Duncan B.

Entrepreneur with two sides- half nerd half fun lover.. A few degrees, and a lot of travels and experiences.. from Monte Carlo to mathematics, I love it all…

[Duncan B. @d__b006]

@UchennaF28384 This does not exhibit properties even for spherical triangles (interior sum angles > 2 pi) . So a solution is elusive.

[Duncan B. @d__b006]

@RHSTUDYZONE It doesn’t say the yellow and green are squares. Therefore insufficient information - no unique solution.

[Duncan B. @d__b006]

@Infinite_Logiz Sin^3x dx = (1-cos^2x)(sin x) dx
= (u^2 -1) du [subbing u=cosx]
= [1/3 x u^3 - u]
=[1/3 cos^3x -cos x] I resubbed cos x back in but you don’t have to if you simply change the limits)
Cos pi = -1 & Cos 0 = 1
So = [1/3 x -1 + 1] - [1/3 x 1 - 1]
= 2/3 + 2/3
= 4/3

[Duncan B. @d__b006]

@Infinite_Logiz I just learnt something… Always watch a person who wears their watch on their right hand.. of course, I appreciate there are limits.. 🤪

[Duncan B. @d__b006]

@MathMath901 3rd line. Radicals dont apply the same way with imaginary numbers. One reason is that √ is defined as the principal root, and is always positive, which creates anomalies when dealing with squaring negative numbers. indeed √-1 = ±i not just i. !! 🙂

[Duncan B. @d__b006]

@UchennaF28384 Of course we can !!. But it’s the working rather than the answer which reveals all.
Set domain x ≠ 0 ; then
x ² - x = 10 x;
x ² - 11x = 0;
x(x-11) = 0
so x = 11 OR 0, however domain x ≠ 0, so only one solution x = 11. !! 🙂

[Duncan B. @d__b006]

@YasuoHitori @Eserogee @Simi_2210_ Ok Yasuo!! x² = 25 is a good eg. It’s a quadratic, so we can’t simply root both sides and say√ x² = √25… rather it’s x² -25 = 0, then (x-5)(x+5)=0 thus x = ±5. But as we know the √ definition and it’s a diff of 2 sqrs, we often bypass those steps and simply say x=±√25 = ±5.

[Duncan B. @d__b006]

@LeroyLeroi001 @Eserogee @YasuoHitori @Simi_2210_ Agree completely. Functions (as opposed to relations), by definition , only have one output (remember the vertical line test in school !!).. And this function, ie. the square root, therefore only has one, and it’s the positive value. I think the formal definition uses ABS Val.

[Duncan B. @d__b006]

@YasuoHitori @Eserogee @Simi_2210_ With respect, you are wrong. And if you are studying or using math, it is positively essential (excuse the pun) you understand this key concept. Many high school students mix this up too. Might I suggest a great explanation by a great teacher: https://t.co/TPS3SfoLb5

[Duncan B. @d__b006]

@Eserogee @YasuoHitori @Simi_2210_ It is, it’s called the principal square root, and that is always positive. That is what the square root symbol means .. so if I said to you this .. sqr( (-5)^2) what would be your answer?

[Duncan B. @d__b006]

@YasuoHitori @Simi_2210_ Root is formally defined as the positive square root, so your answer is incorrect. The answer is only 100.

[Duncan B. @d__b006]

@Airaasayss I get 55

[Duncan B. @d__b006]

@Infinite_Logiz x = (eln(pi)-pi)/(1- ln(pi)) but you can use the identity e^i pi=-1 and go further.

[Duncan B. @d__b006]

@Sam_Axiom Square root is a formally defined function, and means the “positive square root”. Which is why the answer is +5.

[Duncan B. @d__b006]

@Infinite_Logiz Don’t bother with parts. Just use sub method u=cos(sqr(x)) and it’s pretty simple from there, so ans = - ln(cos(x))+ c

[Duncan B. @d__b006]

@Beno10_MFC Took 2-3 secs to solve. Simply by saying what integer times another integer gives 1. Can be only one answer. lol .

[Duncan B. @d__b006]

@kenlife202010 Answer : 1/32 , and time wise it took me around hmmm 10 secs to answer. So not an instant, but I’m happy.😃

[Duncan B. @d__b006]

@MinaAsamixo Well you’re helpin me along..

[Duncan B. @d__b006]

@Liza_6610 48

[Duncan B. @d__b006]

@Nova__2210 @SqSehrish lol.. most well known name in world… Alexa.. !!