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Question Number 202041 Answers: 1 Comments: 0

Simplify: (((√2) − sinα − cosα)/(sinα − cosα))

$$\mathrm{Simplify}:\:\:\:\frac{\sqrt{\mathrm{2}}\:−\:\mathrm{sin}\alpha\:−\:\mathrm{cos}\alpha}{\mathrm{sin}\alpha\:−\:\mathrm{cos}\alpha} \\ $$

Question Number 202034 Answers: 1 Comments: 0

Question Number 202039 Answers: 1 Comments: 0

Question Number 202037 Answers: 1 Comments: 0

A board has 2, 4, and 6 written on it. One repeatedly chooses values (not necessarily different) for x, y, and z from the board, and writes xyz + xy + yz + zx + x + y + z if and only if those numbers are not already on the board and are also less than or equals 2013. The person repeats this process until no more numbers can be written. How many numbers will be written at the end of this process?

$$ \\ $$A board has 2, 4, and 6 written on it. One repeatedly chooses values (not necessarily different) for x, y, and z from the board, and writes xyz + xy + yz + zx + x + y + z if and only if those numbers are not already on the board and are also less than or equals 2013. The person repeats this process until no more numbers can be written. How many numbers will be written at the end of this process?

Question Number 202035 Answers: 0 Comments: 0

Question Number 202019 Answers: 3 Comments: 0

If α and β are the roots of the ax^2 + 2bx + c = 0 and α + δ and β + δ are the roots of Ax^2 + 2Bx + C = 0 for some constant δ then prove that ((b^2 − ac)/a^2 ) = ((B^2 − AC)/A^2 ) .

$$\mathrm{If}\:\alpha\:\mathrm{and}\:\beta\:\mathrm{are}\:\mathrm{the}\:\mathrm{roots}\:\mathrm{of}\:\mathrm{the}\: \\ $$$${ax}^{\mathrm{2}} \:+\:\mathrm{2}{bx}\:+\:{c}\:=\:\mathrm{0}\:\mathrm{and}\:\alpha\:+\:\delta\:\mathrm{and}\:\beta\:+\:\delta\:\mathrm{are} \\ $$$$\mathrm{the}\:\mathrm{roots}\:\mathrm{of}\:{Ax}^{\mathrm{2}} \:+\:\mathrm{2}{Bx}\:+\:{C}\:=\:\mathrm{0}\:\mathrm{for}\:\mathrm{some}\: \\ $$$$\mathrm{constant}\:\delta\:\mathrm{then}\:\mathrm{prove}\:\mathrm{that} \\ $$$$\frac{{b}^{\mathrm{2}} \:−\:{ac}}{{a}^{\mathrm{2}} }\:=\:\frac{{B}^{\mathrm{2}} \:−\:{AC}}{{A}^{\mathrm{2}} }\:. \\ $$

Question Number 202017 Answers: 3 Comments: 0

Question Number 202016 Answers: 1 Comments: 0

Question Number 202011 Answers: 0 Comments: 0

Question Number 202009 Answers: 0 Comments: 0

Question Number 202003 Answers: 0 Comments: 3

what is meant by ξ

$${what}\:{is}\:{meant}\:{by}\:\xi \\ $$

Question Number 202001 Answers: 1 Comments: 0

If a circle of radius r is inscribed in a triangl ABC. Express r in terms of a,b and c only

$${If}\:{a}\:{circle}\:{of}\:{radius}\:{r}\:{is}\:{inscribed}\:{in} \\ $$$${a}\:{triangl}\:{ABC}.\:{Express}\:{r}\:{in}\:{terms}\:{of} \\ $$$${a},{b}\:{and}\:{c}\:{only} \\ $$

Question Number 202000 Answers: 0 Comments: 0

Question Number 201995 Answers: 1 Comments: 0

Question Number 201994 Answers: 0 Comments: 0

Question Number 201991 Answers: 2 Comments: 0

Solve ((1/x) − (1/x^3 ))^(1/2) + ((1/x^2 ) − (1/x^3 ))^(1/2) = 1

$$\boldsymbol{\mathrm{Solve}} \\ $$$$\left(\frac{\mathrm{1}}{{x}}\:−\:\frac{\mathrm{1}}{{x}^{\mathrm{3}} }\right)^{\frac{\mathrm{1}}{\mathrm{2}}} \:+\:\left(\frac{\mathrm{1}}{{x}^{\mathrm{2}} }\:−\:\frac{\mathrm{1}}{{x}^{\mathrm{3}} }\right)^{\frac{\mathrm{1}}{\mathrm{2}}} \:=\:\mathrm{1} \\ $$

Question Number 201989 Answers: 1 Comments: 0

Question Number 201952 Answers: 1 Comments: 0

(gof)_x =2x−1 (fog)_x ^(−1) =3x+2 (fof)_3 =?

$$\left({gof}\right)_{{x}} =\mathrm{2}{x}−\mathrm{1}\:\: \\ $$$$\left({fog}\right)_{{x}} ^{−\mathrm{1}} =\mathrm{3}{x}+\mathrm{2} \\ $$$$\left({fof}\right)_{\mathrm{3}} =? \\ $$

Question Number 201950 Answers: 0 Comments: 0

Question Number 201949 Answers: 1 Comments: 0

Question Number 201947 Answers: 1 Comments: 0

Question Number 201941 Answers: 2 Comments: 1

x^4 −((17)/(18))x^2 +((40)/3)x+((1625)/(144))=0 Find roots. (Two are real and two are complex)★

$${x}^{\mathrm{4}} −\frac{\mathrm{17}}{\mathrm{18}}{x}^{\mathrm{2}} +\frac{\mathrm{40}}{\mathrm{3}}{x}+\frac{\mathrm{1625}}{\mathrm{144}}=\mathrm{0} \\ $$$${Find}\:{roots}.\:\left({Two}\:{are}\:{real}\:{and}\:{two}\:\right. \\ $$$$\left.{are}\:{complex}\right)\bigstar \\ $$

Question Number 201940 Answers: 1 Comments: 0

tan^3 (xy^2 +y)=x find (dy/dx)

$$\boldsymbol{{tan}}^{\mathrm{3}} \left(\boldsymbol{{xy}}^{\mathrm{2}} +\boldsymbol{{y}}\right)=\boldsymbol{{x}}\:\:\boldsymbol{{find}}\:\frac{\boldsymbol{{dy}}}{\boldsymbol{{dx}}} \\ $$

Question Number 201936 Answers: 0 Comments: 1

Question Number 201934 Answers: 0 Comments: 1

Question Number 201931 Answers: 1 Comments: 0

if (a−2)^2 = 4a find: 5a + 4 + ((16)/(5a + 4)) = ?

$$\mathrm{if}\:\:\:\left(\mathrm{a}−\mathrm{2}\right)^{\mathrm{2}} \:=\:\mathrm{4a} \\ $$$$\mathrm{find}:\:\:\:\mathrm{5a}\:+\:\mathrm{4}\:+\:\frac{\mathrm{16}}{\mathrm{5a}\:+\:\mathrm{4}}\:=\:? \\ $$

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