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AlgebraQuestion and Answers: Page 253

Question Number 95608 Answers: 3 Comments: 2

Question Number 95560 Answers: 1 Comments: 1

Question Number 95502 Answers: 1 Comments: 3

6 man + 8 woman ⇒working a job in 10 days 26 man + 48 woman ⇒ in 2 days if 15 man + 20 woman ⇒ ?? days

$$\mathrm{6}\:\mathrm{man}\:+\:\mathrm{8}\:\mathrm{woman}\:\Rightarrow\mathrm{working}\:\mathrm{a}\:\mathrm{job}\:\mathrm{in}\:\mathrm{10}\:\mathrm{days} \\ $$$$\mathrm{26}\:\mathrm{man}\:+\:\mathrm{48}\:\mathrm{woman}\:\Rightarrow\:\mathrm{in}\:\mathrm{2}\:\mathrm{days} \\ $$$$\mathrm{if}\:\mathrm{15}\:\mathrm{man}\:+\:\mathrm{20}\:\mathrm{woman}\:\Rightarrow\:??\:\mathrm{days} \\ $$

Question Number 95469 Answers: 0 Comments: 1

(9b^2 −25) why is this inside the bracket as it is a diffetence of two squares?

$$\left(\mathrm{9b}^{\mathrm{2}} −\mathrm{25}\right) \\ $$$$\mathrm{why}\:\mathrm{is}\:\mathrm{this}\:\mathrm{inside}\:\mathrm{the}\:\mathrm{bracket}\:\mathrm{as}\:\mathrm{it}\:\mathrm{is}\:\mathrm{a}\:\mathrm{diffetence}\:\mathrm{of}\:\mathrm{two}\:\mathrm{squares}? \\ $$

Question Number 95447 Answers: 1 Comments: 0

can I write the solution of ay′′+by′+cy=0 y= { ((c_1 e^(((−b+(√(b^2 −4ac)))/2)x) +c_2 e^(((−b−(√(b^2 −4ac)))/2)x) ,when b^2 −4ac≠0)),((c_1 e^(((−b)/2)x) +c_2 xe^(((−b)/2)x) ,when b^2 −4ac=0)) :} in one sentence not in the form of piecewide-define function

$${can}\:{I}\:{write}\:{the}\:{solution}\:{of} \\ $$$${ay}''+{by}'+{cy}=\mathrm{0} \\ $$$${y}=\begin{cases}{{c}_{\mathrm{1}} {e}^{\frac{−{b}+\sqrt{{b}^{\mathrm{2}} −\mathrm{4}{ac}}}{\mathrm{2}}{x}} +{c}_{\mathrm{2}} {e}^{\frac{−{b}−\sqrt{{b}^{\mathrm{2}} −\mathrm{4}{ac}}}{\mathrm{2}}{x}} ,{when}\:{b}^{\mathrm{2}} −\mathrm{4}{ac}\neq\mathrm{0}}\\{{c}_{\mathrm{1}} {e}^{\frac{−{b}}{\mathrm{2}}{x}} +{c}_{\mathrm{2}} {xe}^{\frac{−{b}}{\mathrm{2}}{x}} ,{when}\:{b}^{\mathrm{2}} −\mathrm{4}{ac}=\mathrm{0}}\end{cases} \\ $$$${in}\:{one}\:{sentence} \\ $$$${not}\:{in}\:{the}\:{form}\:{of}\:{piecewide}-{define}\:{function} \\ $$

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