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GeometryQuestion and Answers: Page 115

Question Number 9661 Answers: 0 Comments: 3

a) 2^i = b) (a_1 + b_1 i)^(a_2 + b_2 i) = Powers of complex numbers ???

$$\left.{a}\right)\:\mathrm{2}^{{i}} \:=\: \\ $$$$ \\ $$$$\left.{b}\right)\:\left({a}_{\mathrm{1}} \:+\:{b}_{\mathrm{1}} {i}\right)^{{a}_{\mathrm{2}} \:+\:{b}_{\mathrm{2}} {i}} \:=\: \\ $$$${Powers}\:{of}\:{complex}\:{numbers}\:??? \\ $$

Question Number 9627 Answers: 1 Comments: 2

Question Number 9603 Answers: 2 Comments: 0

A regular hexagon has sides of lenght 8 cm. Find the perpendicular distance between two opposite faces.

$$\mathrm{A}\:\mathrm{regular}\:\mathrm{hexagon}\:\mathrm{has}\:\mathrm{sides}\:\mathrm{of}\:\mathrm{lenght}\:\mathrm{8}\:\mathrm{cm}. \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{perpendicular}\:\mathrm{distance}\:\mathrm{between}\:\mathrm{two} \\ $$$$\mathrm{opposite}\:\mathrm{faces}. \\ $$

Question Number 9523 Answers: 1 Comments: 0

3a = (b + c + d)^(2014) 3b = (a + c + d)^(2014) 3c = (a + b + d)^(2014) 3d = (a + b + c)^(2014) Find all the solution of (a, b, c, d) if a, b, c, d ∈ R

$$\mathrm{3}{a}\:=\:\left({b}\:+\:{c}\:+\:{d}\right)^{\mathrm{2014}} \\ $$$$\mathrm{3}{b}\:=\:\left({a}\:+\:{c}\:+\:{d}\right)^{\mathrm{2014}} \\ $$$$\mathrm{3}{c}\:=\:\left({a}\:+\:{b}\:+\:{d}\right)^{\mathrm{2014}} \\ $$$$\mathrm{3}{d}\:=\:\left({a}\:+\:{b}\:+\:{c}\right)^{\mathrm{2014}} \\ $$$$\mathrm{Find}\:\mathrm{all}\:\mathrm{the}\:\mathrm{solution}\:\mathrm{of}\:\left({a},\:{b},\:{c},\:{d}\right)\:\mathrm{if}\:{a},\:{b},\:{c},\:{d}\:\in\:\mathbb{R} \\ $$

Question Number 9453 Answers: 1 Comments: 0

find dc′s dr′s of a mormal to the plane 2x+(5/2)y+(7/8)z=23

$$\mathrm{find}\:\mathrm{dc}'\mathrm{s}\:\mathrm{dr}'\mathrm{s}\:\mathrm{of}\:\mathrm{a}\:\mathrm{mormal}\:\mathrm{to}\:\mathrm{the}\: \\ $$$$\mathrm{plane}\:\mathrm{2x}+\frac{\mathrm{5}}{\mathrm{2}}\mathrm{y}+\frac{\mathrm{7}}{\mathrm{8}}\mathrm{z}=\mathrm{23} \\ $$

Question Number 9438 Answers: 1 Comments: 0

Solve for x, y and z 2xy = x + y ...... (i) 6xz = 6z − 2x ....... (ii) 3yz = 3y + 4z ......... (iii) That is the correct question sir.

$$\mathrm{Solve}\:\mathrm{for}\:\mathrm{x},\:\mathrm{y}\:\mathrm{and}\:\mathrm{z} \\ $$$$\mathrm{2xy}\:=\:\mathrm{x}\:+\:\mathrm{y}\:\:\:\:\:\:......\:\left(\mathrm{i}\right) \\ $$$$\mathrm{6xz}\:=\:\mathrm{6z}\:−\:\mathrm{2x}\:\:\:\:.......\:\left(\mathrm{ii}\right) \\ $$$$\mathrm{3yz}\:=\:\mathrm{3y}\:+\:\mathrm{4z}\:\:\:\:.........\:\left(\mathrm{iii}\right) \\ $$$$ \\ $$$$\mathrm{That}\:\mathrm{is}\:\mathrm{the}\:\mathrm{correct}\:\mathrm{question}\:\mathrm{sir}. \\ $$

Question Number 9436 Answers: 2 Comments: 0

If they said that Σ_(k=1) ^∞ k diverges, why 1 + 2 + 3 + 4 + ... = − (1/(12)) ?

$$\mathrm{If}\:\mathrm{they}\:\mathrm{said}\:\mathrm{that}\:\underset{{k}=\mathrm{1}} {\overset{\infty} {\sum}}\:{k}\:\mathrm{diverges},\:\mathrm{why} \\ $$$$\mathrm{1}\:+\:\mathrm{2}\:+\:\mathrm{3}\:+\:\mathrm{4}\:+\:...\:=\:−\:\frac{\mathrm{1}}{\mathrm{12}}\:? \\ $$

Question Number 9348 Answers: 0 Comments: 0

pH = pK_a + lg(C_b /C_a )

$$\mathrm{pH}\:=\:\mathrm{pK}_{\mathrm{a}} \:+\:\mathrm{lg}\frac{\mathrm{C}_{\mathrm{b}} }{\mathrm{C}_{\mathrm{a}} } \\ $$

Question Number 9347 Answers: 0 Comments: 0

pH = (1/2) (14 − pK_b + pK_a )

$$\mathrm{pH}\:=\:\frac{\mathrm{1}}{\mathrm{2}}\:\left(\mathrm{14}\:−\:\mathrm{pK}_{\mathrm{b}} \:+\:\mathrm{pK}_{\mathrm{a}} \:\right) \\ $$

Question Number 9346 Answers: 0 Comments: 0

pH = 14 − (1/2) ( pK_b − lgC_b )

$$\mathrm{pH}\:=\:\mathrm{14}\:−\:\frac{\mathrm{1}}{\mathrm{2}}\:\left(\:\mathrm{pK}_{\mathrm{b}} \:\:−\:\:\mathrm{lgC}_{\mathrm{b}} \:\right) \\ $$

Question Number 9233 Answers: 1 Comments: 0

The gamma function Γ(s) = ∫_0 ^∞ e^(−x) x^(s−1) dx How to calculate the gamma function in an easy and not time-consuming way?

$$\mathrm{The}\:\mathrm{gamma}\:\mathrm{function}\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\Gamma\left({s}\right)\:=\:\int_{\mathrm{0}} ^{\infty} {e}^{−{x}} {x}^{{s}−\mathrm{1}} \:{dx} \\ $$$$\mathrm{How}\:\mathrm{to}\:\mathrm{calculate}\:\mathrm{the}\:\mathrm{gamma}\:\mathrm{function} \\ $$$$\mathrm{in}\:\mathrm{an}\:\mathrm{easy}\:\mathrm{and}\:\mathrm{not}\:\mathrm{time}-\mathrm{consuming}\: \\ $$$$\mathrm{way}? \\ $$$$ \\ $$

Question Number 9144 Answers: 1 Comments: 0

Let f(x)=x^(2013) +2 (a).Find the remainder when f(x) is divided by x+1.(done) (b). Show that when 7^(2013) +2 is divided by 8, the remainder is 1. (please help!)

$${Let}\:{f}\left({x}\right)={x}^{\mathrm{2013}} +\mathrm{2} \\ $$$$\left({a}\right).{Find}\:{the}\:{remainder}\:{when}\:{f}\left({x}\right)\:{is}\:{divided}\:{by}\:{x}+\mathrm{1}.\left({done}\right) \\ $$$$\left({b}\right).\:{Show}\:{that}\:{when}\:\mathrm{7}^{\mathrm{2013}} +\mathrm{2}\:{is}\:{divided}\:{by}\:\mathrm{8},\:{the}\:{remainder} \\ $$$$\:\:\:\:\:\:\:\:\:\:{is}\:\mathrm{1}.\:\:\:\:\left({please}\:{help}!\right) \\ $$$$ \\ $$

Question Number 9125 Answers: 1 Comments: 0

A polygon has two interior angles of 120° each and the others are each 150°. calculate (a) The number of sides of the polygon . (b) The sum of the interior angles.

$$\mathrm{A}\:\mathrm{polygon}\:\mathrm{has}\:\mathrm{two}\:\mathrm{interior}\:\mathrm{angles}\:\mathrm{of}\:\mathrm{120}°\:\mathrm{each} \\ $$$$\mathrm{and}\:\mathrm{the}\:\mathrm{others}\:\mathrm{are}\:\mathrm{each}\:\mathrm{150}°.\:\mathrm{calculate} \\ $$$$\left(\mathrm{a}\right)\:\mathrm{The}\:\mathrm{number}\:\mathrm{of}\:\mathrm{sides}\:\mathrm{of}\:\mathrm{the}\:\mathrm{polygon}\:. \\ $$$$\left(\mathrm{b}\right)\:\mathrm{The}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{interior}\:\mathrm{angles}. \\ $$

Question Number 8933 Answers: 1 Comments: 0

3x+3y+2z=1,x+2y=4,10y+3z=−2, 2x−3y−z=5

$$\mathrm{3x}+\mathrm{3y}+\mathrm{2z}=\mathrm{1},\mathrm{x}+\mathrm{2y}=\mathrm{4},\mathrm{10y}+\mathrm{3z}=−\mathrm{2}, \\ $$$$\mathrm{2x}−\mathrm{3y}−\mathrm{z}=\mathrm{5} \\ $$

Question Number 8917 Answers: 0 Comments: 0

Proposed by Rasheed Soomro. What will be possible minimum area of a quadrilateral, whose all the sides touch a circle of radius r ?

$$\mathrm{Proposed}\:\mathrm{by}\:\mathrm{Rasheed}\:\mathrm{Soomro}. \\ $$$$\mathrm{What}\:\mathrm{will}\:\mathrm{be}\:\mathrm{possible}\:\mathrm{minimum}\:\mathrm{area} \\ $$$$\mathrm{of}\:\mathrm{a}\:\mathrm{quadrilateral},\:\mathrm{whose}\:\mathrm{all}\:\mathrm{the}\:\mathrm{sides} \\ $$$$\mathrm{touch}\:\mathrm{a}\:\mathrm{circle}\:\mathrm{of}\:\mathrm{radius}\:\:\mathrm{r}\:? \\ $$

Question Number 8685 Answers: 0 Comments: 0

Divide a circle in two equal parts by drawing an arc.

$$\mathrm{Divide}\:\mathrm{a}\:\mathrm{circle}\:\mathrm{in}\:\mathrm{two}\:\mathrm{equal}\:\mathrm{parts} \\ $$$$\mathrm{by}\:\mathrm{drawing}\:\mathrm{an}\:\mathrm{arc}. \\ $$

Question Number 8618 Answers: 1 Comments: 1

Question Number 8582 Answers: 1 Comments: 0

9×9

$$\mathrm{9}×\mathrm{9} \\ $$

Question Number 8528 Answers: 2 Comments: 0

A(2,b) translation T_1 = (((−3)),(( b)) ) followed by translation T_2 = ((a),(4) ) A′=(b−1,a−3) determine the value of a+b=...?

$${A}\left(\mathrm{2},{b}\right)\:{translation}\:{T}_{\mathrm{1}} =\begin{pmatrix}{−\mathrm{3}}\\{\:\:\:{b}}\end{pmatrix} \\ $$$${followed}\:{by}\:{translation}\:{T}_{\mathrm{2}} =\begin{pmatrix}{{a}}\\{\mathrm{4}}\end{pmatrix} \\ $$$${A}'=\left({b}−\mathrm{1},{a}−\mathrm{3}\right) \\ $$$${determine}\:{the}\:{value}\:{of}\:{a}+{b}=...? \\ $$

Question Number 8471 Answers: 1 Comments: 2

∫_(−∞) ^∞ e^(−2∣x∣dx_ ) ?

$$\underset{−\infty} {\overset{\infty} {\int}}{e}^{−\mathrm{2}\mid{x}\mid{d}\underset{} {{x}}} \:\:\:\:\:\:?\:\: \\ $$

Question Number 8427 Answers: 1 Comments: 0

In a circle PQRST center O, PQRS is a cyclic quadrilateral and T is on the circle. QS is a diameter and angle QOR is 86° if PTQ is 28° . Find the angles of the quadrilateral PQRS.

$$\mathrm{In}\:\mathrm{a}\:\mathrm{circle}\:\mathrm{PQRST}\:\mathrm{center}\:\mathrm{O},\:\mathrm{PQRS}\:\mathrm{is}\:\mathrm{a}\: \\ $$$$\mathrm{cyclic}\:\mathrm{quadrilateral}\:\mathrm{and}\:\mathrm{T}\:\mathrm{is}\:\mathrm{on}\:\mathrm{the}\:\mathrm{circle}. \\ $$$$\mathrm{QS}\:\mathrm{is}\:\mathrm{a}\:\mathrm{diameter}\:\mathrm{and}\:\mathrm{angle}\:\mathrm{QOR}\:\mathrm{is}\:\mathrm{86}° \\ $$$$\mathrm{if}\:\mathrm{PTQ}\:\mathrm{is}\:\mathrm{28}°\:.\:\mathrm{Find}\:\mathrm{the}\:\mathrm{angles}\:\mathrm{of}\:\mathrm{the}\: \\ $$$$\mathrm{quadrilateral}\:\mathrm{PQRS}. \\ $$

Question Number 8389 Answers: 1 Comments: 0

Question Number 8362 Answers: 1 Comments: 0

(√(2(√(2(√(2(√(2(√(2(√(2.....))))))))))))=?

$$ \\ $$$$ \\ $$$$\sqrt{\mathrm{2}\sqrt{\mathrm{2}\sqrt{\mathrm{2}\sqrt{\mathrm{2}\sqrt{\mathrm{2}\sqrt{\mathrm{2}.....}}}}}}=? \\ $$$$ \\ $$$$ \\ $$

Question Number 8359 Answers: 1 Comments: 1

prove that 10 divides 11^(10) −1

$${prove}\:{that}\: \\ $$$$\mathrm{10}\:{divides}\:\mathrm{11}^{\mathrm{10}} −\mathrm{1} \\ $$

Question Number 8357 Answers: 0 Comments: 1

who is bigger ? 1000^(1000) or 101^(999 ) please answer in details.

$${who}\:{is}\:{bigger}\:? \\ $$$$\mathrm{1000}^{\mathrm{1000}} \:{or}\:\mathrm{101}^{\mathrm{999}\:} \\ $$$${please}\:{answer}\:{in}\:{details}. \\ $$$$ \\ $$

Question Number 8356 Answers: 0 Comments: 0

find factor: a^(10) +a^5 +1

$${find}\:{factor}: \\ $$$${a}^{\mathrm{10}} +{a}^{\mathrm{5}} +\mathrm{1} \\ $$

Pg 110 Pg 111 Pg 112 Pg 113 Pg 114 Pg 115 Pg 116 Pg 117 Pg 118 Pg 119

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