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Question Number 180990    Answers: 1   Comments: 0

2 blondes hair of 6 girls will sit around a circular table, whatβ€²s 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) ?

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

Question Number 180976    Answers: 2   Comments: 0

(dy/dx)=((xβˆ’yβˆ’2)/(x+y+6)) solve

$$\frac{\mathrm{dy}}{\mathrm{dx}}=\frac{\mathrm{x}βˆ’\mathrm{y}βˆ’\mathrm{2}}{\mathrm{x}+\mathrm{y}+\mathrm{6}} \\ $$$$ \\ $$$$\mathrm{solve} \\ $$

Question Number 180974    Answers: 0   Comments: 1

Question Number 180954    Answers: 1   Comments: 0

A tugboat is travelling from Asaba to Onitsha across the River Niger with a resultant velocity of 20 knots. If the river flows at 12 knots, the direction of motion of the boat relative to the direction of water flow is?

A tugboat is travelling from Asaba to Onitsha across the River Niger with a resultant velocity of 20 knots. If the river flows at 12 knots, the direction of motion of the boat relative to the direction of water flow is?

Question Number 180953    Answers: 2   Comments: 0

Whatβ€²s the smallest value of a^2 +b^2 +(1/(ab)) for a, b>0?

$${What}'{s}\:{the}\:{smallest}\:{value}\:{of} \\ $$$${a}^{\mathrm{2}} +{b}^{\mathrm{2}} +\frac{\mathrm{1}}{{ab}}\:{for}\:{a},\:{b}>\mathrm{0}? \\ $$

Question Number 181066    Answers: 1   Comments: 1

Find the value of the expression: 2arcctg(tg3) βˆ’ 3arctg(ctg2) a)2Ο€βˆ’3 b)12 c)βˆ’6 d)Ο€βˆ’4/2 e)3Ο€/2

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{the}\:\mathrm{expression}: \\ $$$$\mathrm{2arcctg}\left(\mathrm{tg3}\right)\:βˆ’\:\mathrm{3arctg}\left(\mathrm{ctg2}\right) \\ $$$$\left.\mathrm{a}\left.\right)\left.\mathrm{2}\left.\pi\left.βˆ’\mathrm{3}\:\:\mathrm{b}\right)\mathrm{12}\:\:\mathrm{c}\right)βˆ’\mathrm{6}\:\:\mathrm{d}\right)\piβˆ’\mathrm{4}/\mathrm{2}\:\:\mathrm{e}\right)\mathrm{3}\pi/\mathrm{2} \\ $$

Question Number 180943    Answers: 2   Comments: 0

if: a , bc^(βˆ’) = 1 + (1/2) + (3/(50)) find: a+b+c=?

$$\mathrm{if}:\:\:\:\overline {\mathrm{a}\:,\:\mathrm{bc}}\:=\:\mathrm{1}\:+\:\frac{\mathrm{1}}{\mathrm{2}}\:+\:\frac{\mathrm{3}}{\mathrm{50}} \\ $$$$\mathrm{find}:\:\:\:\mathrm{a}+\mathrm{b}+\mathrm{c}=? \\ $$

Question Number 180939    Answers: 0   Comments: 2

Question Number 180938    Answers: 2   Comments: 0

ab^(βˆ’) + ba^(βˆ’) = c3^(βˆ’) find: a+b+2c=?

$$\overline {\mathrm{ab}}\:+\:\overline {\mathrm{ba}}\:=\:\overline {\mathrm{c3}} \\ $$$$\mathrm{find}:\:\:\:\mathrm{a}+\mathrm{b}+\mathrm{2c}=? \\ $$

Question Number 180935    Answers: 2   Comments: 0

∫_ ((x+1)/(x^2 +1))dx

$$\int_{} \frac{{x}+\mathrm{1}}{{x}^{\mathrm{2}} +\mathrm{1}}{dx} \\ $$

Question Number 180931    Answers: 0   Comments: 2

Question Number 180927    Answers: 2   Comments: 1

Question Number 180926    Answers: 0   Comments: 9

For this problem, we define the fractional part of x∈R_(β‰₯0) as {x} = x βˆ’ ⌊xβŒ‹ where ⌊xβŒ‹ is the integer part of x, i.e the greatest integer less than or equal to x. (a) Draw the function {x} in a cordinate system for 0≀x≀3 (b) Find the area A_n , under the graph of {x} between 0 and n∈N as given by A_n =∫_0 ^n {x}dx. M.m

$$\mathrm{For}\:\mathrm{this}\:\mathrm{problem},\:\mathrm{we}\:\mathrm{define}\:\mathrm{the}\: \\ $$$$\mathrm{fractional}\:\mathrm{part}\:\mathrm{of}\:\mathrm{x}\in\mathbb{R}_{\geqslant\mathrm{0}} \:\mathrm{as} \\ $$$$\left\{\mathrm{x}\right\}\:=\:\mathrm{x}\:βˆ’\:\lfloor\mathrm{x}\rfloor \\ $$$$\mathrm{where}\:\lfloor\mathrm{x}\rfloor\:\mathrm{is}\:\mathrm{the}\:\mathrm{integer}\:\mathrm{part}\:\mathrm{of}\:\mathrm{x},\:\mathrm{i}.\mathrm{e} \\ $$$$\mathrm{the}\:\mathrm{greatest}\:\mathrm{integer}\:\mathrm{less}\:\mathrm{than}\:\mathrm{or}\:\mathrm{equal} \\ $$$$\mathrm{to}\:\mathrm{x}. \\ $$$$\left(\mathrm{a}\right)\:\mathrm{Draw}\:\mathrm{the}\:\mathrm{function}\:\left\{\mathrm{x}\right\}\:\mathrm{in}\:\mathrm{a}\:\mathrm{cordinate} \\ $$$$\mathrm{system}\:\mathrm{for}\:\mathrm{0}\leqslant\mathrm{x}\leqslant\mathrm{3} \\ $$$$\left(\mathrm{b}\right)\:\mathrm{Find}\:\mathrm{the}\:\mathrm{area}\:\mathrm{A}_{\mathrm{n}} \:,\:\mathrm{under}\:\mathrm{the}\:\mathrm{graph} \\ $$$$\mathrm{of}\:\left\{\mathrm{x}\right\}\:\mathrm{between}\:\mathrm{0}\:\mathrm{and}\:\mathrm{n}\in\mathbb{N}\:\mathrm{as}\:\mathrm{given}\:\mathrm{by} \\ $$$$\mathrm{A}_{\mathrm{n}} =\int_{\mathrm{0}} ^{\mathrm{n}} \left\{\mathrm{x}\right\}\mathrm{dx}. \\ $$$$ \\ $$$$ \\ $$$$\mathrm{M}.\mathrm{m} \\ $$

Question Number 180923    Answers: 1   Comments: 0

Question Number 180919    Answers: 1   Comments: 0

Question Number 180917    Answers: 1   Comments: 0

Question Number 180890    Answers: 0   Comments: 2

We have 7 sets with 2 subsets each (yes and no are the 2 subsets of each of the 7 sets) how many possible combinations are there if one of the subset is picked for each of the 7 sets.

We have 7 sets with 2 subsets each (yes and no are the 2 subsets of each of the 7 sets) how many possible combinations are there if one of the subset is picked for each of the 7 sets.

Question Number 180889    Answers: 0   Comments: 1

the average of 10 numbers is 5. the sum of their squares is 5000. how large can the largest number among them at most be and how small can the smallest number among them at most be?

$${the}\:{average}\:{of}\:\mathrm{10}\:{numbers}\:{is}\:\mathrm{5}.\:{the} \\ $$$${sum}\:{of}\:{their}\:{squares}\:{is}\:\mathrm{5000}.\:{how}\: \\ $$$${large}\:{can}\:{the}\:{largest}\:{number}\:{among} \\ $$$${them}\:{at}\:{most}\:{be}\:{and}\:{how}\:{small}\:{can}\: \\ $$$${the}\:{smallest}\:{number}\:{among}\:{them} \\ $$$${at}\:{most}\:{be}? \\ $$

Question Number 180886    Answers: 1   Comments: 0

Question Number 180882    Answers: 1   Comments: 1

Question Number 180877    Answers: 1   Comments: 1

Q. find the largest value of such that the positive integers a, b > 1 satisfy. a^b .b^a + a^b + b^a = 5329

$$\boldsymbol{\mathrm{Q}}.\:\boldsymbol{\mathrm{find}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{largest}}\:\boldsymbol{\mathrm{value}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{such}}\:\boldsymbol{\mathrm{that}}\:\boldsymbol{\mathrm{the}} \\ $$$$\boldsymbol{\mathrm{positive}}\:\boldsymbol{\mathrm{integers}}\:\:\boldsymbol{\mathrm{a}},\:\boldsymbol{\mathrm{b}}\:>\:\mathrm{1}\:\boldsymbol{\mathrm{satisfy}}. \\ $$$$\:\boldsymbol{\mathrm{a}}^{\boldsymbol{\mathrm{b}}} .\boldsymbol{\mathrm{b}}^{\boldsymbol{\mathrm{a}}} \:+\:\boldsymbol{\mathrm{a}}^{\boldsymbol{\mathrm{b}}} \:+\:\boldsymbol{\mathrm{b}}^{\boldsymbol{\mathrm{a}}} \:=\:\mathrm{5329} \\ $$

Question Number 180874    Answers: 1   Comments: 2

Question Number 180873    Answers: 1   Comments: 2

If a,b,c<0 and abc(a+b+c)=64 Then find min of P=2a+b+c

$$\mathrm{If}\:\:\:\mathrm{a},\mathrm{b},\mathrm{c}<\mathrm{0}\:\:\:\mathrm{and}\:\:\:\mathrm{abc}\left(\mathrm{a}+\mathrm{b}+\mathrm{c}\right)=\mathrm{64} \\ $$$$\mathrm{Then}\:\mathrm{find}\:\mathrm{min}\:\mathrm{of}\:\:\:\mathrm{P}=\mathrm{2a}+\mathrm{b}+\mathrm{c} \\ $$

Question Number 180871    Answers: 0   Comments: 1

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