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Question Number 102638    Answers: 1   Comments: 6

to Mr W i forgot the formula to find the area of a triangle by using the three height line

$${to}\:{Mr}\:{W} \\ $$$${i}\:{forgot}\:{the}\:{formula}\:{to}\:{find} \\ $$$${the}\:{area}\:{of}\:{a}\:{triangle}\:{by} \\ $$$${using}\:{the}\:{three}\:{height}\:{line} \\ $$

Question Number 102635    Answers: 2   Comments: 0

Question Number 102627    Answers: 3   Comments: 0

show that: cosθ + cos2θ + ....cos nθ= ((cos (1/2)(n +1)θ sin(1/2)nθ)/(sin (1/2)nθ)) Show that: sin θ + sin 2θ + ....+ sin nθ = ((sin (1/2)(n + 1)θ sin(1/2)nθ)/(sin (1/2)nθ)) where θ ∈ R and θ ≠2πk , k ∈Z

$$\mathrm{show}\:\mathrm{that}:\:\mathrm{cos}\theta\:+\:\mathrm{cos2}\theta\:+\:....\mathrm{cos}\:{n}\theta=\:\frac{\mathrm{cos}\:\frac{\mathrm{1}}{\mathrm{2}}\left({n}\:+\mathrm{1}\right)\theta\:\mathrm{sin}\frac{\mathrm{1}}{\mathrm{2}}{n}\theta}{\mathrm{sin}\:\frac{\mathrm{1}}{\mathrm{2}}{n}\theta} \\ $$$$\mathrm{Show}\:\mathrm{that}:\:\mathrm{sin}\:\theta\:+\:\mathrm{sin}\:\mathrm{2}\theta\:+\:....+\:\mathrm{sin}\:{n}\theta\:=\:\frac{\mathrm{sin}\:\frac{\mathrm{1}}{\mathrm{2}}\left({n}\:+\:\mathrm{1}\right)\theta\:\mathrm{sin}\frac{\mathrm{1}}{\mathrm{2}}{n}\theta}{\mathrm{sin}\:\frac{\mathrm{1}}{\mathrm{2}}{n}\theta} \\ $$$$\mathrm{where}\:\theta\:\in\:\mathbb{R}\:\mathrm{and}\:\theta\:\neq\mathrm{2}\pi{k}\:,\:{k}\:\in\mathbb{Z} \\ $$$$ \\ $$

Question Number 102624    Answers: 1   Comments: 4

v2.095 has been uploaded. Changes: Go To: opens in a pop window Drawing: Fix for drawing tool not usable in some countries. Uploaded to playstore.

$$\mathrm{v2}.\mathrm{095}\:\mathrm{has}\:\mathrm{been}\:\mathrm{uploaded}. \\ $$$$\boldsymbol{\mathrm{Changes}}: \\ $$$$\mathrm{Go}\:\mathrm{To}:\:\mathrm{opens}\:\mathrm{in}\:\mathrm{a}\:\mathrm{pop}\:\mathrm{window} \\ $$$$\mathrm{Drawing}:\:\mathrm{Fix}\:\mathrm{for}\:\mathrm{drawing}\:\mathrm{tool}\:\mathrm{not}\:\mathrm{usable} \\ $$$$\mathrm{in}\:\mathrm{some}\:\mathrm{countries}.\: \\ $$$$\mathrm{Uploaded}\:\mathrm{to}\:\mathrm{playstore}. \\ $$

Question Number 102606    Answers: 2   Comments: 1

what is the volume of region bounded by y =x^2 −2x and y=x that is rotated about y=4 ?

$${what}\:{is}\:{the}\:{volume}\:{of}\:{region} \\ $$$${bounded}\:{by}\:{y}\:={x}^{\mathrm{2}} −\mathrm{2}{x}\:{and} \\ $$$${y}={x}\:{that}\:{is}\:{rotated}\:{about} \\ $$$${y}=\mathrm{4}\:? \\ $$

Question Number 102600    Answers: 0   Comments: 0

Question Number 102598    Answers: 2   Comments: 0

Question Number 102588    Answers: 4   Comments: 3

solve 109x +103y = 5 for x,y are integer

$${solve}\:\mathrm{109}{x}\:+\mathrm{103}{y}\:=\:\mathrm{5}\:{for}\:{x},{y}\:{are}\:{integer} \\ $$

Question Number 102581    Answers: 4   Comments: 0

If x+iy = 3+2xi . find y

$${If}\:{x}+{iy}\:=\:\mathrm{3}+\mathrm{2}{xi}\: \\ $$$$.\:{find}\:{y} \\ $$

Question Number 102587    Answers: 2   Comments: 1

Prove that cot7.5°=(√2)+(√3)+(√4)+(√6)

$$\mathrm{Prove}\:\mathrm{that} \\ $$$$\mathrm{cot7}.\mathrm{5}°=\sqrt{\mathrm{2}}+\sqrt{\mathrm{3}}+\sqrt{\mathrm{4}}+\sqrt{\mathrm{6}} \\ $$

Question Number 102576    Answers: 2   Comments: 0

let A_1 A_2 ...A_n a regular polygon of n sides with length l each, let X a point such that A_1 X=x∙l where 0<x<1 (as shown) what is the length of the shortest path begins fromX touching all sides once and ends at X (there′s a problem shape can′t be loaded)

$${let}\:{A}_{\mathrm{1}} {A}_{\mathrm{2}} ...{A}_{{n}} \:\:{a}\:{regular}\:{polygon}\:{of}\:{n}\:{sides} \\ $$$${with}\:{length}\:{l}\:{each},\:{let}\:{X}\:{a}\:{point}\:{such} \\ $$$${that}\:{A}_{\mathrm{1}} {X}={x}\centerdot{l}\:{where}\:\mathrm{0}<{x}<\mathrm{1}\:\left({as}\:{shown}\right) \\ $$$${what}\:{is}\:{the}\:{length}\:{of}\:{the}\:{shortest}\:{path} \\ $$$${begins}\:{fromX}\:{touching}\:{all}\:{sides}\:{once} \\ $$$${and}\:{ends}\:{at}\:{X} \\ $$$$\left({there}'{s}\:{a}\:{problem}\:{shape}\:{can}'{t}\:{be}\:{loaded}\right) \\ $$

Question Number 102572    Answers: 0   Comments: 6

App updates: Version 2.094 has been uploaded to playstore: Enhancements: • paste plain text • Auto wrapping of lines (settings) • New construct as shown below. strike thru underline underbrace font size for selected text page breaks to split images These new constructs are disabled while posting in forum to allow all users time to update app Any issues you can report by email, telegram or as a comment to this post.

$$\mathrm{App}\:\mathrm{updates}:\: \\ $$$$\mathrm{Version}\:\mathrm{2}.\mathrm{094}\:\mathrm{has}\:\mathrm{been}\:\mathrm{uploaded} \\ $$$$\mathrm{to}\:\mathrm{playstore}: \\ $$$$\mathrm{Enhancements}: \\ $$$$\bullet\:\mathrm{paste}\:\mathrm{plain}\:\mathrm{text} \\ $$$$\bullet\:\mathrm{Auto}\:\mathrm{wrapping}\:\mathrm{of}\:\mathrm{lines}\:\left(\mathrm{settings}\right) \\ $$$$\bullet\:\mathrm{New}\:\mathrm{construct}\:\mathrm{as}\:\mathrm{shown}\:\mathrm{below}. \\ $$$$\:\:\:\:\mathrm{strike}\:\mathrm{thru} \\ $$$$\:\:\:\:\mathrm{underline} \\ $$$$\:\:\:\:\mathrm{underbrace} \\ $$$$\:\:\:\:\mathrm{font}\:\mathrm{size}\:\mathrm{for}\:\mathrm{selected}\:\mathrm{text} \\ $$$$\:\:\:\:\mathrm{page}\:\mathrm{breaks}\:\mathrm{to}\:\mathrm{split}\:\mathrm{images} \\ $$$$\:\:\:\:\mathrm{These}\:\mathrm{new}\:\mathrm{constructs}\:\mathrm{are}\:\mathrm{disabled} \\ $$$$\:\:\:\:\mathrm{while}\:\mathrm{posting}\:\mathrm{in}\:\mathrm{forum}\:\mathrm{to}\:\mathrm{allow}\:\mathrm{all} \\ $$$$\:\:\:\:\mathrm{users}\:\mathrm{time}\:\mathrm{to}\:\mathrm{update}\:\mathrm{app} \\ $$$$\mathrm{Any}\:\mathrm{issues}\:\mathrm{you}\:\mathrm{can}\:\mathrm{report}\:\mathrm{by}\:\mathrm{email}, \\ $$$$\mathrm{telegram}\:\mathrm{or}\:\mathrm{as}\:\mathrm{a}\:\mathrm{comment}\:\mathrm{to}\:\mathrm{this} \\ $$$$\mathrm{post}. \\ $$

Question Number 102553    Answers: 1   Comments: 3

Question Number 102551    Answers: 0   Comments: 0

Question Number 102549    Answers: 0   Comments: 0

let A=[1,46] show that for any p∈A we have q∈Z such as p×q≡1[47] please i need your help

$$ \\ $$$$\boldsymbol{{let}}\:\boldsymbol{{A}}=\left[\mathrm{1},\mathrm{46}\right]\: \\ $$$$\boldsymbol{{show}}\:\boldsymbol{{that}}\:\boldsymbol{{for}}\:\boldsymbol{{any}}\:\boldsymbol{{p}}\in\boldsymbol{{A}}\:{we}\:\boldsymbol{{have}}\:\boldsymbol{{q}}\in\mathbb{Z} \\ $$$$\boldsymbol{{such}}\:\boldsymbol{{as}}\:\boldsymbol{{p}}×\boldsymbol{{q}}\equiv\mathrm{1}\left[\mathrm{47}\right] \\ $$$$\boldsymbol{{pleas}}{e}\:{i}\:\boldsymbol{{need}}\:\boldsymbol{{your}}\:\boldsymbol{{help}} \\ $$$$ \\ $$$$ \\ $$$$ \\ $$

Question Number 102548    Answers: 0   Comments: 0

if n is a real number,find the least possible number of n,if n^2 −3n+(√(n−3)) −(√(n+3))

$${if}\:{n}\:{is}\:{a}\:{real}\:{number},{find}\:{the}\:{least}\:{possible}\:{number}\:{of}\:{n},{if} \\ $$$${n}^{\mathrm{2}} −\mathrm{3}{n}+\sqrt{{n}−\mathrm{3}}\:−\sqrt{{n}+\mathrm{3}} \\ $$

Question Number 102545    Answers: 1   Comments: 0

Question Number 102544    Answers: 2   Comments: 0

Question Number 102539    Answers: 3   Comments: 2

2+3.3+4.3^2 +5.3^2 +.....up to n terms

$$\mathrm{2}+\mathrm{3}.\mathrm{3}+\mathrm{4}.\mathrm{3}^{\mathrm{2}} +\mathrm{5}.\mathrm{3}^{\mathrm{2}} +.....{up}\:{to}\:{n}\:{terms} \\ $$

Question Number 102530    Answers: 0   Comments: 1

Question Number 102527    Answers: 3   Comments: 0

2y′′−y′+y = cos 3x

$$\mathrm{2}{y}''−{y}'+{y}\:=\:\mathrm{cos}\:\mathrm{3}{x}\: \\ $$

Question Number 102524    Answers: 1   Comments: 1

Question Number 102517    Answers: 0   Comments: 1

(1+x^2 )dy + (1+y^2 )dx = 0

$$\left(\mathrm{1}+{x}^{\mathrm{2}} \right){dy}\:+\:\left(\mathrm{1}+{y}^{\mathrm{2}} \right){dx}\:=\:\mathrm{0} \\ $$

Question Number 102515    Answers: 2   Comments: 0

((x/y))y′= ((2y^2 +1)/(x+1))

$$\left(\frac{{x}}{{y}}\right){y}'=\:\frac{\mathrm{2}{y}^{\mathrm{2}} +\mathrm{1}}{{x}+\mathrm{1}} \\ $$

Question Number 102510    Answers: 2   Comments: 0

lim_(△x→0) ((sin^2 ((1/3)x+(1/3)△x)−sin^2 (1/3)x)/(△x))=?

$${li}\underset{\bigtriangleup{x}\rightarrow\mathrm{0}} {{m}}\frac{{sin}^{\mathrm{2}} \left(\frac{\mathrm{1}}{\mathrm{3}}{x}+\frac{\mathrm{1}}{\mathrm{3}}\bigtriangleup{x}\right)−{sin}^{\mathrm{2}} \frac{\mathrm{1}}{\mathrm{3}}{x}}{\bigtriangleup{x}}=? \\ $$

Question Number 102508    Answers: 0   Comments: 5

lim_(△x→0) ((e^(sin(x−△x)) −e^(sinx) )/(△x))=?

$${li}\underset{\bigtriangleup{x}\rightarrow\mathrm{0}} {{m}}\frac{{e}^{{sin}\left({x}−\bigtriangleup{x}\right)} −{e}^{{sinx}} }{\bigtriangleup{x}}=? \\ $$

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