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Question Number 14816 Answers: 1 Comments: 0

Question Number 14811 Answers: 1 Comments: 0

why (√x^2 )=∣x∣ ?

$${why}\:\:\:\:\:\sqrt{{x}^{\mathrm{2}} }=\mid{x}\mid\:\:\:\:?\: \\ $$

Question Number 14810 Answers: 0 Comments: 0

7 real numbers are given in the interval (1, 13). Prove that atleast 3 of them are the lengths of a triangle′s sides.

$$\mathrm{7}\:\mathrm{real}\:\mathrm{numbers}\:\mathrm{are}\:\mathrm{given}\:\mathrm{in}\:\mathrm{the}\:\mathrm{interval} \\ $$$$\left(\mathrm{1},\:\mathrm{13}\right).\:\mathrm{Prove}\:\mathrm{that}\:\mathrm{atleast}\:\mathrm{3}\:\mathrm{of}\:\mathrm{them} \\ $$$$\mathrm{are}\:\mathrm{the}\:\mathrm{lengths}\:\mathrm{of}\:\mathrm{a}\:\mathrm{triangle}'\mathrm{s}\:\mathrm{sides}. \\ $$

Question Number 14809 Answers: 1 Comments: 2

Let ABC be an acute triangle. Find the positions of the points M, N, P on the sides BC, CA, AB, respectively, such that the perimeter of the triangle MNP is minimal.

$$\mathrm{Let}\:{ABC}\:\mathrm{be}\:\mathrm{an}\:\mathrm{acute}\:\mathrm{triangle}.\:\mathrm{Find} \\ $$$$\mathrm{the}\:\mathrm{positions}\:\mathrm{of}\:\mathrm{the}\:\mathrm{points}\:{M},\:{N},\:{P}\:\mathrm{on} \\ $$$$\mathrm{the}\:\mathrm{sides}\:{BC},\:{CA},\:{AB},\:\mathrm{respectively}, \\ $$$$\mathrm{such}\:\mathrm{that}\:\mathrm{the}\:\mathrm{perimeter}\:\mathrm{of}\:\mathrm{the}\:\mathrm{triangle} \\ $$$${MNP}\:\mathrm{is}\:\mathrm{minimal}. \\ $$

Question Number 14807 Answers: 0 Comments: 0

Prove that the medians of a given triangle can form a triangle.

$$\mathrm{Prove}\:\mathrm{that}\:\mathrm{the}\:\mathrm{medians}\:\mathrm{of}\:\mathrm{a}\:\mathrm{given} \\ $$$$\mathrm{triangle}\:\mathrm{can}\:\mathrm{form}\:\mathrm{a}\:\mathrm{triangle}. \\ $$

Question Number 14797 Answers: 1 Comments: 12

Question Number 14775 Answers: 1 Comments: 0

Using the remainder theorem to factorize completely the expression x^3 (y − z) + y^3 (z − x) + z^3 (x − y)

$$\mathrm{Using}\:\mathrm{the}\:\mathrm{remainder}\:\mathrm{theorem}\:\mathrm{to}\:\mathrm{factorize}\:\mathrm{completely}\:\mathrm{the}\:\mathrm{expression}\: \\ $$$$\mathrm{x}^{\mathrm{3}} \left(\mathrm{y}\:−\:\mathrm{z}\right)\:+\:\mathrm{y}^{\mathrm{3}} \left(\mathrm{z}\:−\:\mathrm{x}\right)\:+\:\mathrm{z}^{\mathrm{3}} \left(\mathrm{x}\:−\:\mathrm{y}\right)\: \\ $$

Question Number 14752 Answers: 1 Comments: 4

Find ordered pair of (x, y) given x, y ∈ [0, 2π] if 3^(sin x + cos y) = 1 and 5^(sin^2 x + cos^2 y) = 5

$$\mathrm{Find}\:\mathrm{ordered}\:\mathrm{pair}\:\mathrm{of}\:\left({x},\:{y}\right)\:\mathrm{given}\:{x},\:{y}\:\in \\ $$$$\left[\mathrm{0},\:\mathrm{2}\pi\right]\:\mathrm{if}\:\mathrm{3}^{\mathrm{sin}\:{x}\:+\:\mathrm{cos}\:{y}} \:=\:\mathrm{1}\:\mathrm{and} \\ $$$$\mathrm{5}^{\mathrm{sin}^{\mathrm{2}} \:{x}\:+\:\mathrm{cos}^{\mathrm{2}} \:{y}} \:=\:\mathrm{5} \\ $$

Question Number 14749 Answers: 1 Comments: 0

x+3=5

$${x}+\mathrm{3}=\mathrm{5} \\ $$

Question Number 14747 Answers: 1 Comments: 0

ε>0 6−ε≤xy≤6+ε 5−ε≤x+y≤5+ε Find x & y

$$\epsilon>\mathrm{0} \\ $$$$\mathrm{6}−\epsilon\leqslant{xy}\leqslant\mathrm{6}+\epsilon \\ $$$$\mathrm{5}−\epsilon\leqslant{x}+{y}\leqslant\mathrm{5}+\epsilon \\ $$$${Find}\:{x}\:\&\:{y} \\ $$

Question Number 14742 Answers: 0 Comments: 3

x+y=(1/8) (x)^(1/4) +(y)^(1/4) =1 solve system

$$\boldsymbol{{x}}+\boldsymbol{{y}}=\frac{\mathrm{1}}{\mathrm{8}} \\ $$$$\sqrt[{\mathrm{4}}]{\boldsymbol{{x}}}+\sqrt[{\mathrm{4}}]{\boldsymbol{{y}}}=\mathrm{1} \\ $$$$\boldsymbol{{solve}}\:\boldsymbol{{system}} \\ $$

Question Number 14724 Answers: 2 Comments: 1

Question Number 14719 Answers: 0 Comments: 8

Question Number 14715 Answers: 2 Comments: 2

Find the remainder when 55^(99) is divided by 14

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{remainder}\:\mathrm{when}\:\:\:\mathrm{55}^{\mathrm{99}} \:\:\mathrm{is}\:\mathrm{divided}\:\mathrm{by}\:\:\mathrm{14} \\ $$

Question Number 14708 Answers: 1 Comments: 0

Calculate the PH of 0.05 mol/dm^3 phosporic acid

$$\mathrm{Calculate}\:\mathrm{the}\:\mathrm{PH}\:\mathrm{of}\:\:\mathrm{0}.\mathrm{05}\:\mathrm{mol}/\mathrm{dm}^{\mathrm{3}} \:\mathrm{phosporic}\:\mathrm{acid} \\ $$

Question Number 14703 Answers: 0 Comments: 1

Question Number 14702 Answers: 1 Comments: 0

Question Number 14701 Answers: 1 Comments: 2

Question Number 14692 Answers: 1 Comments: 0

Question Number 14688 Answers: 2 Comments: 0

∫ (1/(sin^2 (x) cos^2 (x))) dx

$$\int\:\frac{\mathrm{1}}{\mathrm{sin}^{\mathrm{2}} \left(\mathrm{x}\right)\:\mathrm{cos}^{\mathrm{2}} \left(\mathrm{x}\right)}\:\mathrm{dx} \\ $$

Question Number 14682 Answers: 1 Comments: 0

Question Number 14677 Answers: 1 Comments: 0

A stone of mass 100g is tied to the end of a string of 50 cm long . The stone is whirled as a conical pendulum so that it rotates in horizontal circle radius 30 cm. Determine the angular speed and the tension in the string.

$$\mathrm{A}\:\mathrm{stone}\:\mathrm{of}\:\mathrm{mass}\:\mathrm{100g}\:\mathrm{is}\:\mathrm{tied}\:\mathrm{to}\:\mathrm{the}\:\mathrm{end}\:\mathrm{of}\:\mathrm{a}\:\mathrm{string}\:\mathrm{of}\:\mathrm{50}\:\mathrm{cm}\:\mathrm{long}\:.\:\mathrm{The}\:\mathrm{stone}\:\mathrm{is} \\ $$$$\mathrm{whirled}\:\mathrm{as}\:\mathrm{a}\:\mathrm{conical}\:\mathrm{pendulum}\:\mathrm{so}\:\mathrm{that}\:\mathrm{it}\:\mathrm{rotates}\:\mathrm{in}\:\mathrm{horizontal}\:\mathrm{circle}\:\mathrm{radius} \\ $$$$\mathrm{30}\:\mathrm{cm}.\:\mathrm{Determine}\:\mathrm{the}\:\mathrm{angular}\:\mathrm{speed}\:\mathrm{and}\:\mathrm{the}\:\mathrm{tension}\:\mathrm{in}\:\mathrm{the}\:\mathrm{string}. \\ $$

Question Number 14667 Answers: 1 Comments: 2

Question Number 14668 Answers: 2 Comments: 3

Question Number 14664 Answers: 1 Comments: 0

What is the transformed equation of a parabola given by y=2x^2 +(8/5)x−((109)/(50)) , if the coordinate axes is rotated anticlockwise by 𝛂=tan^(−1) (3/4) .

$$\:{What}\:{is}\:{the}\:{transformed}\: \\ $$$${equation}\:{of}\:{a}\:{parabola}\:{given}\:{by} \\ $$$$\:\:\boldsymbol{{y}}=\mathrm{2}\boldsymbol{{x}}^{\mathrm{2}} +\frac{\mathrm{8}}{\mathrm{5}}\boldsymbol{{x}}−\frac{\mathrm{109}}{\mathrm{50}}\:,\:{if}\:{the} \\ $$$${coordinate}\:{axes}\:{is}\:{rotated}\: \\ $$$$\:{anticlockwise}\:{by}\:\:\boldsymbol{\alpha}=\mathrm{tan}^{−\mathrm{1}} \frac{\mathrm{3}}{\mathrm{4}}\:. \\ $$

Question Number 14661 Answers: 1 Comments: 1

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