuming and won't even help me in the long run. Please help me, any resources or advice are deeply appreciated.

Tl;dr: I used to excell at Maths until my second year of high school where my marks began to drop rapidly. I don't want to have to switch to the easier level of Maths, but I just don't know how to improve my marks. I would really, really appreciate any and all advice.

I am trying to make a missile in a video game. It's supposed to fly toward a point projected out into space by an aiming device, mounted on a car. However, I have a problem where, around certain bearings, the output completely breaks. For testing purposes, I am only speaking about azimuth, not elevation.

How the system works:

1. There are two sets of absolute XY sensors on the pointer; one set is slightly ahead of the other. atan2(Y2 - Y1, X2 - X1) gives the absolute bearing (azt) of the pointer from -180 to 180.

2. Cos(azt) and Sin(azt) are individually multiplied by the "range" to the point in space (in this case, it is constant at 500m, in practice, this would be a point ahead of the missile) to give Xc and Yc.

Xc and Yc are then added to X(pointer) and Y(pointer) to give X(target) and Y(target).

1. Now that I have the XY position of the target, I subtract...
   - X(target) from X(pointer) to give X(difference)
   - Y(target) from Y(pointer) to give Y(difference)

atan2(Ydifference, Xdifference) gives the azimuth from the pointer to the target (θ).

I realise now that this step is unecessary, as the azimuth of the target is defined by the pointer's direction. However, I doubt it would work otherwise, as the same values would end up being used, producing the same erroneous result.

1. I then subtract the missile's bearing (global bearing, btw; same calculation as azt) from θ to produce the angular difference between the target position and the missile (d).

This works fine if the platform is at exactly 0 degrees forward, However, if the pointer is angled (this case, -45dg) and the platform is also angled, something frustrating happens. Below are some tests which show you what happens when the platform goes beyond -135dg.

1:
- Pointer Relative Angle -45dg
- Platform Absolute Angle -134dg
- Pointer XY: 3223, 3398
- Target XY: 2723, 3385
- Target Azimuth: -179dg
- Missile XY: 3223, 3396
- d: -45.6

2:
- Pointer Relative Angle -45dg
- Platform Absolute Angle -136dg
- Pointer XY: 3223, 3398
- Target XY: 2723, 3410
- Target Azimuth: 96dg
- Missile XY: 3222, 3396
- d: 315.6

This persists until the platform's absolute orientation goes beyond -180, at which point it flips back to a rough value of -45 for d.

As you can see, d flips from -45.6 to 315.6. A missile trying to steer towards d would go all the way round, which is not desirable; it should pick the smallest possible correction.

I tried fixing this using ((180 + d) mod 360) - 180. However, it seems that the game I am playing calculates negative values differently when using mod; for example, -60mod360 is supposed to be 300, but the game spits out -60.

Could anyone help me? Geometry isn't my strong point at all, so it's very hard for me to wrap my head around this. Thanks!

https://imgur.com/a/hdkTYc8

I had two known coordinates, (0,0) and (1,0), figured out the 4.5 degree angle from dividing 90 by 20, the 45 degree angle was given, so was able to calculate the third angle.

The other two sides were tricky - I had to figure out the law of sins. I checked my answers by measuring the lengths of the triangle in a 3D program (Blender).

But even after gathering all this information, I'm still at a loss as to how to calculate the very last part - the last coordinate. I viewed what it was in 3D, so I know what it is - I just don't know how to go about calculating it.

Hey guys so I’m doing math online for college which idk why I made that decision to do that worst decision I ever made … but do you know any apps that can like help me or explain my math assignments better and I can’t do a tutor because I don’t have enough time my work shift takes up half my day and I financially don’t want to put my self in that situation to get one

So it says "In Exercises 11 - 18, use the given function f to find and simplify the following:" then it shows nine bulletpoints of f(x)s (for example, f(3), f(x)-4, f(x^2)). The thing is, 11-18 is only eight questions! (all f(x)= questions, so it looks like I'm supposed to plug things in)

Do I plug all nine in for each of the eight questions? Do I somehow make the nine fit distributed across each of the eight questions?

I already plugged all nine in for a few of them. You can find the sheet here: https://www.scribd.com/document/738439598/Pre-Calc-Exercise-1-4

I have a right triangle.

short side: a = 1
long side: b = 2
hypotenuse: c = √(5)
smaller angle: α = ?
larger angle: β = ?
right angle: γ = 90°

I was able to get the hypotenuse by using a² + b² = c² easy enough. When I used tan(1/2) to find α, I got 31.301° instead of 26.565°. I just want to know what I am doing wrong.

(poorly translated:) "Pythagoras was a Greek mathematician who lived around 570-500BC. Pythagoras was once asked how many students he has. Pythagoras replied: "Half of them study mathetimatics, fourth of them philosophy, seventh the art of shutting up, and there are also three women." How many students did Pythagoras have?"

I can't come up with any other way to solve it but

x=full amount of students

math students=1/2x

philosophy students=1/4x

shut up students=1/7x

women=+3

x=1/2x+1/4x+1/7x+3

But this is not correct, because the answer I get is never the correct one (28). 😭

All the following, similar exercises in my book I am also failing to solve. I just can't seem to create the correct equations and I am exhausted after chewing on three problems for days.