fossilesque@lemmy.dbzer0.comM to Science Memes@mander.xyzEnglish · 4 days agoomglemmy.dbzer0.comimagemessage-square36fedilinkarrow-up1444arrow-down112
arrow-up1432arrow-down1imageomglemmy.dbzer0.comfossilesque@lemmy.dbzer0.comM to Science Memes@mander.xyzEnglish · 4 days agomessage-square36fedilink
minus-squarebleistift2@sopuli.xyzlinkfedilinkEnglisharrow-up29·edit-24 days agoObserve the identities a / b = a × b^(-1) (A) sqrt(a) = a ^ (1/2) (B) a^b × a^c = a^(b+c) (C) (a^b)^c = a^(b × c) (D) and derive 2 / sqrt(2) = 2 / 2^(1/2) (B) = 2 × [2^(1/2)] ^ (-1) (A) = 2 × 2^(1/2 × (-1)) (D) = 2 × 2^(-1/2) = 2 ^ [1 + (-1 / 2)] (C) = 2 ^ (1/2) = sqrt(2) (B)
minus-squarePutItOutWithYourBootsTed@piefed.sociallinkfedilinkEnglisharrow-up7·4 days agoNeat breakdown! Can you explain why this line =2^(1+ -1/2) =>2^(-1/2) shouldn’t it be 2^(1/2) or am I missing something? Second guessing myself here lol
minus-squarebleistift2@sopuli.xyzlinkfedilinkEnglisharrow-up14·4 days agoNo, that’s a mistake. Incredible how many mistakes one can make in a simple derivation. Thanks for pointing it out.
minus-squarePutItOutWithYourBootsTed@piefed.sociallinkfedilinkEnglisharrow-up3·4 days agoAll good! Thanks for the very helpful explanation.
Observe the identities
a / b = a × b^(-1) (A) sqrt(a) = a ^ (1/2) (B) a^b × a^c = a^(b+c) (C) (a^b)^c = a^(b × c) (D)and derive
2 / sqrt(2) = 2 / 2^(1/2) (B) = 2 × [2^(1/2)] ^ (-1) (A) = 2 × 2^(1/2 × (-1)) (D) = 2 × 2^(-1/2) = 2 ^ [1 + (-1 / 2)] (C) = 2 ^ (1/2) = sqrt(2) (B)Neat breakdown! Can you explain why this line =2^(1+ -1/2) =>2^(-1/2) shouldn’t it be 2^(1/2) or am I missing something? Second guessing myself here lol
No, that’s a mistake. Incredible how many mistakes one can make in a simple derivation.
Thanks for pointing it out.
All good! Thanks for the very helpful explanation.