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Question Number 68941    Answers: 3   Comments: 3

Question Number 68930    Answers: 0   Comments: 3

In the figure we have 7 circles having the same radius. Determine the ratio between the perimeter of one of the circle and the perimeter of the gray region.

$$\mathrm{In}\:\mathrm{the}\:\mathrm{figure}\:\mathrm{we}\:\mathrm{have}\:\mathrm{7}\:\mathrm{circles}\:\mathrm{having} \\ $$$$\mathrm{the}\:\mathrm{same}\:\mathrm{radius}.\:\mathrm{Determine}\:\mathrm{the}\:\mathrm{ratio} \\ $$$$\mathrm{between}\:\mathrm{the}\:\mathrm{perimeter}\:\mathrm{of}\:\mathrm{one}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{circle}\:\mathrm{and}\:\mathrm{the}\:\mathrm{perimeter}\:\mathrm{of}\:\mathrm{the}\:\mathrm{gray}\:\mathrm{region}. \\ $$

Question Number 68831    Answers: 1   Comments: 3

The square ABCD has side equal to 1 and the distance AP is (1/8). Calculate the side of the equilateral triangle PMN inscribed in the square.

$$\mathrm{The}\:\mathrm{square}\:{ABCD}\:\mathrm{has}\:\mathrm{side}\:\mathrm{equal}\:\mathrm{to}\:\mathrm{1} \\ $$$$\mathrm{and}\:\mathrm{the}\:\mathrm{distance}\:{AP}\:\:\mathrm{is}\:\:\frac{\mathrm{1}}{\mathrm{8}}. \\ $$$$\mathrm{Calculate}\:\mathrm{the}\:\mathrm{side}\:\mathrm{of}\:\mathrm{the}\:\mathrm{equilateral} \\ $$$$\mathrm{triangle}\:{PMN}\:\mathrm{inscribed}\:\mathrm{in}\:\mathrm{the}\:\mathrm{square}. \\ $$

Question Number 68664    Answers: 1   Comments: 0

In a equilateral triangle ABC whose side is a, the points M and N are taken on the side BC, such that the triangles ABM, AMN and ANC have the same perimeter. Calculate the distances from vertex A to points M and N. (solve in detail.)

$$\mathrm{In}\:\mathrm{a}\:\mathrm{equilateral}\:\mathrm{triangle}\:{ABC}\:\mathrm{whose} \\ $$$$\mathrm{side}\:\mathrm{is}\:\boldsymbol{{a}},\:\mathrm{the}\:\mathrm{points}\:{M}\:\mathrm{and}\:{N}\:\mathrm{are}\:\mathrm{taken} \\ $$$$\mathrm{on}\:\mathrm{the}\:\mathrm{side}\:{BC},\:\mathrm{such}\:\mathrm{that}\:\mathrm{the}\:\mathrm{triangles} \\ $$$${ABM},\:{AMN}\:\mathrm{and}\:{ANC}\:\mathrm{have}\:\mathrm{the}\:\mathrm{same}\: \\ $$$$\mathrm{perimeter}.\:\mathrm{Calculate}\:\mathrm{the}\:\mathrm{distances}\:\mathrm{from} \\ $$$$\mathrm{vertex}\:{A}\:\mathrm{to}\:\mathrm{points}\:{M}\:\mathrm{and}\:{N}. \\ $$$$\left(\boldsymbol{\mathrm{solve}}\:\boldsymbol{\mathrm{in}}\:\boldsymbol{\mathrm{detail}}.\right) \\ $$

Question Number 68666    Answers: 1   Comments: 2

Question Number 68629    Answers: 1   Comments: 0

Question Number 68611    Answers: 1   Comments: 0

Question Number 68601    Answers: 0   Comments: 4

ABCD is a side square 1. B, F and E are collinear. FDE is a right triangle with hypotenuse 1 and the DE cathetus is worth x. What is the value of x? (Solve with algebra)

$${ABCD}\:\mathrm{is}\:\mathrm{a}\:\mathrm{side}\:\mathrm{square}\:\mathrm{1}.\: \\ $$$${B},\:{F}\:\mathrm{and}\:{E}\:\mathrm{are}\:\mathrm{collinear}. \\ $$$${FDE}\:\mathrm{is}\:\mathrm{a}\:\mathrm{right}\:\mathrm{triangle}\:\mathrm{with}\:\mathrm{hypotenuse}\:\mathrm{1} \\ $$$$\mathrm{and}\:\mathrm{the}\:{DE}\:\mathrm{cathetus}\:\mathrm{is}\:\mathrm{worth}\:\boldsymbol{{x}}.\: \\ $$$$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\boldsymbol{{x}}? \\ $$$$\left(\mathrm{Solve}\:\mathrm{with}\:\mathrm{algebra}\right) \\ $$

Question Number 68503    Answers: 0   Comments: 8

Question Number 68524    Answers: 1   Comments: 0

Question Number 68493    Answers: 1   Comments: 0

My question is about the analogical axiams of the foundation geometry in mathematocs. As it Is a well knowen axum in geometry starts from the sefinition of a point which gives gives the path analogically to line, plane, and solids. Know my truoble comes at these axiumes areise from not ne being they are aziyma ^ but the analogu effect at giving the definatiom of the solid} 1−Apoimt is a dimenstin less. mathematixal abstruct. 2− a line is the collextom of points which has only one dimension. 3− a plane is the collection of lines which have onlu?two dimensions 3−a solid is the collwxripm of plans which has three dimensions. Now the first three definationa arsties are mathe are mathematical ideasor abstruct while the last mathematical abstruct is real. ow on earth a real object is formed from the collextion of unreal planes

$${My}\:{question}\:{is}\:{about}\:{the}\:{analogical} \\ $$$${axiams}\:{of}\:{the}\:{foundation}\:{geometry}\:{in} \\ $$$${mathematocs}. \\ $$$${As}\:{it}\:{Is}\:\:{a}\:{well}\:{knowen}\:{axum}\:{in}\:\:{geometry} \\ $$$${starts}\:{from}\:{the}\:{sefinition}\:{of}\:{a}\:{point}\:{which}\:{gives} \\ $$$${gives}\:{the}\:{path}\:{analogically}\:\:{to}\:{line},\:{plane},\:{and}\: \\ $$$${solids}. \\ $$$${Know}\:{my}\:{truoble}\:\:{comes}\:{at}\:{these} \\ $$$${axiumes}\:{areise}\:{from}\:{not}\:{ne}\:{being}\:{they} \\ $$$${are}\:{aziyma}\bar {\:}{but}\:{the}\:{analogu}\:{effect}\:{at} \\ $$$$\left.{giving}\:{the}\:{definatiom}\:{of}\:{the}\:{solid}\right\} \\ $$$$\mathrm{1}−{Apoimt}\:{is}\:{a}\:{dimenstin}\:{less}. \\ $$$$\:{mathematixal}\:{abstruct}. \\ $$$$\mathrm{2}−\:{a}\:{line}\:{is}\:{the}\:{collextom}\:{of}\:{points} \\ $$$$\:\:{which}\:{has}\:{only}\:{one}\:{dimension}. \\ $$$$\mathrm{3}−\:{a}\:{plane}\:{is}\:{the}\:{collection}\:\:{of}\:{lines}\: \\ $$$${which}\:{have}\:{onlu}?{two}\:{dimensions}\: \\ $$$$\mathrm{3}−{a}\:\:{solid}\:{is}\:{the}\:{collwxripm}\:{of}\:{plans} \\ $$$${which}\:{has}\:{three}\:{dimensions}. \\ $$$$ \\ $$$$\:\:\:\:\:\:{Now}\:{the}\:{first}\:{three}\:{definationa}\:{arsties}\:{are}\:{mathe} \\ $$$${are}\:{mathematical}\:{ideasor}\:{abstruct} \\ $$$${while}\:{the}\:{last}\:{mathematical}\:{abstruct}\:{is}\:{real}. \\ $$$${ow}\:{on}\:{earth}\:{a}\:{real}\:{object}\:{is}\:{formed} \\ $$$${from}\:{the}\:{collextion}\:{of}\:{unreal}\:{planes} \\ $$

Question Number 68425    Answers: 1   Comments: 2

Question Number 68309    Answers: 1   Comments: 3

Question Number 68305    Answers: 1   Comments: 3

Question Number 68303    Answers: 0   Comments: 0

Question Number 68289    Answers: 1   Comments: 0

A circle is divided into two equal parts By An arc with center on the circle. Determine (a) The length of the arc (b)The ratio in which the arc divides the diameter meeting the center of the arc.

$$\mathrm{A}\:\mathrm{circle}\:\mathrm{is}\:\mathrm{divided}\:\mathrm{into}\:\mathrm{two}\:\mathrm{equal}\:\mathrm{parts} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{By} \\ $$$$\:\mathrm{An}\:\mathrm{arc}\:\mathrm{with}\:\mathrm{center}\:\mathrm{on}\:\mathrm{the}\:\mathrm{circle}. \\ $$$$\mathcal{D}{etermine} \\ $$$$\:\:\left({a}\right)\:{The}\:{length}\:{of}\:{the}\:{arc} \\ $$$$\:\:\left({b}\right){The}\:{ratio}\:{in}\:{which}\:{the}\:{arc} \\ $$$$\:\:\:\:\:\:\:\:{divides}\:{the}\:{diameter}\: \\ $$$$\:\:\:\:\:\:\:\:{meeting}\:{the}\:{center}\:{of}\:{the}\:{arc}. \\ $$

Question Number 68183    Answers: 0   Comments: 1

Question Number 68150    Answers: 0   Comments: 0

Question Number 68132    Answers: 0   Comments: 3

Question Number 68110    Answers: 0   Comments: 2

Question Number 68092    Answers: 0   Comments: 4

Question Number 68041    Answers: 0   Comments: 1

Question Number 67977    Answers: 1   Comments: 1

Question Number 67973    Answers: 0   Comments: 5

Question Number 67969    Answers: 0   Comments: 0

Two triangles △_1 and △_2 are given,such that length of sides of triangle 1,are equail to length of medians of triangle 2. 1.find the ratio of areas of triangles. 2.given that small side of △_1 , be equail to:(√2) and one angle be:90^• . find at least one angle of △_2 . 3.solve part#2,if replace: △_2 with: △_1 . 4.solve part#2,if great side of:△_1 ,be equail to :(√2).

$$\boldsymbol{\mathrm{Two}}\:\boldsymbol{\mathrm{triangles}}\:\bigtriangleup_{\mathrm{1}} \:\boldsymbol{\mathrm{and}}\:\bigtriangleup_{\mathrm{2}} \:\boldsymbol{\mathrm{are}}\:\boldsymbol{\mathrm{given}},\boldsymbol{\mathrm{such}}\: \\ $$$$\boldsymbol{\mathrm{that}}\:\boldsymbol{\mathrm{length}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{sides}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{triangle}}\:\mathrm{1},\boldsymbol{\mathrm{are}}\: \\ $$$$\boldsymbol{\mathrm{equail}}\:\boldsymbol{\mathrm{to}}\:\boldsymbol{\mathrm{length}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{medians}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{triangle}}\:\mathrm{2}. \\ $$$$\mathrm{1}.\boldsymbol{\mathrm{find}}\:\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{ratio}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{areas}}\:\boldsymbol{\mathrm{of}}\:\:\boldsymbol{\mathrm{triangles}}. \\ $$$$\mathrm{2}.\boldsymbol{\mathrm{given}}\:\boldsymbol{\mathrm{that}}\:\boldsymbol{\mathrm{small}}\:\boldsymbol{\mathrm{side}}\:\boldsymbol{\mathrm{of}}\:\bigtriangleup_{\mathrm{1}} ,\:\boldsymbol{\mathrm{be}}\:\boldsymbol{\mathrm{equail}}\:\boldsymbol{\mathrm{to}}:\sqrt{\mathrm{2}} \\ $$$$\boldsymbol{\mathrm{and}}\:\boldsymbol{\mathrm{one}}\:\boldsymbol{\mathrm{angle}}\:\boldsymbol{\mathrm{be}}:\mathrm{90}^{\bullet} . \\ $$$$\boldsymbol{\mathrm{find}}\:\boldsymbol{\mathrm{at}}\:\boldsymbol{\mathrm{least}}\:\boldsymbol{\mathrm{one}}\:\boldsymbol{\mathrm{angle}}\:\boldsymbol{\mathrm{of}}\:\bigtriangleup_{\mathrm{2}} . \\ $$$$\mathrm{3}.\boldsymbol{\mathrm{solve}}\:\boldsymbol{\mathrm{part}}#\mathrm{2},\boldsymbol{\mathrm{if}}\:\boldsymbol{\mathrm{replace}}:\:\bigtriangleup_{\mathrm{2}} \boldsymbol{\mathrm{with}}:\:\bigtriangleup_{\mathrm{1}} . \\ $$$$\mathrm{4}.\boldsymbol{\mathrm{solve}}\:\boldsymbol{\mathrm{part}}#\mathrm{2},\boldsymbol{\mathrm{if}}\:\boldsymbol{\mathrm{great}}\:\boldsymbol{\mathrm{side}}\:\boldsymbol{\mathrm{of}}:\bigtriangleup_{\mathrm{1}} ,\boldsymbol{\mathrm{be}}\:\boldsymbol{\mathrm{equail}}\: \\ $$$$\boldsymbol{\mathrm{to}}\::\sqrt{\mathrm{2}}. \\ $$

Question Number 67948    Answers: 0   Comments: 0

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