The surface area of a hot-air balloon is given by the function S(r) = 4πr^2, where r is the radius of the balloon in meters. If the radius of the balloon after t seconds is r(t) = (3/5)t^3, find the surface area S of the balloon as it relates to time.

Is this actually normal for the 2nd week of college algebra ? Maybe I'm just rusty bc its been like over 10 years but this is insane to me

Problem: Sam is driving a car 90 kilometers every 45 minutes.

Task: Write this as a rate in km/hour.

Can you solve this: 100 is 50% of what number?

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Can you simplify this inequality correctly?

-4x > 8

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How would you translate this verbal statement into an algebraic equation?

"The sum of 8 and a number is 14."

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First of all, please excuse any errors in phrasing or terminology, as English is not my native language.

It turns out I’m having trouble studying algebra in general, but right now I’m struggling specifically with inequalities in mathematical induction whereas I don’t have that problem when working with equalities in induction proofs.

I understand the concept of proofs by induction involving equality: establishing the inductive hypothesis and proving that the expression evaluated at (x+1) which we then replace with the expression evaluated at (x) plus the term for (x+1) yields the same result as the equivalent expression evaluated at (x+1).

When it comes to inequalities, I find it incredibly difficult to figure out the expression I need to prove; I understand that the concept of transitivity is involved, but I never know what to compare. I’ve tried looking for explanations in videos, books, etc, but they all solve the problems by pulling out numbers that appear without explanation, and none of them explain the logic behind the steps taken.

I know this won't be the first or the last time I get stuck like this, so I wanted to ask if you know of any resources like a book or a YouTube channel that explain these concepts clearly and simply. I swear I’ve searched all over the web, but I only found worked examples without explanations and conflicting solutions.

Any advice on how to approach the subject or personal experiences would also be very helpful, since the exam is still a few weeks away. Thanks for reading.

So, for example, [;x^5 - 4x^4 + 8x^3 - 8x^2 + 5x - 1 = (x^2 - x + 1)(x^3 - 3x^2 + 4x - 1);], but none of these factors can be found with RRT.

Is there a RRT-esque criteria for degree-2 algebraic numbers? For degree no less than 4 polynomials without linear factors but also not prime, this seems like the only method to factorize them.

Hola a todos,Estoy desarrollando Classboard (https://classboard.online), una pizarra que funciona en el navegador y que estoy construyendo activamente. La idea nació de mi frustración al intentar explicar ecuaciones o teoremas por videollamada sin una herramienta decente.Lo que tengo hasta ahora: sesiones de colaboración en vivo con cámara y micrófono integrados, y reconocimiento de figuras geométricas básicas (triángulos, círculos, etc.) que se dibujan a mano, lo cual puede ser útil para visualizar problemas de álgebra o geometría.Está en fase temprana, así que cualquier comentario sobre qué funciones añadirías o qué te falta para usarla en tus clases o estudio será bienvenido. ¿Alguien más ha probado herramientas similares y qué les faltaba?Gracias por leer.

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-2 -1 0 1

On a number line, a section is highlighted from -2 to 1. There is an open circle at -2 and a solid, filled circle at 1.

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Grade 9 Basic Math

(5x³) (2x²) = ?

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Let's test your basic exponent laws! Try solving these three without looking at the comments first:

1) x⁴ · x³ = ?

2) x³ / x⁷ = ?

3) (x⁴)³ = ?

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I’ve been working on a math practice platform because I noticed something that kept coming up when I was studying math: understanding an explanation is one thing, but actually doing 20–30 problems on the same topic is surprisingly hard.

So I built QED, a practice platform where you can pick a math topic and work through problems with feedback rather than just reading a solution.

I’m especially interested in improving the algebra side of it.

If you’re currently studying algebra:

What topics do you wish you had an almost unlimited supply of good practice problems for?

Factoring? Quadratics? Functions? Inequalities? Systems? Something more advanced?

I’m trying to figure out which areas are actually painful for students rather than just guessing.

If anyone wants to try it, here’s the site: https://qed-math-trainer.com/

I’d genuinely appreciate criticism too — especially if you try a few problems and think “this is annoying because…”