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AlgebraQuestion and Answers: Page 265

Question Number 95440    Answers: 1   Comments: 0

Question Number 95416    Answers: 1   Comments: 4

It takes 12 hours to fill a swimming pool using 2 pipes. If the larger pipe used , for 4 hours and the small pipe for 9 hours, only half the pool is filled. How long would it take for each pipe alone to fill the pool?

$$\mathrm{It}\:\mathrm{takes}\:\mathrm{12}\:\mathrm{hours}\:\mathrm{to}\:\mathrm{fill}\:\mathrm{a}\:\mathrm{swimming}\: \\ $$$$\mathrm{pool}\:\mathrm{using}\:\mathrm{2}\:\mathrm{pipes}.\:\mathrm{If}\:\mathrm{the}\:\mathrm{larger}\: \\ $$$$\mathrm{pipe}\:\mathrm{used}\:,\:\mathrm{for}\:\mathrm{4}\:\mathrm{hours}\:\mathrm{and}\:\mathrm{the}\: \\ $$$$\mathrm{small}\:\mathrm{pipe}\:\mathrm{for}\:\mathrm{9}\:\mathrm{hours},\:\mathrm{only}\:\mathrm{half} \\ $$$$\mathrm{the}\:\mathrm{pool}\:\mathrm{is}\:\mathrm{filled}.\:\mathrm{How}\:\mathrm{long}\:\mathrm{would}\: \\ $$$$\mathrm{it}\:\mathrm{take}\:\mathrm{for}\:\mathrm{each}\:\mathrm{pipe}\:\mathrm{alone}\:\mathrm{to}\: \\ $$$$\mathrm{fill}\:\mathrm{the}\:\mathrm{pool}? \\ $$

Question Number 95394    Answers: 0   Comments: 31

Solve: x + y = 3 .... (i) x^y + y^x = 6 ..... (ii)

$$\mathrm{Solve}:\:\:\:\mathrm{x}\:\:+\:\:\mathrm{y}\:\:=\:\:\mathrm{3}\:\:\:\:\:\:....\:\left(\mathrm{i}\right) \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{x}^{\mathrm{y}} \:\:+\:\:\mathrm{y}^{\mathrm{x}} \:\:=\:\:\mathrm{6}\:\:\:\:.....\:\:\left(\mathrm{ii}\right) \\ $$

Question Number 95373    Answers: 1   Comments: 2

Find the value of m for which the roots of the equation x^3 + 6x^2 + 11x +m = 0 form a linear sequence.

$$\: \\ $$$$\:\mathrm{Find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:{m}\:\mathrm{for}\:\mathrm{which}\:\mathrm{the}\:\mathrm{roots} \\ $$$$\:\mathrm{of}\:\mathrm{the}\:\mathrm{equation}\:{x}^{\mathrm{3}} \:+\:\mathrm{6}{x}^{\mathrm{2}} \:+\:\mathrm{11}{x}\:+{m}\:=\:\mathrm{0} \\ $$$$\:\mathrm{form}\:\mathrm{a}\:\mathrm{linear}\:\mathrm{sequence}. \\ $$$$ \\ $$

Question Number 95328    Answers: 0   Comments: 3

Question Number 95324    Answers: 0   Comments: 2

If sin A + (sin A)^2 = 1 Then the value of (cos A)^(12) + 3(cos A)^(10) + 3(cos A)^8 + (cos A)^6 − 1 is ? (a) 0 (b) 1 (c) − 1 (d) 2

$$\mathrm{If}\:\:\:\mathrm{sin}\:\mathrm{A}\:\:+\:\:\left(\mathrm{sin}\:\mathrm{A}\right)^{\mathrm{2}} \:\:\:=\:\:\:\mathrm{1} \\ $$$$\mathrm{Then}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of} \\ $$$$\:\:\:\:\:\:\:\:\left(\mathrm{cos}\:\mathrm{A}\right)^{\mathrm{12}} \:\:+\:\:\mathrm{3}\left(\mathrm{cos}\:\mathrm{A}\right)^{\mathrm{10}} \:\:+\:\:\mathrm{3}\left(\mathrm{cos}\:\mathrm{A}\right)^{\mathrm{8}} \:\:+\:\:\left(\mathrm{cos}\:\mathrm{A}\right)^{\mathrm{6}} \:\:−\:\:\mathrm{1}\:\:\:\:\:\mathrm{is}\:? \\ $$$$ \\ $$$$\left(\mathrm{a}\right)\:\:\:\:\:\:\:\mathrm{0} \\ $$$$\left(\mathrm{b}\right)\:\:\:\:\:\:\:\:\mathrm{1} \\ $$$$\left(\mathrm{c}\right)\:\:\:\:−\:\mathrm{1} \\ $$$$\left(\mathrm{d}\right)\:\:\:\:\:\:\mathrm{2} \\ $$

Question Number 95309    Answers: 1   Comments: 0

if y = [ 2x+5 ] = 3[x−4] then [ 3x+y ] = ?

$$\mathrm{if}\:\mathrm{y}\:=\:\left[\:\mathrm{2x}+\mathrm{5}\:\right]\:=\:\mathrm{3}\left[\mathrm{x}−\mathrm{4}\right]\: \\ $$$$\mathrm{then}\:\left[\:\mathrm{3x}+\mathrm{y}\:\right]\:=\:?\: \\ $$

Question Number 95294    Answers: 1   Comments: 2

3 men, 4 women & 6 boy together working a job within 25 day. if 2 men , 3 women and 4 boy working the same job, complete in ?

$$\mathrm{3}\:\mathrm{men},\:\mathrm{4}\:\mathrm{women}\:\&\:\mathrm{6}\:\mathrm{boy}\:\mathrm{together} \\ $$$$\mathrm{working}\:\mathrm{a}\:\mathrm{job}\:\mathrm{within}\:\mathrm{25}\:\mathrm{day}.\:\mathrm{if}\:\mathrm{2}\:\mathrm{men}\: \\ $$$$,\:\mathrm{3}\:\mathrm{women}\:\mathrm{and}\:\mathrm{4}\:\mathrm{boy}\:\mathrm{working}\:\mathrm{the}\: \\ $$$$\mathrm{same}\:\mathrm{job},\:\mathrm{complete}\:\mathrm{in}\:? \\ $$

Question Number 95277    Answers: 2   Comments: 4

Question Number 95269    Answers: 0   Comments: 3

Question Number 95262    Answers: 3   Comments: 0

3x^2 +5x^4 −7 plz help to solve this equation

$$\mathrm{3x}^{\mathrm{2}} +\mathrm{5x}^{\mathrm{4}} −\mathrm{7} \\ $$$$\mathrm{plz}\:\mathrm{help}\:\mathrm{to}\:\mathrm{solve}\:\mathrm{this}\:\mathrm{equation} \\ $$

Question Number 95232    Answers: 3   Comments: 6

Question Number 95222    Answers: 1   Comments: 0

{ ((x^2 + x ((xy^2 ))^(1/(3 )) = 80 )),((y^2 + y ((x^2 y))^(1/(3 )) = 5 )) :} find x and y

$$\begin{cases}{{x}^{\mathrm{2}} \:+\:{x}\:\sqrt[{\mathrm{3}\:\:}]{{xy}^{\mathrm{2}} }\:=\:\mathrm{80}\:}\\{{y}^{\mathrm{2}} \:+\:{y}\:\sqrt[{\mathrm{3}\:\:}]{{x}^{\mathrm{2}} {y}}\:=\:\mathrm{5}\:}\end{cases} \\ $$$${find}\:{x}\:{and}\:{y}\: \\ $$

Question Number 95182    Answers: 1   Comments: 0

Question Number 95167    Answers: 0   Comments: 2

the first term in a geometric series is (((2x + 7))/(2x−5)) and the common ratio is (((2x−5))/(2x + 7)) find the set of values of x for which all the terms are possible.

$$\mathrm{the}\:\mathrm{first}\:\mathrm{term}\:\mathrm{in}\:\mathrm{a}\:\mathrm{geometric}\:\mathrm{series}\:\mathrm{is}\:\frac{\left(\mathrm{2}{x}\:+\:\mathrm{7}\right)}{\mathrm{2}{x}−\mathrm{5}}\:\mathrm{and}\:\mathrm{the}\:\mathrm{common}\:\mathrm{ratio}\:\mathrm{is} \\ $$$$\:\frac{\left(\mathrm{2}{x}−\mathrm{5}\right)}{\mathrm{2}{x}\:+\:\mathrm{7}}\:\mathrm{find}\:\mathrm{the}\:\mathrm{set}\:\mathrm{of}\:\mathrm{values}\:\mathrm{of}\:{x}\:\mathrm{for}\:\mathrm{which}\:\mathrm{all}\:\mathrm{the}\:\mathrm{terms}\:\mathrm{are}\:\mathrm{possible}. \\ $$

Question Number 95164    Answers: 0   Comments: 3

if a_k =tan (θ+((kπ)/n)), find ((Σ_(k=1) ^n a_k )/(Π_(k=1) ^n a_k ))=?

$${if}\:{a}_{{k}} =\mathrm{tan}\:\left(\theta+\frac{{k}\pi}{{n}}\right), \\ $$$${find}\:\frac{\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}{a}_{{k}} }{\underset{{k}=\mathrm{1}} {\overset{{n}} {\prod}}{a}_{{k}} }=? \\ $$

Question Number 95159    Answers: 1   Comments: 1

((8−x))^(1/(3 )) + (√x) = 2

$$\sqrt[{\mathrm{3}\:\:}]{\mathrm{8}−\mathrm{x}}\:+\:\sqrt{\mathrm{x}}\:=\:\mathrm{2}\: \\ $$

Question Number 95158    Answers: 0   Comments: 0

find the domain and range f(x)=⌊(1/(sin{x}))⌋

$${find}\:{the}\:{domain}\:{and}\:{range} \\ $$$${f}\left({x}\right)=\lfloor\frac{\mathrm{1}}{{sin}\left\{{x}\right\}}\rfloor \\ $$

Question Number 95127    Answers: 0   Comments: 1

Question Number 95106    Answers: 2   Comments: 0

{ ((x+y+z = 7)),((x^2 +y^2 +z^2 = 49)),((x^3 +y^3 +z^3 = 7)) :} find x; y ; z

$$\begin{cases}{{x}+{y}+{z}\:=\:\mathrm{7}}\\{{x}^{\mathrm{2}} +{y}^{\mathrm{2}} +{z}^{\mathrm{2}} \:=\:\mathrm{49}}\\{{x}^{\mathrm{3}} +{y}^{\mathrm{3}} +{z}^{\mathrm{3}} \:=\:\mathrm{7}}\end{cases} \\ $$$${find}\:{x};\:\mathrm{y}\:;\:{z}\: \\ $$

Question Number 95093    Answers: 2   Comments: 0

Solve: x^2 + y^2 = 13 ....... (i) 2x^2 + 3y = 2xy^2 ....... (ii)

$$\mathrm{Solve}: \\ $$$$\:\:\:\:\:\:\:\:\mathrm{x}^{\mathrm{2}} \:\:+\:\:\mathrm{y}^{\mathrm{2}} \:\:=\:\:\mathrm{13}\:\:\:\:\:\:\:\:\:\:.......\:\left(\mathrm{i}\right) \\ $$$$\:\:\:\:\:\:\mathrm{2x}^{\mathrm{2}} \:\:+\:\:\mathrm{3y}\:\:=\:\:\mathrm{2xy}^{\mathrm{2}} \:\:\:\:\:\:\:\:\:\:.......\:\left(\mathrm{ii}\right) \\ $$

Question Number 95062    Answers: 0   Comments: 7

solve for x, y, z ∈C such that ∣x∣=∣y∣=∣z∣=1 x+y+z=1 xyz=1

$${solve}\:{for}\:{x},\:{y},\:{z}\:\in\mathbb{C}\:{such}\:{that} \\ $$$$\mid{x}\mid=\mid{y}\mid=\mid{z}\mid=\mathrm{1} \\ $$$${x}+{y}+{z}=\mathrm{1} \\ $$$${xyz}=\mathrm{1} \\ $$

Question Number 95048    Answers: 0   Comments: 1

a_1 =−(1/(30)) a_2 =−(1/(12)) a_3 =−(1/6) a_4 =−(7/(24)) a_5 =−(7/(15)) a_6 =−(7/(10)) a_7 =−1 find a_k

$${a}_{\mathrm{1}} =−\frac{\mathrm{1}}{\mathrm{30}} \\ $$$${a}_{\mathrm{2}} =−\frac{\mathrm{1}}{\mathrm{12}} \\ $$$${a}_{\mathrm{3}} =−\frac{\mathrm{1}}{\mathrm{6}} \\ $$$${a}_{\mathrm{4}} =−\frac{\mathrm{7}}{\mathrm{24}} \\ $$$${a}_{\mathrm{5}} =−\frac{\mathrm{7}}{\mathrm{15}} \\ $$$${a}_{\mathrm{6}} =−\frac{\mathrm{7}}{\mathrm{10}} \\ $$$${a}_{\mathrm{7}} =−\mathrm{1} \\ $$$${find}\:{a}_{{k}} \\ $$

Question Number 95014    Answers: 0   Comments: 10

If y_(n + 1) − y_n = 6, and y_0 = 7 Find y_n

$$\boldsymbol{\mathrm{If}}\:\:\:\:\:\:\boldsymbol{\mathrm{y}}_{\boldsymbol{\mathrm{n}}\:\:+\:\:\mathrm{1}} \:\:−\:\:\boldsymbol{\mathrm{y}}_{\boldsymbol{\mathrm{n}}} \:\:\:=\:\:\:\mathrm{6},\:\:\:\:\:\:\:\boldsymbol{\mathrm{and}}\:\:\:\:\:\boldsymbol{\mathrm{y}}_{\mathrm{0}} \:\:=\:\:\:\mathrm{7} \\ $$$$\boldsymbol{\mathrm{Find}}\:\:\:\:\:\boldsymbol{\mathrm{y}}_{\boldsymbol{\mathrm{n}}} \\ $$

Question Number 94960    Answers: 2   Comments: 0

Question Number 94874    Answers: 1   Comments: 1

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