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AlgebraQuestion and Answers: Page 264

Question Number 88372 Answers: 0 Comments: 10

There are four boxes, each of them contains exactly the same numbers: 1,2,3,...,n. Four different numbers are drawn from the boxes and multiplicated with each other to get a product. What′s the sum of all products? Σ_(a≠b≠c≠d) abcd=?

$${There}\:{are}\:{four}\:{boxes},\:{each}\:{of}\:{them} \\ $$$${contains}\:{exactly}\:{the}\:{same}\:{numbers}: \\ $$$$\mathrm{1},\mathrm{2},\mathrm{3},...,{n}. \\ $$$${Four}\:{different}\:{numbers}\:{are}\:{drawn} \\ $$$${from}\:{the}\:{boxes}\:{and}\:{multiplicated} \\ $$$${with}\:{each}\:{other}\:{to}\:{get}\:{a}\:{product}. \\ $$$${What}'{s}\:{the}\:{sum}\:{of}\:{all}\:{products}? \\ $$$$\underset{{a}\neq{b}\neq{c}\neq{d}} {\sum}{abcd}=? \\ $$

Question Number 88360 Answers: 0 Comments: 2

(e/(√e)) × ((e)^(1/(3 )) /(e)^(1/(4 )) ) × ((e)^(1/(5 )) /(e)^(1/(6 )) ) × ((e)^(1/(7 )) /(e)^(1/(8 )) )×...=?

$$\frac{\mathrm{e}}{\sqrt{\mathrm{e}}}\:×\:\frac{\sqrt[{\mathrm{3}\:\:}]{\mathrm{e}}}{\sqrt[{\mathrm{4}\:\:}]{\mathrm{e}}}\:×\:\frac{\sqrt[{\mathrm{5}\:\:}]{\mathrm{e}}}{\sqrt[{\mathrm{6}\:\:}]{\mathrm{e}}}\:×\:\frac{\sqrt[{\mathrm{7}\:\:}]{\mathrm{e}}}{\sqrt[{\mathrm{8}\:\:}]{\mathrm{e}}}×...=? \\ $$

Question Number 88329 Answers: 0 Comments: 4

Question Number 88314 Answers: 2 Comments: 1

( a,b )are complex numbers and a^2 +ab+b^2 =0 find ((a/(a+b)))^(2020) +((b/(a+b)))^(2020)

$$\left(\:{a},{b}\:\right){are}\:{complex}\:{numbers}\:{and}\:{a}^{\mathrm{2}} +{ab}+{b}^{\mathrm{2}} =\mathrm{0} \\ $$$${find}\:\left(\frac{{a}}{{a}+{b}}\right)^{\mathrm{2020}} +\left(\frac{{b}}{{a}+{b}}\right)^{\mathrm{2020}} \\ $$$$ \\ $$

Question Number 88252 Answers: 0 Comments: 0

Question Number 88251 Answers: 0 Comments: 0

Question Number 88239 Answers: 0 Comments: 0

Question Number 88232 Answers: 0 Comments: 0

Question Number 88203 Answers: 0 Comments: 0

y=ax^(−3) , meets: y=e^x and y=−e^(−x) at: A and B,such that: AB is minimum. find: possible value(s) of: a and min of AB.

Question Number 88160 Answers: 2 Comments: 1

solve : x^2 = 3x + 6y ; xy = 5x + 4y

$${solve}\::\:{x}^{\mathrm{2}} \:=\:\mathrm{3}{x}\:+\:\mathrm{6}{y}\:;\:{xy}\:=\:\mathrm{5}{x}\:+\:\mathrm{4}{y} \\ $$

Question Number 88141 Answers: 1 Comments: 0

Question Number 88137 Answers: 1 Comments: 2

Mr mjs x, 3,7,13,27,33,y find x & y ? any formula to generally?

$${Mr}\:{mjs}\: \\ $$$${x},\:\mathrm{3},\mathrm{7},\mathrm{13},\mathrm{27},\mathrm{33},{y} \\ $$$${find}\:{x}\:\&\:{y}\:?\:{any}\:{formula} \\ $$$${to}\:{generally}? \\ $$

Question Number 88128 Answers: 1 Comments: 0

given 27^a = 64^b = 216^c = 72 find ((2020abc)/(3ab+3ac+3bc)) + ((ab+ac+bc)/(2020abc))

$${given}\:\mathrm{27}^{{a}} \:=\:\mathrm{64}^{{b}} \:=\:\mathrm{216}^{{c}} \:=\:\mathrm{72} \\ $$$${find}\:\frac{\mathrm{2020}{abc}}{\mathrm{3}{ab}+\mathrm{3}{ac}+\mathrm{3}{bc}}\:+\:\frac{{ab}+{ac}+{bc}}{\mathrm{2020}{abc}} \\ $$

Question Number 88088 Answers: 0 Comments: 0

Question Number 88067 Answers: 1 Comments: 0

Question Number 88040 Answers: 0 Comments: 2

Find the max and min of function ((a+bsin x)/(b+asin x)) where b>a>0 in the interval 0≤x≤2π.sketch a=4 and b=5

$${Find}\:{the}\:{max}\:{and}\:{min} \\ $$$${of}\:{function} \\ $$$$\frac{{a}+{b}\mathrm{sin}\:{x}}{{b}+{a}\mathrm{sin}\:{x}} \\ $$$${where}\:{b}>{a}>\mathrm{0}\:{in}\:{the}\: \\ $$$${interval}\:\mathrm{0}\leqslant{x}\leqslant\mathrm{2}\pi.{sketch} \\ $$$${a}=\mathrm{4}\:{and}\:{b}=\mathrm{5} \\ $$

Question Number 88039 Answers: 1 Comments: 0

Obtain the first four term of the expansion (4−x)^(1/3) when (1)∣x∣<1 (ii)∣x∣>1

$${Obtain}\:{the}\:{first}\:{four} \\ $$$${term}\:{of}\:{the}\:{expansion} \\ $$$$\left(\mathrm{4}−{x}\right)^{\frac{\mathrm{1}}{\mathrm{3}}} {when} \\ $$$$\left(\mathrm{1}\right)\mid{x}\mid<\mathrm{1} \\ $$$$\left({ii}\right)\mid{x}\mid>\mathrm{1} \\ $$

Question Number 88014 Answers: 2 Comments: 0

If there is no second′s hand on a clock and the minute and hour hand move in continuous fashion, then exactly at what time between 02:10 and 02:15 does the position of the two hands exactly coincide?

$${If}\:{there}\:{is}\:{no}\:{second}'{s}\:{hand}\:{on} \\ $$$${a}\:{clock}\:{and}\:{the}\:{minute}\:{and}\:{hour} \\ $$$${hand}\:{move}\:{in}\:{continuous}\:{fashion}, \\ $$$${then}\:{exactly}\:{at}\:{what}\:{time}\:{between} \\ $$$$\mathrm{02}:\mathrm{10}\:\:{and}\:\mathrm{02}:\mathrm{15}\:{does}\:{the}\:{position} \\ $$$${of}\:{the}\:{two}\:{hands}\:{exactly}\:{coincide}? \\ $$

Question Number 87988 Answers: 0 Comments: 0

solve the PDE 1−Z=px+py−q(√(pq)) 2−Z=px+qy+sin(p+q) 3−p(1+q^2 )=q(Z−a) 4−Z=xyp^2

$${solve}\:{the}\:{PDE} \\ $$$$\mathrm{1}−{Z}={px}+{py}−{q}\sqrt{{pq}} \\ $$$$\mathrm{2}−{Z}={px}+{qy}+{sin}\left({p}+{q}\right) \\ $$$$\mathrm{3}−{p}\left(\mathrm{1}+{q}^{\mathrm{2}} \right)={q}\left({Z}−{a}\right) \\ $$$$\mathrm{4}−{Z}={xyp}^{\mathrm{2}} \\ $$

Question Number 87886 Answers: 1 Comments: 2