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Question Number 181099 Answers: 2 Comments: 0

prove that for every positivenumber p e q wee have: p+q≥(√(4pq))

$$ \\ $$$$\mathrm{prove}\:\mathrm{that}\:\mathrm{for}\:\mathrm{every}\: \\ $$$$\mathrm{positivenumber}\:\mathrm{p}\:\mathrm{e}\:\mathrm{q}\:\mathrm{wee} \\ $$$$\mathrm{hav}{e}: \\ $$$${p}+{q}\geqslant\sqrt{\mathrm{4}{pq}} \\ $$

Question Number 181089 Answers: 1 Comments: 0

Question Number 181085 Answers: 1 Comments: 3

Question Number 181084 Answers: 1 Comments: 0

Question Number 181079 Answers: 6 Comments: 2

Solve for x : (((x + a)/(x + b)))^3 = ((x + 2a − b)/(x − a + 2b))

$$\mathrm{Solve}\:\mathrm{for}\:{x}\:: \\ $$$$\left(\frac{{x}\:+\:{a}}{{x}\:+\:{b}}\right)^{\mathrm{3}} =\:\frac{{x}\:+\:\mathrm{2}{a}\:−\:{b}}{{x}\:−\:{a}\:+\:\mathrm{2}{b}} \\ $$

Question Number 181070 Answers: 2 Comments: 2

Question Number 181062 Answers: 0 Comments: 0

Q180886

$${Q}\mathrm{180886} \\ $$

Question Number 181055 Answers: 2 Comments: 14

Question Number 181052 Answers: 2 Comments: 3

Question Number 181051 Answers: 1 Comments: 0

Question Number 181041 Answers: 0 Comments: 0

If f(x)= x − ⌊ ((x−1)/3) ⌋ , g( x)= 2^( x) then , R_( gof) = ?

$$ \\ $$$$\:\:\:\mathrm{I}{f}\:\:\:\:{f}\left({x}\right)=\:{x}\:−\:\lfloor\:\frac{{x}−\mathrm{1}}{\mathrm{3}}\:\rfloor\:,\:\:{g}\left(\:{x}\right)=\:\mathrm{2}^{\:{x}} \\ $$$$\:\:\:\:\:\:\:{then}\:\:,\:\:\:\:\:\:{R}_{\:{gof}} \:=\:? \\ $$

Question Number 181039 Answers: 0 Comments: 3

Prove that for all a^2 divisible by b, a is also divisible by b for all a, b ∈ N

$${Prove}\:{that}\:{for}\:{all}\:{a}^{\mathrm{2}} \:{divisible}\:{by}\:{b}, \\ $$$${a}\:{is}\:{also}\:{divisible}\:{by}\:{b} \\ $$$${for}\:{all}\:{a},\:{b}\:\in\:\mathbb{N} \\ $$

Question Number 181053 Answers: 1 Comments: 0

An open pipe of r_o = 10 Cm, ℓ= 3m has an outer layer of ice that is melting at the rate of 2π Cm^3 per minute with thickness of 20 mm. How many days untill all the ice melts? and how fast is the thickness of the ice decreasing per hour?

$${An}\:{open}\:{pipe}\:{of}\:{r}_{{o}} =\:\mathrm{10}\:{Cm},\:\ell=\:\mathrm{3}{m}\:{has}\:{an}\:{outer} \\ $$$$\:{layer}\:{of}\:{ice}\:{that}\:{is}\:{melting}\:{at}\:{the}\:{rate}\:{of}\:\mathrm{2}\pi\:{Cm}^{\mathrm{3}} \\ $$$$\:{per}\:{minute}\:{with}\:{thickness}\:{of}\:\mathrm{20}\:{mm}.\:{How}\:{many} \\ $$$$\:{days}\:{untill}\:{all}\:{the}\:{ice}\:{melts}?\:{and}\:{how}\:{fast}\:{is}\:{the} \\ $$$$\:{thickness}\:{of}\:{the}\:{ice}\:{decreasing}\:{per}\:{hour}? \\ $$

Question Number 181025 Answers: 0 Comments: 1

Send you solutions to kinmatics@gmail.com

$$\mathrm{Send}\:\mathrm{you}\:\mathrm{solutions}\:\mathrm{to}\:\boldsymbol{\mathrm{kinmatics}}@\boldsymbol{\mathrm{gmail}}.\boldsymbol{\mathrm{com}} \\ $$

Question Number 181023 Answers: 1 Comments: 0

Question Number 181245 Answers: 1 Comments: 7

(x−(1/x))(x^(4/3) +x^(2/3) )=x^(1/3) (x^2 −(1/x^2 )) prove LHS=RHS

$$\left(\mathrm{x}−\frac{\mathrm{1}}{\mathrm{x}}\right)\left(\mathrm{x}^{\frac{\mathrm{4}}{\mathrm{3}}} +\mathrm{x}^{\frac{\mathrm{2}}{\mathrm{3}}} \right)=\mathrm{x}^{\frac{\mathrm{1}}{\mathrm{3}}} \left(\mathrm{x}^{\mathrm{2}} −\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{2}} }\right) \\ $$$$ \\ $$$$\mathrm{prove}\:\mathrm{LHS}=\mathrm{RHS} \\ $$

Question Number 181251 Answers: 1 Comments: 1

Question Number 181020 Answers: 1 Comments: 0

solve for x>0 ∫_0 ^x ⌊t⌋^2 dt=2(x−1) (Q180780 reposted)

$${solve}\:{for}\:{x}>\mathrm{0} \\ $$$$\int_{\mathrm{0}} ^{{x}} \lfloor{t}\rfloor^{\mathrm{2}} {dt}=\mathrm{2}\left({x}−\mathrm{1}\right) \\ $$$$ \\ $$$$\left({Q}\mathrm{180780}\:{reposted}\right) \\ $$

Question Number 181019 Answers: 1 Comments: 0

Question Number 181015 Answers: 1 Comments: 0

If z=xy−7x+4y, evaluate (∂z/(∂x )) and (∂z/∂y) .

$$\mathrm{If}\:\mathrm{z}=\mathrm{xy}−\mathrm{7x}+\mathrm{4y},\:\:\:\mathrm{evaluate}\:\frac{\partial\mathrm{z}}{\partial\mathrm{x}\:}\:\mathrm{and}\:\frac{\partial\mathrm{z}}{\partial\mathrm{y}} \\ $$$$ \\ $$$$. \\ $$$$ \\ $$

Question Number 181014 Answers: 0 Comments: 5

If f(x)=3−x^2 , find ((f(3+h)−f(3))/h) .

$$\mathrm{If}\:\mathrm{f}\left(\mathrm{x}\right)=\mathrm{3}−\mathrm{x}^{\mathrm{2}} ,\:\:\:\:\mathrm{find}\:\frac{\mathrm{f}\left(\mathrm{3}+\mathrm{h}\right)−\mathrm{f}\left(\mathrm{3}\right)}{\mathrm{h}} \\ $$$$ \\ $$$$. \\ $$

Question Number 180998 Answers: 2 Comments: 0

Question Number 181007 Answers: 1 Comments: 0

[Question from Frix sir] ... I once played the game Tetris. You got points for each filled line, depending on how many lines you filled at once: 1 line = 1 point 2 lines = 3 points 3 lines = 6 points 4 lines = 10 points If you made 100 points, which possible combinations of lines did you fill when you filled 31 lines?

$$\left[{Question}\:{from}\:{Frix}\:{sir}\right] \\ $$$$...\:\mathrm{I}\:\mathrm{once}\:\mathrm{played}\:\mathrm{the}\:\mathrm{game}\:\mathrm{Tetris}.\: \\ $$$$\mathrm{You}\:\mathrm{got}\:\mathrm{points}\:\mathrm{for}\:\mathrm{each}\:\mathrm{filled}\:\mathrm{line},\: \\ $$$$\mathrm{depending}\:\mathrm{on}\:\mathrm{how}\:\mathrm{many}\:\mathrm{lines}\:\mathrm{you}\: \\ $$$$\mathrm{filled}\:\mathrm{at}\:\mathrm{once}: \\ $$$$\mathrm{1}\:\mathrm{line}\:=\:\mathrm{1}\:\mathrm{point} \\ $$$$\mathrm{2}\:\mathrm{lines}\:=\:\mathrm{3}\:\mathrm{points} \\ $$$$\mathrm{3}\:\mathrm{lines}\:=\:\mathrm{6}\:\mathrm{points} \\ $$$$\mathrm{4}\:\mathrm{lines}\:=\:\mathrm{10}\:\mathrm{points} \\ $$$$\mathrm{If}\:\mathrm{you}\:\mathrm{made}\:\mathrm{100}\:\mathrm{points},\:\mathrm{which}\:\mathrm{possible} \\ $$$$\mathrm{combinations}\:\mathrm{of}\:\mathrm{lines}\:\mathrm{did}\:\mathrm{you}\:\mathrm{fill}\:\mathrm{when} \\ $$$$\mathrm{you}\:\mathrm{filled}\:\mathrm{31}\:\mathrm{lines}? \\ $$

Question Number 180990 Answers: 1 Comments: 0

2 blondes hair of 6 girls will sit around a circular table, what′s the probability that those two girls sitting next to each other?

$$\mathrm{2}\:{blondes}\:{hair}\:{of}\:\mathrm{6}\:{girls}\:{will}\:{sit}\:{around}\:{a}\:{circular} \\ $$$$\:{table},\:{what}'{s}\:{the}\:{probability}\:{that}\:{those}\:{two}\:{girls} \\ $$$$\:{sitting}\:{next}\:{to}\:{each}\:{other}? \\ $$

Question Number 181572 Answers: 0 Comments: 0

2 𝚫 5=49 3 𝚫 4=36 4 𝚫 5=81 5 𝚫 5=?

$$ \\ $$$$\mathrm{2}\:\boldsymbol{\Delta}\:\mathrm{5}=\mathrm{49} \\ $$$$\mathrm{3}\:\boldsymbol{\Delta}\:\mathrm{4}=\mathrm{36} \\ $$$$\mathrm{4}\:\boldsymbol{\Delta}\:\mathrm{5}=\mathrm{81} \\ $$$$\mathrm{5}\:\boldsymbol{\Delta}\:\mathrm{5}=? \\ $$$$ \\ $$

Question Number 180977 Answers: 3 Comments: 0

what is larger, 3^(100) +4^(100) or 5^(100) ?

$${what}\:{is}\:{larger},\:\mathrm{3}^{\mathrm{100}} +\mathrm{4}^{\mathrm{100}} \:{or}\:\:\mathrm{5}^{\mathrm{100}} ? \\ $$

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