BC MATHS

Saved by @Mollyycolllinss

Algebra Etc.
@AlgebraFact 4 years, 5 months ago 772 views

Save to PDF Share See On Twitter

How to mentally compute the cube root of the cube of a two digit number.

Thread (1/10)

In base 10, the last digits of the cubes of digits are distinct.

If d = 0, 1, 4, 5, 6, or 9, then d^3 ends in d.

If d = 2, 3, 7, or 8, then d^3 ends in 10-d.

(2/10)

So if you're given the cube of an integer, you can figure out the last digit of the cube root.

For example, if 50653 is the cube of an integer, it's the cube of a number ending in 7.

(3/10)

Let n = 10a + b be a two-digit number, with a and b single digit numbers.

Then 10a <= n <= 10(a+1), and so n^3 is between (10a)^3 and (10(a+1))^3, i.e. between 1000 a^3 and 1000 (a+1)^3.

(4/10)

So suppose x is the cube of a two-digit number n = 10a + b.

Chop off the last three digits of x.

Then a, the first digit of n, is the largest number whose cube is no greater than what's left of x.

(5/10)

This means that if you know the cubes of the digits, you can find the first digit of the cube of a two-digit number.

(6/10)

For example, suppose we know 50653 is a cube.

Lopping off the last three digits gives 50.

3^3 < 50 < 4^3, so the first digit of the cube root of 50653 is 3.

(7/10)

At the beginning of this thread we showed how to find the last digit of the cube root, and now we've shown how to find the first digit.

(8/10)

Another example. Suppose you know that 438976 is a cube.

The last digit of the cube root must be 6.

438 is between 7^3 and 8^3 and so the first digit of the cube root must be 7.

438976 = 76^3.

(9/10)

Final example. Suppose you know x = 103823 is a cube, x = n^3.

Then the last digit of n is 7 because 7^3 ends in 3.

103 is between 4^3 = 64 and 5^3 = 125, so the first digit of n is 4.

n = 47.

(10/10)

More from Maths

Arthouse-Kuklite
@Miltantvibes

1st grade mathematics work sheets and my mother's mathematics teaching style. Mathematics will not be so terrible, since it seems that parents are interested in preparing their little ones for mathematics before school age.

I grew up without understanding how people talk about mathematics as difficult as they do, it was my best topic at school.

Riuji
@weakconvergence

When I was starting out as a grad student, I remember being frustrated with analysis problems where it didn't use DIRECTLY the things we spent so much time proving in class.

As an example, let's look at a standard real analysis problem:

(1/23)

The problem looks like it can be done using the dominated convergence theorem.

This is an important theorem and is used in a lot of places outside a grad real analysis class. A student would go through a lot of buildup leading to this theorem.

(2/23)

Now, let's see whether the conditions for DCT are satisfied.

First, for fixed 00 as n->infinity.

So we have a.e. convergence of the integrand in [0,1].

To the student, this builds a stronger case to use DCT to solve the problem.

(3/23)

Finding an integrable dominating function is where the problem starts.

It would seem NATURAL (at least for me) to bound it with:

p.s. it feels "natural" to me because it is reminiscent of squeeze theorem problems, math students encounter in calculus.

(4/23)

However, 1/x^n is not integrable in (0,1) and hence cannot be (further) dominated by an integrable function.

So, what I would do is since I know it converges a.e. to 1, maybe it converges uniformly to 1?

This leads me into a BAD detour.

(5/23)

Advertisement

Patrick K A Kearns
@kearnsneuro

It is trying when mathematicians declare condescendingly that there is no point doing things because their models tell them so. Well maybe some of the assumptions don't hold up. How did that work out for the no additional risk from large events and no point in border controls...

Oh for crying out loud. I don't know anyone who thinks we can get R below 0.9 with this new variant. It's 22 virus generations to even get from 50,000 cases to 5,000 at R=0.9 - that's 4 months. TTI is a complete fantasy right now: spend the money on the vaccine rollout. https://t.co/MyeBt8tC1w
— Oliver Johnson (@BristOliver) January 3, 2021

During wave 1 cases fell very fast, faster than I think most people were expecting. Particularly in Scotland. Rt was probably ~0.5 until we started easing off.

This was despite a constant leak of cases coming out of hospitals and LTC facilities as we were rationing PPE and are policies were nowhere near ideal. There was insistence from infection control that droplet protections were sufficient. We have all learned a lot since then.

Not to mention we have learned to avoid the shit show of actively importing cases into care homes. We've learned not to repeat that. Other sectors have learned too.

We've learned a lot and there's no reason we can't control this new variant. But we will not manage if we don't try and act with clarity of purpose.

$Spencer Greenberg \U0001f50d$

Spencer Greenberg 🔍...
@SpencrGreenberg

Ten components of being compassionate to yourself:

1. Self-friendship: treat yourself at least as well as you would treat a friend who is going through the same situation

[thread]

2. Worthiness: remember that you have value (as all people do), and that your happiness and preferences matter.

3. Self-talk: notice when you are saying something mean to yourself (aloud, or in your head), and rephrase it in a gentler, kinder, more considerate way.

4. Connectedness: reflect on the fact that, whatever challenge you are facing, there are others who are also facing a similar challenge. You are not alone in your pain.

5. Change: note that everything changes with time. If you are dealing with feelings that are difficult to stand at this moment, they will subside. This too shall pass. Things are usually not as important or permanent as they seem to us in the moment that we are focused on them.

6. Self-empathy: orient towards yourself with tenderness, understanding and compassion, especially when you are suffering. Take on the perspective that you would towards a child or loved one that was hurting.

Arthouse-Kuklite
@Miltantvibes

Algebra 1 and pre-algebra worksheets are something that all would love to have been able to dominate in high school. Sometimes they do not dominate it there and that's when it could be a bit difficult.

But after learning and doing problems of algebra and pre-Algebra and worksheets online, it will no longer be a problem. There are many cases in all the life of a person where they have to learn.

You May Also Like

Vibhu Vashisth
@VIBHU_Tweet

🌺श्री गरुड़ पुराण - संक्षिप्त वर्णन🌺

हिन्दु धर्म के 18 पुराणों में से एक गरुड़ पुराण का हिन्दु धर्म में बड़ा महत्व है। गरुड़ पुराण में मृत्यु के बाद सद्गती की व्याख्या मिलती है। इस पुराण के अधिष्ठातृ देव भगवान विष्णु हैं, इसलिए ये वैष्णव पुराण है।

गरुड़ पुराण के अनुसार हमारे कर्मों का फल हमें हमारे जीवन-काल में तो मिलता ही है परंतु मृत्यु के बाद भी अच्छे बुरे कार्यों का उनके अनुसार फल मिलता है। इस कारण इस पुराण में निहित ज्ञान को प्राप्त करने के लिए घर के किसी सदस्य की मृत्यु के बाद का समय निर्धारित किया गया है...

..ताकि उस समय हम जीवन-मरण से जुड़े सभी सत्य जान सकें और मृत्यु के कारण बिछडने वाले सदस्य का दुख कम हो सके।
गरुड़ पुराण में विष्णु की भक्ति व अवतारों का विस्तार से उसी प्रकार वर्णन मिलता है जिस प्रकार भगवत पुराण में।आरम्भ में मनु से सृष्टि की उत्पत्ति,ध्रुव चरित्र की कथा मिलती है।

तदुपरांत सुर्य व चंद्र ग्रहों के मंत्र, शिव-पार्वती मंत्र,इन्द्र सम्बंधित मंत्र,सरस्वती मंत्र और नौ शक्तियों के बारे में विस्तार से बताया गया है।
इस पुराण में उन्नीस हज़ार श्लोक बताए जाते हैं और इसे दो भागों में कहा जाता है।
प्रथम भाग में विष्णुभक्ति और पूजा विधियों का उल्लेख है।

मृत्यु के उपरांत गरुड़ पुराण के श्रवण का प्रावधान है ।
पुराण के द्वितीय भाग में 'प्रेतकल्प' का विस्तार से वर्णन और नरकों में जीव के पड़ने का वृत्तांत मिलता है। मरने के बाद मनुष्य की क्या गति होती है, उसका किस प्रकार की योनियों में जन्म होता है, प्रेत योनि से मुक्ति के उपाय...

$Billy Bostickson \U0001f3f4\U0001f441&\U0001f441 \U0001f193$

Billy Bostickson 🏴👁&👁 ...
@BillyBostickson

Keep dwelling on this:
Further Examination of the Motif near PRRA Reveals Close Structural Similarity to the SEB Superantigen as well as Sequence Similarities to Neurotoxins and a Viral SAg.

The insertion PRRA together with 7 sequentially preceding residues & succeeding R685 (conserved in β-CoVs) form a motif, Y674QTQTNSPRRAR685, homologous to those of neurotoxins from Ophiophagus (cobra) and Bungarus genera, as well as neurotoxin-like regions from three RABV strains

(20) (Fig. 2D). We further noticed that the same segment bears close similarity to the HIV-1 glycoprotein gp120 SAg motif F164 to V174.
https://t.co/EwwJOSa8RK

In (B), the segment S680PPRAR685 including the PRRA insert and highly conserved cleavage site *R685* is shown in van der Waals representation (black labels) and nearby CDR residues of the TCRVβ domain are labeled in blue/white
https://t.co/BsY8BAIzDa

Sequence Identity %
https://t.co/BsY8BAIzDa
Y674 - QTQTNSPRRA - R685
Similar to neurotoxins from Ophiophagus (cobra) & Bungarus genera & neurotoxin-like regions from three RABV strains
T678 - NSPRRA- R685
Superantigenic core, consistently aligned against bacterial or viral SAgs

Advertisement

Pegasus of Dharma
@HarduttSuhas

The BATTLE OF PAVAN KHIND (13 July 1660)

300 MARATHAS against 10000+ ADIL SHAHI TROOPS

A Sparta style last man stand at a mountain pass which ensured Shivaji Maharaj's safety.

Valour, loyalty and sacrifice!

Baji Prabhu Deshpande was one of the most able lieutenants of Shivaji. He sacrificed his life defending Shivaji in a heroic last stand known as the "Battle of Pavan Khind" in which his force was hugely outnumbered.(1)

In this battle he became a martyr, but managed to halt the enemy forces for several hours, which secured Shivaji’s safety and victory on another front. Without this heroic last stand Shivaji’s glorious career may have been cut short.(2)

Baji Prabhu was senior to Shivaji. In the beginning he opposed Shivaji being from a rival Maratha clan, but realised that Shivaji stood for national resurgence. Henceforth he became a friend and loyal supporter of Shivaji.(3)

In 1660, Shivaji was trapped in the fort of Panhala, under siege and vastly outnumbered by an Adilshahi army led by general Siddhi Jauhar.(4)

Priyanka (Astrology Gu...
@AstroAmigo

1

From today, we will memorize the names of 27 Nakshatras in Vedic Jyotish to never forget in life.

I will write 4 names. Repeat them in SAME sequence twice in morning, noon, evening. Each day, revise new names + recall all previously learnt names.

Pls RT if you are in.

2

Today's Nakshatras are:-

1. Ashwini - अश्विनी

2. Bharani - भरणी

3. Krittika - कृत्तिका

4. Rohini - रोहिणी

Ashwini - अश्विनी is the FIRST Nakshatra.

Repeat these names TWICE now, tomorrow morning, noon and evening. Like this tweet if you have revised 8 times as told.

3

Today's Nakshatras are:-

5. Mrigashira - मृगशिरा

6. Ardra - आर्द्रा

7. Punarvasu - पुनर्वसु

8. Pushya - पुष्य

First recall previously learnt Nakshatras twice. Then recite these TWICE now, tomorrow morning, noon & evening in SAME order. Like this tweet only after doing so.

4

Today's Nakshatras are:-

9. Ashlesha - अश्लेषा

10. Magha - मघा

11. Purvaphalguni - पूर्वाफाल्गुनी

12. Uttaraphalguni - उत्तराफाल्गुनी

Purva means that comes before (P se Purva, P se pehele), and Uttara comes later.

Read next tweet too.

5

Purva, Uttara prefixes come in other Nakshatras too. Purva= pehele wala. Remember.

First recall previously learnt 8 Nakshatras twice. Then recite those in Tweet #4 TWICE now, tomorrow morning, noon & evening in SAME order. Like this tweet if you have read Tweets #4 & 5, both.

WORLD OF SANATAN DHARM...
@world_sanatan

WHY BABUR NEVER TRIED TO ATTACK SRI KRISHNADEVARAYA ?

A🧵u must read

It is very well known that Babur considered Krishna Dev Raya as the strongest ruler of the entire subcontinent, and Vijayanagar empire the strongest during that time in India.

1/10

The Vijayanagar empire reached its peak during 1509-1529 around the reign of Krishna Dev Raya.

Vijayanagar’s famed elephant brigade 👇

2/10

At his command there were over 50000 elite troops with a regiment of Portuguese gunners and 3200 cavalry with 600 elephants.

3/10

Along with that more than four hundred thousand ( four lakh) peasant levies and irregular military made this empire one of the largest in all of South Asia.

A typical Vijayanagar levie soldier 👇

4/10

During Baburs invasion, Krishna Dev Raya ruled supreme in all of deccan.

In fact, in an all our brawl, Krisha Dev Raya will beat Babur fair and square.

Babur could muster at max 50000 troops with 50 canons.

While Krishna Dev Raya had these numbers in Hampi alone

5/10