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AlgebraQuestion and Answers: Page 327
Question Number 40965 Answers: 1 Comments: 0
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Question Number 40764 Answers: 1 Comments: 0
$$\boldsymbol{\mathrm{a}}\:\boldsymbol{\mathrm{piece}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{wire}}\:\mathrm{40}\boldsymbol{\mathrm{cm}}\:\boldsymbol{\mathrm{long}} \\ $$$$\boldsymbol{\mathrm{is}}\:\boldsymbol{\mathrm{cut}}\:\boldsymbol{\mathrm{into}}\:\boldsymbol{\mathrm{two}}\:\boldsymbol{\mathrm{parts}}\:\boldsymbol{\mathrm{and}}\:\boldsymbol{\mathrm{each}}\:\boldsymbol{\mathrm{part}} \\ $$$$\boldsymbol{\mathrm{is}}\:\boldsymbol{\mathrm{then}}\:\boldsymbol{\mathrm{bent}}\:\boldsymbol{\mathrm{into}}\:\boldsymbol{\mathrm{a}}\:\boldsymbol{\mathrm{square}}.\boldsymbol{\mathrm{if}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{sum}} \\ $$$$\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{these}}\:\boldsymbol{\mathrm{squares}}\:\boldsymbol{\mathrm{is}}\:\mathrm{68}\boldsymbol{\mathrm{cm}}^{\mathrm{2}} \\ $$$$\boldsymbol{\mathrm{find}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{lengths}}\:\boldsymbol{\mathrm{of}}\:\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{two}} \\ $$$$\boldsymbol{\mathrm{pieces}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{wire}}. \\ $$
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Question Number 40222 Answers: 1 Comments: 0
$$\mathrm{please}\:\mathrm{help} \\ $$$$\mathrm{Kate}\:\mathrm{was}\:\mathrm{given}\:\mathrm{602}.\mathrm{00}\:\mathrm{dollas}\:\mathrm{for}\: \\ $$$$\mathrm{shopping}.\:\mathrm{She}\:\mathrm{spent}\:\frac{\mathrm{1}}{\mathrm{4}}\:\mathrm{on}\:\mathrm{chocolate} \\ $$$$\mathrm{and}\:\mathrm{later}\:\frac{\mathrm{2}}{\mathrm{3}}\:\mathrm{on}\:\mathrm{goods}.\:\mathrm{How}\:\mathrm{much} \\ $$$$\mathrm{money}\:\mathrm{was}\:\mathrm{left}? \\ $$
Question Number 40042 Answers: 0 Comments: 0
$$\left.\mathrm{1}\right)\:{find}\:{the}\:{roots}\:{of}\:\: \\ $$$${p}\left({x}\right)=\left(\mathrm{1}+{ix}\:+{x}^{\mathrm{2}} \right)^{{n}} −\left(\mathrm{1}−{ix}+{x}^{\mathrm{2}} \right)^{{n}} \:{with}\:{n}\:{integr} \\ $$$${natural} \\ $$$$\left.\mathrm{2}\right)\:{factorize}\:{p}\left({x}\right)\:{inside}\:\:{C}\left({x}\right) \\ $$$$\left.\mathrm{3}\right)\:{give}\:{p}\left({x}\right)\:{at}\:{form}\:\:\Sigma\:{a}_{{p}} {x}^{{p}} \\ $$
Question Number 39995 Answers: 2 Comments: 0
Question Number 39971 Answers: 3 Comments: 0
$${a}>\mathrm{0},{b}>\mathrm{0}, \\ $$$${What}\:{is}\:{the}\:{minimum}\:{value}\:{of} \\ $$$$\frac{{b}^{\mathrm{2}} +\mathrm{2}}{{a}+{b}}+\frac{{a}^{\mathrm{2}} }{{ab}+\mathrm{1}}\:\:\:? \\ $$
Question Number 39868 Answers: 2 Comments: 0
$${a},{b},{c}>\mathrm{0},{if} \\ $$$$\frac{\mathrm{8}{a}^{\mathrm{2}} }{{a}^{\mathrm{2}} +\mathrm{9}}={b},\:\:\frac{\mathrm{10}{b}^{\mathrm{2}} }{{b}^{\mathrm{2}} +\mathrm{16}}={c},\:\:\frac{\mathrm{6}{c}^{\mathrm{2}} }{{c}^{\mathrm{2}} +\mathrm{25}}={a}, \\ $$$${then},{what}\:{is}\:{the}\:{minimum}\:{value}\:{of}\:\:{a}+{b}+{c}? \\ $$
Question Number 39814 Answers: 2 Comments: 0
$$\mathrm{kwame},\:\mathrm{ama}\:\mathrm{and}\:\mathrm{yaw}\:\mathrm{shared}\:\mathrm{an}\:\mathrm{amount}\:\mathrm{of}\:\mathrm{money} \\ $$$$\mathrm{in}\:\mathrm{the}\:\mathrm{ratio}\:\mathrm{3}:\mathrm{4}:\mathrm{5}.\:\mathrm{if}\:\mathrm{ama}\:\mathrm{had}\:\$\mathrm{8},\mathrm{400}\:\mathrm{more}\:\mathrm{than}\:\mathrm{kwame}. \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{total}\:\mathrm{amount}\:\mathrm{shared}. \\ $$
Question Number 39783 Answers: 1 Comments: 0
$${Find}\:{roots}\:{of} \\ $$$${f}\left({x}\right)={x}^{\mathrm{4}} −\mathrm{10}{x}^{\mathrm{3}} +\mathrm{35}{x}^{\mathrm{2}} −\mathrm{50}{x}+\mathrm{24} \\ $$
Question Number 39779 Answers: 1 Comments: 0
$${f}\left({x}\right)={x}^{\mathrm{4}} −\mathrm{2}{x}^{\mathrm{3}} +\mathrm{3}{x}^{\mathrm{2}} −\mathrm{4}{x}+\mathrm{5} \\ $$$${Find}\:{the}\:{roots}. \\ $$
Question Number 39639 Answers: 1 Comments: 0
Question Number 39636 Answers: 1 Comments: 0
$${let}\:{P}_{\alpha} \left({x}\right)\:={x}^{\mathrm{3}} \:\:+\mathrm{2}\alpha\:{x}\:−\mathrm{3} \\ $$$$\left.\mathrm{1}\right)\:{determine}\:{the}\:{roots}\:{of}\:{P}_{\alpha} \\ $$$$\left.\mathrm{2}\right)\:{determine}\:{the}\:{roots}\:{of}\:\:{P}_{−\mathrm{1}} \\ $$
Question Number 39524 Answers: 0 Comments: 0
Question Number 39332 Answers: 0 Comments: 1
$$\left.\mathrm{1}\right)\:{simplify}\:{S}_{{n}} \left({x}\right)=\sum_{{k}=\mathrm{1}} ^{{n}} \:{sin}^{\mathrm{2}} \left({kx}\right) \\ $$$$\left.\mathrm{2}\right){simplify}\:\:{A}_{{n}} =\sum_{{k}=\mathrm{1}} ^{{n}} \:{sin}^{\mathrm{2}} \left(\frac{{k}\pi}{{n}}\right) \\ $$
Question Number 39218 Answers: 1 Comments: 0
Question Number 39026 Answers: 2 Comments: 0
$${find}\:{the}\:{roots}\:{of}\:\:\mathrm{8}{x}^{\mathrm{3}} \:−\mathrm{4}{x}−\mathrm{1}\:=\mathrm{0} \\ $$
Question Number 39022 Answers: 0 Comments: 1
$${let}\:{p}\left({x}\right)=\:\left(\mathrm{1}+{e}^{{i}\theta} {x}\right)^{{n}} \:−\left(\mathrm{1}−{e}^{{i}\theta} {x}\right)^{{n}} \:{with}\:{n}\:{integr}\:{natural} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{the}\:{roots}\:{of}\:{p}\left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{fctorize}\:{inside}\:{C}\left[{x}\right]\:{p}\left({x}\right) \\ $$$$\left.\mathrm{3}\right)\:{factorize}\:{inside}\:{R}\left[{x}\right]\:{p}\left({x}\right).\:\:\theta\:\in{R} \\ $$
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