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Question Number 180698 Answers: 1 Comments: 0

2+(x/(2+(x/(2+(x/:)))))=3 x=?

$$\mathrm{2}+\frac{{x}}{\mathrm{2}+\frac{{x}}{\mathrm{2}+\frac{{x}}{:}}}=\mathrm{3}\:\:\:\:\:\:\:\:\:\:\:{x}=? \\ $$

Question Number 180689 Answers: 1 Comments: 0

value of ∫_o ^(+oo) e^(E(x)) dx

$${value}\:{of}\: \\ $$$$\int_{{o}} ^{+{oo}} {e}^{{E}\left({x}\right)} {dx} \\ $$

Question Number 180695 Answers: 1 Comments: 0

Find all k, m, n ∈ N such that k!+3^m =3^n

$${Find}\:{all}\:{k},\:{m},\:{n}\:\in\:\mathbb{N}\:{such}\:{that} \\ $$$${k}!+\mathrm{3}^{{m}} =\mathrm{3}^{{n}} \\ $$

Question Number 180684 Answers: 1 Comments: 0

Question Number 180683 Answers: 1 Comments: 0

(b) x + y + Kz = 2 3x + 4y + 2z = K 2x + 3y − z = 1

$$\left(\mathrm{b}\right)\:\mathrm{x}\:+\:\mathrm{y}\:+\:\mathrm{Kz}\:=\:\mathrm{2} \\ $$$$\:\:\:\:\mathrm{3x}\:+\:\mathrm{4y}\:+\:\mathrm{2z}\:=\:\mathrm{K} \\ $$$$\:\:\:\:\mathrm{2x}\:+\:\mathrm{3y}\:−\:\mathrm{z}\:=\:\mathrm{1} \\ $$

Question Number 180667 Answers: 3 Comments: 1

Question Number 180680 Answers: 4 Comments: 0

Question Number 180682 Answers: 1 Comments: 0

Determine the value of k such that the following system has (i) a Unique solution (ii) No solution (iii) More than one solution (a) Kx + y + z = 1 x +Ky + z = 1 x + y + Kz = 1

$$\mathrm{Determine}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{k}\:\mathrm{such}\:\mathrm{that}\:\mathrm{the} \\ $$$$\mathrm{following}\:\mathrm{system}\:\mathrm{has}\:\left(\mathrm{i}\right)\:\mathrm{a}\:\mathrm{Unique}\: \\ $$$$\mathrm{solution}\:\left(\mathrm{ii}\right)\:\mathrm{No}\:\mathrm{solution}\:\left(\mathrm{iii}\right)\:\mathrm{More}\:\mathrm{than} \\ $$$$\mathrm{one}\:\mathrm{solution} \\ $$$$ \\ $$$$\left(\mathrm{a}\right)\:\mathrm{Kx}\:+\:\mathrm{y}\:+\:\mathrm{z}\:=\:\mathrm{1} \\ $$$$\:\:\:\:\mathrm{x}\:+\mathrm{Ky}\:+\:\mathrm{z}\:=\:\mathrm{1} \\ $$$$\:\:\:\:\mathrm{x}\:+\:\mathrm{y}\:+\:\mathrm{Kz}\:=\:\mathrm{1} \\ $$

Question Number 180625 Answers: 1 Comments: 0

During the challenge Cup season. Team A scored 15 goals more than Team B. They have 121 goals between them. how many goals did each team score?

$$\mathrm{During}\:\mathrm{the}\:\mathrm{challenge}\:\mathrm{Cup}\:\mathrm{season}.\:\mathrm{Team} \\ $$$$\mathrm{A}\:\mathrm{scored}\:\mathrm{15}\:\mathrm{goals}\:\mathrm{more}\:\mathrm{than}\:\mathrm{Team}\:\mathrm{B}. \\ $$$$\mathrm{They}\:\mathrm{have}\:\mathrm{121}\:\mathrm{goals}\:\mathrm{between}\:\mathrm{them}. \\ $$$$\mathrm{how}\:\mathrm{many}\:\mathrm{goals}\:\mathrm{did}\:\mathrm{each}\:\mathrm{team}\:\mathrm{score}? \\ $$$$ \\ $$

Question Number 180623 Answers: 1 Comments: 0

Question Number 180621 Answers: 1 Comments: 0

Question Number 180615 Answers: 3 Comments: 0

Question Number 180614 Answers: 0 Comments: 0

Question Number 180604 Answers: 1 Comments: 0

Question Number 180603 Answers: 0 Comments: 1

find the real solution of following equation system: x^2 +xy+y^2 =p y^2 +yz+z^2 =q z^2 +zx+x^2 =r with p,q,r>0

$${find}\:{the}\:{real}\:{solution}\:{of}\:{following} \\ $$$${equation}\:{system}: \\ $$$$\boldsymbol{{x}}^{\mathrm{2}} +\boldsymbol{{xy}}+\boldsymbol{{y}}^{\mathrm{2}} =\boldsymbol{{p}} \\ $$$$\boldsymbol{{y}}^{\mathrm{2}} +\boldsymbol{{yz}}+\boldsymbol{{z}}^{\mathrm{2}} =\boldsymbol{{q}} \\ $$$$\boldsymbol{{z}}^{\mathrm{2}} +\boldsymbol{{zx}}+\boldsymbol{{x}}^{\mathrm{2}} =\boldsymbol{{r}} \\ $$$${with}\:{p},{q},{r}>\mathrm{0} \\ $$

Question Number 180599 Answers: 1 Comments: 0

Find the length PQ.

$${Find}\:{the}\:{length}\:{PQ}. \\ $$

Question Number 180585 Answers: 2 Comments: 0

there are 5 points on a line and 4 points on a parallel line. how many quadrilaterals can be formed with these points as vertrices?

$${there}\:{are}\:\mathrm{5}\:{points}\:{on}\:{a}\:{line}\:{and}\:\mathrm{4}\: \\ $$$${points}\:{on}\:{a}\:{parallel}\:{line}. \\ $$$${how}\:{many}\:{quadrilaterals}\:{can}\:{be}\: \\ $$$${formed}\:{with}\:{these}\:{points}\:{as}\: \\ $$$${vertrices}? \\ $$

Question Number 180582 Answers: 1 Comments: 0

Question Number 180576 Answers: 4 Comments: 1

Question Number 180569 Answers: 1 Comments: 1

(√(x+4)) − (√(x−1)) > (√(4x+5))

$$\sqrt{\boldsymbol{{x}}+\mathrm{4}}\:−\:\sqrt{\boldsymbol{{x}}−\mathrm{1}}\:>\:\sqrt{\mathrm{4}\boldsymbol{{x}}+\mathrm{5}} \\ $$

Question Number 180565 Answers: 2 Comments: 1

(2x+(√(4x^2 +1)))(3y+(√(9y^2 +1)))=1 (4x+6y)^3 =? Show full solution

$$\left(\mathrm{2}{x}+\sqrt{\mathrm{4}{x}^{\mathrm{2}} +\mathrm{1}}\right)\left(\mathrm{3}{y}+\sqrt{\mathrm{9}{y}^{\mathrm{2}} +\mathrm{1}}\right)=\mathrm{1} \\ $$$$\left(\mathrm{4}{x}+\mathrm{6}{y}\right)^{\mathrm{3}} =? \\ $$$${Show}\:{full}\:{solution} \\ $$

Question Number 180558 Answers: 1 Comments: 0

The football team meets in a circle to consult about some plan to play, what′s the probability that the one player of the opponent team who′s trying to eavesdrops is standing behind the goalkeeper?

$${The}\:{football}\:{team}\:{meets}\:{in}\:{a}\:{circle}\:{to}\:{consult} \\ $$$$\:{about}\:{some}\:{plan}\:{to}\:{play},\:{what}'{s}\:{the}\:{probability} \\ $$$$\:{that}\:{the}\:{one}\:{player}\:{of}\:{the}\:{opponent}\:{team}\:{who}'{s} \\ $$$$\:{trying}\:{to}\:{eavesdrops}\:{is}\:{standing}\:{behind}\:{the} \\ $$$$\:{goalkeeper}? \\ $$

Question Number 180554 Answers: 2 Comments: 0

Question Number 180553 Answers: 1 Comments: 2

Question Number 180550 Answers: 1 Comments: 0

Resoudre af^′ (x)+(b/(f(x)))+c=0 (a,b,c)∈R^3

$${Resoudre}\: \\ $$$${af}^{'} \left({x}\right)+\frac{{b}}{{f}\left({x}\right)}+{c}=\mathrm{0}\:\:\:\:\left({a},{b},{c}\right)\in\mathbb{R}^{\mathrm{3}} \\ $$

Question Number 180549 Answers: 0 Comments: 0

Cross fertilization of 130 peas from different pure line yielded the following phenotype (GS, GW, and YW as follow GS only (36), GS and YW (15), all the three phenotype (9), GS and GW (14) YW and GW only (4). the number of those that have only YW or only GW are equal. a) How many peas have GW phenotype? b) How many peas have only one phenotype?

$$\mathrm{Cross}\:\mathrm{fertilization}\:\mathrm{of}\:\mathrm{130}\:\mathrm{peas}\:\mathrm{from} \\ $$$$\mathrm{different}\:\mathrm{pure}\:\mathrm{line}\:\mathrm{yielded}\:\mathrm{the}\:\mathrm{following} \\ $$$$\mathrm{phenotype}\:\left(\mathrm{GS},\:\mathrm{GW},\:\mathrm{and}\:\mathrm{YW}\:\mathrm{as}\:\mathrm{follow}\right. \\ $$$$\mathrm{GS}\:\mathrm{only}\:\left(\mathrm{36}\right),\:\mathrm{GS}\:\mathrm{and}\:\mathrm{YW}\:\left(\mathrm{15}\right),\:\mathrm{all}\:\mathrm{the} \\ $$$$\mathrm{three}\:\mathrm{phenotype}\:\left(\mathrm{9}\right),\:\mathrm{GS}\:\mathrm{and}\:\mathrm{GW}\:\left(\mathrm{14}\right) \\ $$$$\mathrm{YW}\:\mathrm{and}\:\mathrm{GW}\:\mathrm{only}\:\left(\mathrm{4}\right).\:\mathrm{the}\:\mathrm{number}\:\mathrm{of} \\ $$$$\mathrm{those}\:\mathrm{that}\:\mathrm{have}\:\mathrm{only}\:\mathrm{YW}\:\mathrm{or}\:\mathrm{only}\:\mathrm{GW} \\ $$$$\mathrm{are}\:\mathrm{equal}. \\ $$$$\left.\mathrm{a}\right)\:\mathrm{How}\:\mathrm{many}\:\mathrm{peas}\:\mathrm{have}\:\mathrm{GW}\:\mathrm{phenotype}? \\ $$$$\left.\mathrm{b}\right)\:\mathrm{How}\:\mathrm{many}\:\mathrm{peas}\:\mathrm{have}\:\mathrm{only}\:\mathrm{one}\: \\ $$$$\mathrm{phenotype}? \\ $$

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