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AllQuestion and Answers: Page 354

Question Number 186408    Answers: 1   Comments: 0

Question Number 186152    Answers: 1   Comments: 0

I= ∫_2 ^𝛑 ((cos^2 (x) βˆ’ 1 )/(1 + sin (x) βˆ’ tan (x))) dx

$$ \\ $$$$\:\:\:\boldsymbol{{I}}=\:\:\underset{\mathrm{2}} {\overset{\boldsymbol{\pi}} {\int}}\:\:\:\frac{\boldsymbol{{cos}}^{\mathrm{2}} \:\left(\boldsymbol{{x}}\right)\:βˆ’\:\mathrm{1}\:}{\mathrm{1}\:+\:\boldsymbol{{sin}}\:\left(\boldsymbol{{x}}\right)\:βˆ’\:\boldsymbol{{tan}}\:\left(\boldsymbol{{x}}\right)}\:\:\boldsymbol{{dx}}\:\:\:\: \\ $$$$ \\ $$

Question Number 186146    Answers: 0   Comments: 0

Question Number 186144    Answers: 0   Comments: 9

Question Number 186143    Answers: 2   Comments: 0

Question Number 186142    Answers: 0   Comments: 0

Question Number 186141    Answers: 0   Comments: 1

Question Number 186132    Answers: 1   Comments: 4

Question Number 186126    Answers: 0   Comments: 1

Question Number 186125    Answers: 1   Comments: 0

Question Number 186124    Answers: 1   Comments: 1

Question Number 186123    Answers: 0   Comments: 0

Question Number 186111    Answers: 2   Comments: 2

Question Number 186103    Answers: 0   Comments: 0

Let R denote a set of all ordered pairs (x, y) of integers such that xβˆ’y is an integral multiple of 3. Which of the followings ordered pairs belong to R (9,3) (3, 9),( 1 ,2) (1, 5),(7, 2) (0, 4), (4 ,7). (note: a is an integral multiple of b if a=kb where k is an integer)

$$\mathrm{Let}\:\mathrm{R}\:\mathrm{denote}\:\mathrm{a}\:\mathrm{set}\:\mathrm{of}\:\mathrm{all}\:\mathrm{ordered}\:\mathrm{pairs}\:\left(\mathrm{x},\:\mathrm{y}\right)\: \\ $$$$\mathrm{of}\:\mathrm{integers}\:\mathrm{such}\:\mathrm{that}\:\mathrm{x}βˆ’\mathrm{y}\:\mathrm{is}\:\mathrm{an}\:\mathrm{integral} \\ $$$$\:\mathrm{multiple}\:\mathrm{of}\:\mathrm{3}.\:\mathrm{Which}\:\mathrm{of}\:\mathrm{the}\:\mathrm{followings}\:\mathrm{ordered}\:\mathrm{pairs} \\ $$$$\mathrm{belong}\:\mathrm{to}\:\mathrm{R}\:\left(\mathrm{9},\mathrm{3}\right)\:\left(\mathrm{3},\:\mathrm{9}\right),\left(\:\mathrm{1}\:,\mathrm{2}\right)\:\left(\mathrm{1},\:\mathrm{5}\right),\left(\mathrm{7},\:\mathrm{2}\right) \\ $$$$\:\left(\mathrm{0},\:\mathrm{4}\right),\:\left(\mathrm{4}\:,\mathrm{7}\right). \\ $$$$\left(\mathrm{note}:\:\mathrm{a}\:\mathrm{is}\:\mathrm{an}\:\mathrm{integral}\:\mathrm{multiple}\:\mathrm{of}\:\mathrm{b}\:\mathrm{if}\:\mathrm{a}=\mathrm{kb}\right. \\ $$$$\left.\mathrm{whe}{re}\:\mathrm{k}\:\mathrm{is}\:\mathrm{an}\:\mathrm{integer}\right) \\ $$

Question Number 186105    Answers: 3   Comments: 0

a^2 + 1 = a a^(12) + a^6 + 1 = ?

$$\:{a}^{\mathrm{2}} \:+\:\mathrm{1}\:\:=\:{a} \\ $$$$\:{a}^{\mathrm{12}} \:+\:{a}^{\mathrm{6}} \:+\:\mathrm{1}\:=\:?\: \\ $$

Question Number 186099    Answers: 1   Comments: 0

1. Solve for the linear system: xβˆ’2y+3z=5 2x+yβˆ’4z=0 3x+4yβˆ’11z=βˆ’5 2. Ghana railways coβˆ’operation has 20 trains for itβ€²s operations. It is observed that x trains can accommodate 2 passengers, y trains 3 passengers and z trains 5 passengers. Howeer, the totsl number of passrngers always present at Ghana railways are 64. During market day, 3 of x trains, 2 of y trains and 4 of z trains for a total of 10 trains were used. Determine the values of x, y and z.

$$\mathrm{1}.\:{Solve}\:{for}\:{the}\:{linear}\:{system}: \\ $$$${x}βˆ’\mathrm{2}{y}+\mathrm{3}{z}=\mathrm{5} \\ $$$$\mathrm{2}{x}+{y}βˆ’\mathrm{4}{z}=\mathrm{0} \\ $$$$\mathrm{3}{x}+\mathrm{4}{y}βˆ’\mathrm{11}{z}=βˆ’\mathrm{5} \\ $$$$\mathrm{2}.\:{Ghana}\:{railways}\:{co}βˆ’{operation}\:{has}\:\mathrm{20}\: \\ $$$${trains}\:{for}\:{it}'{s}\:{operations}.\:{It}\:{is}\:{observed}\:{that} \\ $$$${x}\:{trains}\:{can}\:{accommodate}\:\mathrm{2}\:{passengers}, \\ $$$${y}\:{trains}\:\mathrm{3}\:{passengers}\:{and}\:{z}\:{trains}\:\mathrm{5}\: \\ $$$${passengers}.\:{Howeer},\:{the}\:{totsl}\:{number}\:{of} \\ $$$${passrngers}\:{always}\:{present}\:{at}\:{Ghana}\: \\ $$$${railways}\:{are}\:\mathrm{64}.\:{During}\:{market}\:{day},\:\mathrm{3}\:{of} \\ $$$${x}\:{trains},\:\mathrm{2}\:{of}\:{y}\:{trains}\:{and}\:\mathrm{4}\:{of}\:{z}\:{trains}\:{for}\: \\ $$$${a}\:{total}\:{of}\:\mathrm{10}\:{trains}\:{were}\:{used}.\:{Determine}\: \\ $$$${the}\:{values}\:{of}\:{x},\:{y}\:{and}\:{z}. \\ $$

Question Number 186094    Answers: 0   Comments: 0

Q1000

$${Q}\mathrm{1000} \\ $$

Question Number 186082    Answers: 0   Comments: 0

Question Number 186080    Answers: 0   Comments: 0

Question Number 186079    Answers: 1   Comments: 0

Question Number 186077    Answers: 1   Comments: 0

Prove that β–½β€’(βˆ…A^βˆ’ )=(β–½βˆ…)β€’A+βˆ…(β–½β€’A^βˆ’ ). Help!

$$\mathrm{Prove}\:\mathrm{that}\: \\ $$$$\bigtriangledown\bullet\left(\varnothing\overset{βˆ’} {\mathrm{A}}\right)=\left(\bigtriangledown\varnothing\right)\bullet\mathrm{A}+\varnothing\left(\bigtriangledown\bullet\overset{βˆ’} {\mathrm{A}}\right). \\ $$$$ \\ $$$$ \\ $$$$\mathrm{Help}! \\ $$

Question Number 186074    Answers: 1   Comments: 0

Prove that div(curlA^βˆ’ )=0 Help!

$$\mathrm{Prove}\:\mathrm{that}\:\mathrm{div}\left(\mathrm{curl}\overset{βˆ’} {\mathrm{A}}\right)=\mathrm{0} \\ $$$$ \\ $$$$ \\ $$$$\mathrm{Help}! \\ $$

Question Number 186069    Answers: 1   Comments: 0

Question Number 186066    Answers: 3   Comments: 0

lim_(xβ†’βˆž) x((√(4x^2 βˆ’12x+7))βˆ’(√(x^2 βˆ’4xβˆ’2))βˆ’x+1) lim_(xβ†’βˆž) ((√(x^2 +3x))βˆ’((x^3 +2x^2 ))^(1/3) )

$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:{x}\left(\sqrt{\mathrm{4}{x}^{\mathrm{2}} βˆ’\mathrm{12}{x}+\mathrm{7}}βˆ’\sqrt{{x}^{\mathrm{2}} βˆ’\mathrm{4}{x}βˆ’\mathrm{2}}βˆ’{x}+\mathrm{1}\right) \\ $$$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\left(\sqrt{{x}^{\mathrm{2}} +\mathrm{3}{x}}βˆ’\sqrt[{\mathrm{3}}]{{x}^{\mathrm{3}} +\mathrm{2}{x}^{\mathrm{2}} }\right) \\ $$$$ \\ $$

Question Number 186065    Answers: 1   Comments: 2

lim_(xβ†’1) ((((x^3 +7x^2 +10x+9))^(1/3) βˆ’(√(6x+3)))/((xβˆ’1)^2 ))

$$\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}\:\frac{\sqrt[{\mathrm{3}}]{{x}^{\mathrm{3}} +\mathrm{7}{x}^{\mathrm{2}} +\mathrm{10}{x}+\mathrm{9}}βˆ’\sqrt{\mathrm{6}{x}+\mathrm{3}}}{\left({x}βˆ’\mathrm{1}\right)^{\mathrm{2}} } \\ $$$$ \\ $$

Question Number 186064    Answers: 1   Comments: 1

lim_(xβ†’βˆž) (cos2x βˆ’cos(√(4x^2 +10)))

$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\left({cos}\mathrm{2}{x}\:βˆ’{cos}\sqrt{\mathrm{4}{x}^{\mathrm{2}} +\mathrm{10}}\right) \\ $$$$ \\ $$

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