109
QUConditional probability is computed using?
@quizverse12
#Exponents In Python
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361
MAThis is Part 2 of Integration in 30 seconds.
Power rule.
Substitution (idea, not algebra).
Area between curves.
Kinematics link.
Watch once.
Save it for revision.
👉 If you missed Part 1, visit the page to watch it first.
@mathwithmudassir
472
THDividing exponents is NOT complicated — it's just subtraction in disguise 🤯
a^m ÷ a^n = a^(m−n)
That's it. That's the whole rule. One subtraction.
Here's the proof 👇
Take a⁵ ÷ a³
Write it out: (a·a·a·a·a) / (a·a·a)
Three a's cancel ❌❌❌
You're left with a·a = a²
5 − 3 = 2 ✅
Now a real problem:
27a⁵ ÷ 9a³
→ Numbers: 27 ÷ 9 = 3
→ Letters: a^(5−3) = a²
→ Answer: 3a² ✅
BUT here's where it gets spicy 🌶️
What if the exponents are the SAME?
a^n ÷ a^n = a^(n−n) = a⁰ = 1
That's right — ANYTHING to the power of zero equals 1.
That's not a trick. That's the rule proving itself. 🔥
One subtraction. That's all exponent division ever was.
📸 SAVE THIS for your next exam — you'll thank yourself later
Tag a friend who still thinks exponents are hard 👇
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#math #exponents #algebra #indexlaws #mathtricks #dividingexponents #zeroexponent #mathtok #studytok #education #mathshorts #algebrahelp #examtips #mathteacher #learnmath #middleschoolmath #mathisfun #studygram #mathhacks #powersandexponents #mathreels #mathproblems #indices #lawsofexponents #mathtutorial #mathcheatsheet #screenshotthis #exponentialrules #simplifyingexpressions
@thesuperschoolclassics
2.8K
134
AS📐 10 Basic Integration Formulas You Must Know!
Integration is a core topic in calculus and appears frequently in board exams, entry tests, and university math.
This video covers the most important basic integrals every student should remember.
🧮 What you’ll learn:
📊 ∫ xⁿ dx = (xⁿ⁺¹)/(n+1) + C
🔢 ∫ 1/x dx = ln|x| + C
📐 ∫ eˣ dx = eˣ + C
📈 ∫ aˣ dx = aˣ / ln a + C
🔁 ∫ sin x dx = −cos x + C
🔁 ∫ cos x dx = sin x + C
📉 ∫ sec²x dx = tan x + C
📉 ∫ csc²x dx = −cot x + C
📐 ∫ sec x tan x dx = sec x + C
📐 ∫ csc x cot x dx = −csc x + C
💡 These formulas are the foundation of advanced integration techniques.
📘 Learn concepts clearly — not by rote memorization
🌐 www.asaanedu.com
📩 info@asaanedu.com
📞 +92 343 6362411
Learn. Grow. Succeed. — Asaan Education
#AsaanEducation #Integration #Calculus #MathConcepts #ExamPreparation #StudentLearning #ConceptClarity #MathMadeEasy
@asaanedu
8.0K
PCMost people see a messy differential equation…
But real learners see a hidden story of power, order, and structure.
At first glance, this equation looks complicated — derivatives, powers, variables tangled together like a puzzle waiting to be solved. But here’s the truth 👇
Mathematics isn’t about fear.
It’s about finding clarity inside chaos.
Every differential equation asks a simple question:
👉 How does something change?
And the degree of that equation?
That tells us how intense that change really is.
Not everything in life is linear.
Not every journey is first order.
Some paths curve. Some accelerate. Some evolve in unexpected ways.
Just like this equation.
When you slow down and observe carefully, you realise — solving isn’t about memorising formulas… it’s about understanding structure.
Break it.
Simplify it.
Respect the highest power of the highest derivative.
Because success in maths — like success in life — comes from identifying what truly matters.
This reel isn’t just about an answer.
It’s about training your brain to see patterns where others see confusion.
So next time a question looks scary…
Pause.
Breathe.
Decode.
Because mastery begins the moment fear ends.
Save this if you love challenging concepts 💡
Share it with someone who thinks maths is tough 🔁
Let’s make learning powerful, not painful.
#MathMindset #DifferentialEquations #STEMLearning #ConceptOverCramming #learnwithlogic🧮
@pcm_w.alle
581
THWhat is (a + b)² ? 👇
If you said a² + b²... you're wrong. And you're not alone — most students make this exact mistake.
The correct answer:
(a + b)² = a² + 2ab + b²
That 2ab in the middle? It's the term everyone forgets.
Here's why it's there:
(a + b)² means (a + b)(a + b)
FOIL it out → a² + ab + ab + b²
Combine → a² + 2ab + b²
And for the minus version:
(a − b)² = a² − 2ab + b²
Same thing — just the middle term flips negative.
Quick test: (3x + 4)² = ?
Answer: 9x² + 24x + 16
Never forget the middle term again 🧠
Save this — you'll need it on every exam 📌
@thesuperschoolclassics
3.0K
PCNot every line is straight… some come with attitude 😌📐
Imagine a line that doesn’t follow the usual “friendly” path along the axes…
Instead, it boldly makes angles of 90°, 135°, and 145° with the x, y, and z axes 🔥
Sounds chaotic?
But here’s the beauty of Mathematics ✨
Even when direction feels confusing…
Even when angles look messy…
There’s always a hidden identity waiting to be discovered 💡
Direction cosines are like the personality of a line —
They tell us how much the line belongs to each axis.
When a line is:
✔️ Completely perpendicular to one axis
✔️ Leaning negatively towards another
✔️ Slightly aligned with the third
It creates a perfect mathematical balance ⚖️
And suddenly…
What looked complicated becomes elegant.
From geometry to vectors, from imagination to precision —
Math always reminds us:
👉 Every direction has meaning
👉 Every angle tells a story
👉 And every problem hides a simple truth beneath the surface
So next time a question looks intimidating…
Don’t panic.
Decode it.
Break it.
Understand its direction.
Because success in PCM isn’t about memorizing formulas…
It’s about seeing the logic behind the lines 💭📊
Stay curious.
Stay analytical.
And keep moving in the right direction 🚀
#VectorMagic #MathMindset #PCMStudents #DirectionCosines #learnwithlogic
@pcm_w.alle
2.5K
THToday I solved the Find Missing and Repeating Numbers problem using two approaches: first with a frequency array achieving O(n) time but O(n) space by counting occurrences of each number (1 to n), then optimized to
O(n) time and O(1) space using mathematical equations calculating the difference between expected and actual sums (S1) and sum of squares (S2) to derive diff1 = repeat - missing and diff2 = repeat² - missing², then solving repeat + missing = diff2/diff1 and repeat - missing = diff1 to extract both numbers without extra space. The mathematical approach leverages formulas sum = n(n+1)/2 and sum_of_squares = n(n+1)(2n+1)/6 to create two equations with two unknowns, eliminating the need for auxiliary arrays while maintaining linear time complexity—demonstrating how mathematical insight transforms space-intensive solutions into constant-space algorithms. This pattern appears frequently in interviews testing optimization skills beyond brute force.
#DSA #MissingRepeating #maths #algorithm
@the.intlovert
6.7K
MNIn mathematics, the bisection method is a root-finding method that applies to any continuous function for which one knows two values with opposite signs. The method consists of repeatedly bisecting the interval defined by these values, then selecting the subinterval in which the function changes sign, which therefore must contain a root. It is a very simple and robust method, but it is also relatively slow. Because of this, it is often used to obtain a rough approximation to a solution which is then used as a starting point for more rapidly converging methods. The method is also called the interval halving method, the binary search method, or the dichotomy method. The corollary Bolzano's theorem states that if a continuous function has values of opposite sign inside an interval, then it has a root in that interval. The theorem depends on, and is equivalent to, the completeness of the real numbers, although Weierstrass Nullstellensatz is a version of the intermediate value theorem for polynomials over a real closed field. In order to determine when the iteration should stop, it is necessary to consider various possible stopping conditions with respect to a tolerance (ϵ). Burden and Faires (2016) identify the three stopping conditions: Absolute tolerance: | cₙ - cₙ₋₁ | < ϵ Relative tolerance: | (cₙ - cₙ₋₁)/cₙ | < ϵ , cₙ ≠ 0 | f(cₙ) | < ϵ | f(cₙ) | < ϵ does not give an accurate result to within ϵ unless | f'(cₙ) | ≥ 1 Follow @mnc_society_nitmz for more 🔥 #math #manim #python #mathematics
@mnc_society_nitmz
120
ANDerivation of Coefficient of determination equal to Correlation coefficient squared in simple linear regression. #regression #rsquared #correlation
@analystrahul
113
QUWhy does diagonalization simplify repeated application of a linear operator?
@quizverse2
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