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Question Number 49621 Answers: 0 Comments: 0

Question Number 49605 Answers: 1 Comments: 3

Question Number 49604 Answers: 2 Comments: 0

Show that: (((a + b)^2 )/2) ≤ a^2 + b^2

$$\mathrm{Show}\:\mathrm{that}:\:\:\:\:\:\:\:\:\:\:\:\frac{\left(\mathrm{a}\:+\:\mathrm{b}\right)^{\mathrm{2}} }{\mathrm{2}}\:\:\leqslant\:\:\mathrm{a}^{\mathrm{2}} \:+\:\mathrm{b}^{\mathrm{2}} \\ $$

Question Number 49602 Answers: 0 Comments: 0

∅=0

$$\varnothing=\mathrm{0} \\ $$

Question Number 71170 Answers: 1 Comments: 1

Question Number 49594 Answers: 0 Comments: 1

How can we insert images in the editor?

$$\:\:\:\:{How}\:{can}\:{we}\:{insert}\:{images}\:{in}\:{the}\:{editor}? \\ $$

Question Number 49651 Answers: 0 Comments: 3

Question Number 49570 Answers: 1 Comments: 0

Eliminate t from this equation: (1) x = 1 + t, y = 1 + (1/t) (2) x = 3 + t^3 , y = 2 + (1/t)

$$\mathrm{Eliminate}\:\:\boldsymbol{\mathrm{t}}\:\:\mathrm{from}\:\mathrm{this}\:\mathrm{equation}:\:\:\left(\mathrm{1}\right)\:\:\:\mathrm{x}\:=\:\mathrm{1}\:+\:\mathrm{t},\:\:\:\mathrm{y}\:=\:\mathrm{1}\:+\:\frac{\mathrm{1}}{\mathrm{t}} \\ $$$$\left(\mathrm{2}\right)\:\:\mathrm{x}\:=\:\mathrm{3}\:+\:\mathrm{t}^{\mathrm{3}} \:,\:\:\:\:\:\mathrm{y}\:=\:\mathrm{2}\:+\:\frac{\mathrm{1}}{\mathrm{t}} \\ $$

Question Number 51422 Answers: 2 Comments: 1

Question Number 49559 Answers: 2 Comments: 1

Question Number 49555 Answers: 0 Comments: 0

Find 4 plz help me sir

$$\mathrm{Find}\:\mathrm{4}\:\: \\ $$$$\mathrm{plz}\:\mathrm{help}\:\mathrm{me}\:\mathrm{sir} \\ $$

Question Number 49554 Answers: 0 Comments: 0

Question Number 49553 Answers: 0 Comments: 1

Question Number 49536 Answers: 3 Comments: 2

Question Number 49534 Answers: 1 Comments: 3

Question Number 49530 Answers: 3 Comments: 3

Question Number 49526 Answers: 1 Comments: 1

Question Number 49583 Answers: 0 Comments: 4

Question Number 49491 Answers: 1 Comments: 0

A rocket of mass 1000kg containing a propellant gas of 3000kg is to be launched vertically.If the fuel is consumed at a steady rate of 60kg/s.Calculate the least velocith of the exhaust gases if the rocket and the content will just lift off the launching pad immediately after firing?

$${A}\:{rocket}\:{of}\:{mass}\:\mathrm{1000}{kg}\:{containing} \\ $$$${a}\:\:{propellant}\:{gas}\:{of}\:\mathrm{3000}{kg}\:{is}\:{to} \\ $$$${be}\:{launched}\:{vertically}.{If}\:{the}\:{fuel} \\ $$$${is}\:{consumed}\:{at}\:{a}\:{steady}\:{rate}\:{of} \\ $$$$\mathrm{60}{kg}/{s}.{Calculate}\:{the}\:{least}\:{velocith} \\ $$$${of}\:{the}\:{exhaust}\:{gases}\:{if}\:{the}\:{rocket} \\ $$$${and}\:{the}\:{content}\:{will}\:{just}\:{lift}\:{off} \\ $$$${the}\:{launching}\:{pad}\:{immediately} \\ $$$${after}\:{firing}? \\ $$

Question Number 49487 Answers: 0 Comments: 2

Find the nth term of the sequence: 5, 5, 35, 65, 275, ... Answer: 3^n − (− 2)^n ple1ase how

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{nth}\:\mathrm{term}\:\mathrm{of}\:\mathrm{the}\:\mathrm{sequence}:\:\:\mathrm{5},\:\:\mathrm{5},\:\:\mathrm{35},\:\mathrm{65},\:\:\mathrm{275},\:... \\ $$$$ \\ $$$$\mathrm{Answer}:\:\:\:\:\:\mathrm{3}^{\boldsymbol{\mathrm{n}}} \:−\:\left(−\:\mathrm{2}\right)^{\boldsymbol{\mathrm{n}}} \:\:\:\:\:\:\:\:\:\:\:\:\boldsymbol{\mathrm{ple}}\mathrm{1ase}\:\mathrm{how} \\ $$

Question Number 49482 Answers: 1 Comments: 14

Find number of 4−letter words which can be formed using the letters of the word ′ALLAHABAD′ such that: NO repetition of letter and word should start “either” from H “or” ends with D ?

$${Find}\:{number}\:{of}\:\mathrm{4}−{letter}\:{words}\:{which} \\ $$$${can}\:{be}\:{formed}\:{using}\:{the}\:{letters}\:{of}\: \\ $$$${the}\:{word}\:'{ALLAHABAD}'\:{such}\:{that}: \\ $$$${NO}\:{repetition}\:{of}\:{letter}\:{and}\:{word}\:{should} \\ $$$${start}\:``{either}''\:{from}\:{H}\:``{or}''\:{ends}\:{with}\:{D}\:? \\ $$

Question Number 49468 Answers: 1 Comments: 0

Question Number 49466 Answers: 0 Comments: 0

show that the area of the triangle whose vertics area (0,0,0) , (x_1 ,y_1 ,z_1 ) , (x_2 ,y_(2,) z_2 ) is 1/2((√(Σ(y_1 z_2 −y_2 z_1 )^2 .))

$${show}\:{that}\:{the}\:{area}\:{of}\:{the}\:{triangle}\:{whose}\:{vertics}\:{area}\:\left(\mathrm{0},\mathrm{0},\mathrm{0}\right)\:,\:\left({x}_{\mathrm{1}} ,{y}_{\mathrm{1}} ,{z}_{\mathrm{1}} \right)\:,\:\left({x}_{\mathrm{2}} ,{y}_{\mathrm{2},} {z}_{\mathrm{2}} \right)\:{is}\:\mathrm{1}/\mathrm{2}\left(\sqrt{\Sigma\left({y}_{\mathrm{1}} {z}_{\mathrm{2}} −{y}_{\mathrm{2}} {z}_{\mathrm{1}} \right)^{\mathrm{2}} \:.}\right. \\ $$

Question Number 49464 Answers: 2 Comments: 2

If 9(√x)=(√(12))+(√(147)), then the value of x is

$$\mathrm{If}\:\:\mathrm{9}\sqrt{{x}}=\sqrt{\mathrm{12}}+\sqrt{\mathrm{147}},\:\mathrm{then}\:\mathrm{the}\:\mathrm{value} \\ $$$$\mathrm{of}\:{x}\:\mathrm{is} \\ $$

Question Number 49463 Answers: 1 Comments: 0

If 7^(log _7 (x^2 −4x+5)) = x−1, x may have values

$$\mathrm{If}\:\:\:\mathrm{7}^{\mathrm{log}\:_{\mathrm{7}} \left({x}^{\mathrm{2}} −\mathrm{4}{x}+\mathrm{5}\right)} =\:{x}−\mathrm{1},\:\:{x}\:\mathrm{may}\:\mathrm{have} \\ $$$$\mathrm{values} \\ $$

Question Number 49462 Answers: 2 Comments: 0

The number of roots of the equation 2∣x∣^2 − 7∣x∣ + 6=0.

$$\mathrm{The}\:\mathrm{number}\:\mathrm{of}\:\mathrm{roots}\:\mathrm{of}\:\mathrm{the}\:\mathrm{equation} \\ $$$$\mathrm{2}\mid{x}\mid^{\mathrm{2}} −\:\mathrm{7}\mid{x}\mid\:+\:\mathrm{6}=\mathrm{0}. \\ $$

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