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Question Number 179659 Answers: 1 Comments: 0

cos((2π)/7)=((ab)/c) cos((4π)/7)=((bc)/a) cos((6π)/7)=((ac)/b) faind a^2 +b^2 +c^2 =?

$${cos}\frac{\mathrm{2}\pi}{\mathrm{7}}=\frac{{ab}}{{c}} \\ $$$${cos}\frac{\mathrm{4}\pi}{\mathrm{7}}=\frac{{bc}}{{a}} \\ $$$${cos}\frac{\mathrm{6}\pi}{\mathrm{7}}=\frac{{ac}}{{b}}\:\:\:\:\:\:\: \\ $$$${faind}\:\:\:{a}^{\mathrm{2}} +{b}^{\mathrm{2}} +{c}^{\mathrm{2}} =? \\ $$

Question Number 179653 Answers: 1 Comments: 0

Question Number 179657 Answers: 1 Comments: 2

prove that lim_(n→∞) ((√((1/2)×(√((1/2)+(1/2)(√(1/2))))))×(√((1/2)+(1/2)(√((1/2)+(1/2)(√(1/2))))))×∙∙∙∙∙(√((1/2)+(1/2)(√((1/2)+(1/2)(√((1/(2+)).....+(1/2)(√(1/2))))))))_(n term) )=(2/π)

Question Number 179655 Answers: 2 Comments: 0

Evaluate ∫6 arctan (8/w) dw

$${Evaluate}\:\int\mathrm{6}\:\mathrm{arctan}\:\frac{\mathrm{8}}{{w}}\:{dw} \\ $$

Question Number 179654 Answers: 2 Comments: 1

Question Number 179650 Answers: 0 Comments: 3

If x and y are positive integers and 2x−4y = 3 then find ((16^x )/(256^y ))

$${If}\:{x}\:{and}\:{y}\:{are}\:{positive} \\ $$$${integers}\:{and}\:\mathrm{2}{x}−\mathrm{4}{y}\:=\:\mathrm{3} \\ $$$${then}\:{find}\:\frac{\mathrm{16}^{{x}} }{\mathrm{256}^{{y}} } \\ $$

Question Number 179631 Answers: 3 Comments: 1

Question Number 179629 Answers: 0 Comments: 0

Question Number 179609 Answers: 3 Comments: 0

Question Number 179593 Answers: 0 Comments: 8

pleas proof the elipse environment formullah p=π(√(2a^2 +2b^2 ))

$${pleas}\:{proof}\:{the}\:{elipse}\:{environment} \\ $$$${formullah} \\ $$$${p}=\pi\sqrt{\mathrm{2}{a}^{\mathrm{2}} +\mathrm{2}{b}^{\mathrm{2}} } \\ $$

Question Number 180648 Answers: 2 Comments: 6

there are 40 people (teachers students and workers) in a school.and there are 40 apples on the table.one teacher can eat 4 apples.and one student can eat 2 apples. 4 workers can eat one apple.find the numbers of teacher students and workers who eat apples. please help me.

$${there}\:{are}\:\mathrm{40}\:{people} \\ $$$$\:\left({teachers}\:{students}\:{and}\:{workers}\right) \\ $$$$\:{in}\:{a}\:{school}.{and}\:{there}\:{are}\:\mathrm{40}\:{apples} \\ $$$$\:{on}\:{the}\:{table}.{one}\:{teacher}\:{can}\:{eat} \\ $$$$\:\mathrm{4}\:{apples}.{and}\:{one}\:{student}\:{can}\:{eat} \\ $$$$\:\:\mathrm{2}\:{apples}.\:\mathrm{4}\:{workers}\:{can}\:{eat}\:{one}\: \\ $$$$\:\:{apple}.{find}\:{the}\:{numbers}\:{of}\:{teacher} \\ $$$$\:\:\:{students}\:\:{and}\:{workers} \\ $$$$\:\:\:\:\:{who}\:{eat}\:{apples}. \\ $$$${please}\:{help}\:{me}. \\ $$

Question Number 179574 Answers: 1 Comments: 6

Find the sum of all positive numbers less than 400 and not divisible by 6.

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{all}\:\mathrm{positive}\:\mathrm{numbers} \\ $$$$\:\mathrm{less}\:\mathrm{than}\:\mathrm{400}\:\mathrm{and}\:\mathrm{not}\:\mathrm{divisible}\:\mathrm{by}\:\mathrm{6}. \\ $$

Question Number 179571 Answers: 0 Comments: 6

Find the sum of all positive even 3-digits numbers divisible by 17.

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{all}\:\mathrm{positive}\:\mathrm{even} \\ $$$$\:\mathrm{3}-\mathrm{digits}\:\mathrm{numbers}\:\mathrm{divisible}\:\mathrm{by}\:\mathrm{17}. \\ $$

Question Number 179570 Answers: 2 Comments: 0

find the minimum value of function f(x)=(√(x^2 +(4/x^2 )−8x−((12)/x)+25)) + (√(x^2 +(4/x^2 )+−16x−((16)/x)+80))

$$\mathrm{find}\:\mathrm{the}\:\mathrm{minimum}\:\mathrm{value}\:\mathrm{of}\:\mathrm{function} \\ $$$$\boldsymbol{\mathrm{f}}\left(\boldsymbol{\mathrm{x}}\right)=\sqrt{\boldsymbol{\mathrm{x}}^{\mathrm{2}} +\frac{\mathrm{4}}{\boldsymbol{\mathrm{x}}^{\mathrm{2}} }−\mathrm{8}\boldsymbol{\mathrm{x}}−\frac{\mathrm{12}}{\boldsymbol{\mathrm{x}}}+\mathrm{25}}\:+\:\sqrt{\boldsymbol{\mathrm{x}}^{\mathrm{2}} +\frac{\mathrm{4}}{\boldsymbol{\mathrm{x}}^{\mathrm{2}} }+−\mathrm{16}\boldsymbol{\mathrm{x}}−\frac{\mathrm{16}}{\boldsymbol{\mathrm{x}}}+\mathrm{80}} \\ $$

Question Number 179567 Answers: 1 Comments: 0

Question Number 179566 Answers: 2 Comments: 0

Question Number 179565 Answers: 0 Comments: 1

Find x: tanx=((x^2 +1)/(2x))

$${Find}\:{x}: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:{tanx}=\frac{{x}^{\mathrm{2}} +\mathrm{1}}{\mathrm{2}{x}} \\ $$

Question Number 179550 Answers: 2 Comments: 0

16cos^5 θ−cos 5θ = (5/2) 0<θ<2π θ =?

$$\:\:\:\mathrm{16cos}\:^{\mathrm{5}} \theta−\mathrm{cos}\:\mathrm{5}\theta\:=\:\frac{\mathrm{5}}{\mathrm{2}}\: \\ $$$$\:\:\:\mathrm{0}<\theta<\mathrm{2}\pi \\ $$$$\:\:\:\theta\:=? \\ $$

Question Number 179545 Answers: 0 Comments: 3

Find the probability that n people (n≤365) selected at random will have n different birthdays.

$$\:\mathrm{Find}\:\mathrm{the}\:\mathrm{probability}\:\mathrm{that}\:\mathrm{n}\:\mathrm{people}\: \\ $$$$\:\:\left(\mathrm{n}\leqslant\mathrm{365}\right)\:\mathrm{selected}\:\mathrm{at}\:\mathrm{random}\:\mathrm{will} \\ $$$$\:\:\mathrm{have}\:\mathrm{n}\:\mathrm{different}\:\mathrm{birthdays}. \\ $$

Question Number 179542 Answers: 1 Comments: 0

A and B play a game in which they alternately toss a pair of dice. The one who is first to get a total of 7 wins the game . Find probability that the one who tosses second will win the game

$$\:\:\:\mathrm{A}\:\mathrm{and}\:\mathrm{B}\:\mathrm{play}\:\mathrm{a}\:\mathrm{game}\:\mathrm{in}\:\mathrm{which}\:\mathrm{they} \\ $$$$\:\:\mathrm{alternately}\:\mathrm{toss}\:\mathrm{a}\:\mathrm{pair}\:\mathrm{of}\:\mathrm{dice}.\:\mathrm{The} \\ $$$$\:\:\mathrm{one}\:\mathrm{who}\:\mathrm{is}\:\mathrm{first}\:\mathrm{to}\:\mathrm{get}\:\mathrm{a}\:\mathrm{total}\:\mathrm{of}\:\mathrm{7}\:\mathrm{wins} \\ $$$$\:\:\mathrm{the}\:\mathrm{game}\:.\:\mathrm{Find}\:\mathrm{probability}\:\mathrm{that}\:\mathrm{the}\:\mathrm{one} \\ $$$$\:\:\mathrm{who}\:\mathrm{tosses}\:\mathrm{second}\:\mathrm{will}\:\mathrm{win}\:\mathrm{the}\:\mathrm{game} \\ $$$$ \\ $$

Question Number 179529 Answers: 3 Comments: 0

(2−(√3))^x +(2+(√3))^x =4 x=?

$$\left(\mathrm{2}−\sqrt{\mathrm{3}}\right)^{{x}} +\left(\mathrm{2}+\sqrt{\mathrm{3}}\right)^{{x}} =\mathrm{4}\:\:\:\:\:\:{x}=? \\ $$

Question Number 179518 Answers: 0 Comments: 2

a−(1/b)=2cos((2π)/(13)) b−(1/c)=2cos((6π)/(13)) c−(1/a)=2cos((8π)/(13)) prove that (abc)^5 −(1/((abc)^5 ))=11

$${a}−\frac{\mathrm{1}}{{b}}=\mathrm{2}{cos}\frac{\mathrm{2}\pi}{\mathrm{13}} \\ $$$${b}−\frac{\mathrm{1}}{{c}}=\mathrm{2}{cos}\frac{\mathrm{6}\pi}{\mathrm{13}} \\ $$$${c}−\frac{\mathrm{1}}{{a}}=\mathrm{2}{cos}\frac{\mathrm{8}\pi}{\mathrm{13}}\:\:\:\:\:\:{prove}\:{that} \\ $$$$\left({abc}\right)^{\mathrm{5}} −\frac{\mathrm{1}}{\left({abc}\right)^{\mathrm{5}} }=\mathrm{11} \\ $$

Question Number 179517 Answers: 0 Comments: 0

22! ≡ x (mod 2024)

$$\:\mathrm{22}!\:\equiv\:\mathrm{x}\:\left(\mathrm{mod}\:\mathrm{2024}\right) \\ $$

Question Number 179515 Answers: 1 Comments: 0