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Question Number 180953 Answers: 2 Comments: 0

What′s 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) − 3arctg(ctg2) a)2π−3 b)12 c)−6 d)π−4/2 e)3π/2

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

Question Number 180943 Answers: 2 Comments: 0

if: a , bc^(−) = 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^(−) + ba^(−) = c3^(−) 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_(≥0) as {x} = x − ⌊x⌋ where ⌊x⌋ 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

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

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.

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