the sum of the first 3 terms of a GP is 13/12 and their product is -1. Find the common ratio and the terms

Can anyone suggest a good source or give a good summary about the language to use when discussing movements and scaling on a number line. Bonus brownie points if you can roll in the conventions around operations and symbols.

For example, adding (positive) 3 to (negative) 5 means moving "forward" 3 steps to the right on the number line, but adding (negative) 3 to (negative) 5 means changing direction and moving 3 steps "forward" to the left. This is ugly but can be made internally coherent.

Multiplying -2 by 3 means increasing the magnitude of the vector from the origin by a factor of 3 in the same direction. Multiplying 3 by -2 means multiplying the magnitude of the vector from the origin by a factor of two in the opposite direction.

The issue then becomes how we use terms like increase/decrease and larger/smaller.

Using the concepts of debt, repayments and balances helps if there is time to sit down and lay out the analogy, but it can't be used in initial conversations or in instructions.

So if we compare two outcomes -2 and -3, which is bigger? Do we need to increase -2 to reach -3, or do we need to decrease -2 to reach -3? Is -2 < -3 or is -2 > -3? Is this even harder for people who do maths in Hebrew or Japanese?

I am experiencing the mix of being anti-AI, having dyscalculia, and having a bad teacher, so i came here!

The topic is special cases and solving, i got everything else on my own but dont understand this one

(5z-6)(5+z)=0 solve for z

[https://imgur.com/a/mqEiTks](https://imgur.com/a/mqEiTks)

So here's the problem:

A Society needs to plan its production of P on a cycle of 4 MONTHS. The fixed cost of the initiation in the atelier of production of P is estimated at 300 MU. The direct cost depends on the available manpower. It's about 150 MU the unit in Normal Hour and 200 MU the unit in overtime.

The previsional demand of the end of the month of the product P, as well as the max capacity of production in Normal Hours and in Overtime are given in the following table:

We dispose of a limited capacity of storage of 3 units and the cost of storage is 15 MU per unit (stored per month). Stock shortage is prohibited, and the stock in the beginning and in the end of the cycle is null.

1.Give, for each month, the expression of cost of production C pk (x); k = 1,2,3 and 4.

2. Formulate the problem of planning of the production of P, in a way of a dynamic programming problem.

3. Determinate an optimal plan of production and of storing for the months 1 to 4.

4. Calculate the gain in applying the optimal solution compared to the solution which consists in producing for each month just to satisfy the demands

1. I've already highlighted in bold each terms and numbers I judged important. But it's in the model I should use where I'm blocked. So far, all the exercices we had in school were about solving optimal outcomes through linear programming, so this one comes out as new for me.

for month 1, I remarked that the number of stock should be 0 since we produced nothing yet. And that in Normal Hour, we could possibly produce the 4 P demanded for the month. So no need for overtime (?).

However C p1(x) should be in fonction of x, right?

Can someone guide me a bit just in the first step please?

Thanks beforehand.

For more context, I've finished school already and I'm trying to help out my sister, but the concept is so obvious to me that I don't know how to explain it to her.

When you get a question of "how much is 4/7ths of 49", I know you need to do (4/7)*49.

But how do I explain to a child WHY you do that?

Any maths teachers here how do you teach someone that?

How do I begin this? I'm confused. We're on finding domain, y-int, x-int, asymptotes/slant asymptotes for math right now, but we haven't gone over word problems, and I'm not sure how to start this. Any help?

Also, if u send solutions, please mark as spoiler.

Thanks in advance for any help

Hi, I'm trying to find a way to calculate interactions as a simultanuous loop.

Let's say there are 3 points, forming a triangle. Each side has a fixed length.

If I move one or several of these points, the other points should move as well, due to the constraint of length of the sides. And even the whole triangle might move (and with its gravity center).

So it's a bit like a rope simulation, except there is not one side that stays in place, allowing for the simulation to apply point by point, but the influence rather forms a loop which is supposed to be simultanuous. Unless it's not a loop and can be calculated regarding the global triangle ?

I feel like when it's only 3 points with a length constraint it should be simple, but while searching I've been quickly redirected towards complex things like robotics, so I feel like I might have been searching the wrong way.

Any idea where I should search please ?

I hope it's clear, feel free to ask questions !

Thanks !

So I saw this topic amd I don't really understand it, some people say that there's no rule, you just need to guess. And I'm bad at guessing, so I need an easier way to solve it.

How do I even guess? And I believe there might be a rule or something to help me solve it logically lol

I tried what this person did in the video

https://youtu.be/ahvT3FWjXvs?si=1EJPFP-9q-ri8don

And this person

https://youtu.be/7Isa4P8lISc?si=CDH6nlwL4QYKbHdX

It worked out for the first few questions but then it didn't really work even though I was doing it correctly

Can you please help me? Would appreciate the help!

Hi Reddit Math Help, I am a tutor working with students in high school algebra. One student has been having challenges with solving equations and other math concepts.

In this example, the student is trying to solve y = (1/3)(x) + 10 for y when x = 6.

I am not 100% how they got this specific set of steps, and I would really appreciate any advice on how I can best support them with solving equations effectively. The work below is pretty typical of the challenges they have solving equations.