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GeometryQuestion and Answers: Page 109

Question Number 8618 Answers: 1 Comments: 1

Question Number 8582 Answers: 1 Comments: 0

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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

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

Question Number 8355 Answers: 2 Comments: 2

if a+b+c=0 then (((a−b)/c)+((b−c)/a)+((c−a)/b))((a/(b−c))+(b/(c−a))+(c/(a−b)))=?

$${if}\:{a}+{b}+{c}=\mathrm{0}\:{then} \\ $$$$ \\ $$$$\left(\frac{{a}−{b}}{{c}}+\frac{{b}−{c}}{{a}}+\frac{{c}−{a}}{{b}}\right)\left(\frac{{a}}{{b}−{c}}+\frac{{b}}{{c}−{a}}+\frac{{c}}{{a}−{b}}\right)=? \\ $$$$ \\ $$$$ \\ $$$$ \\ $$

Question Number 8353 Answers: 1 Comments: 0

(√(240+2(√(14319))))=?

$$\sqrt{\mathrm{240}+\mathrm{2}\sqrt{\mathrm{14319}}}=? \\ $$

Question Number 8351 Answers: 1 Comments: 1

x^2 =816−64(√(77)) x=?[write x like a(√(c ))+b(√d])

$$ \\ $$$$\:\:\:{x}^{\mathrm{2}} =\mathrm{816}−\mathrm{64}\sqrt{\mathrm{77}} \\ $$$$\:\:\:{x}=?\left[{write}\:{x}\:{like}\:{a}\sqrt{{c}\:}+{b}\sqrt{\left.{d}\right]}\right. \\ $$$$ \\ $$

Question Number 8350 Answers: 1 Comments: 0

solve: (5/(3x+2))+(8/(4x+2))=((33)/(9x+8))

$${solve}: \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\frac{\mathrm{5}}{\mathrm{3}{x}+\mathrm{2}}+\frac{\mathrm{8}}{\mathrm{4}{x}+\mathrm{2}}=\frac{\mathrm{33}}{\mathrm{9}{x}+\mathrm{8}} \\ $$

Question Number 8345 Answers: 1 Comments: 0

y=(x+2)^2 −3 Translation T_1 = ((a),(b) ) y′=x^2 a=? b=?

$${y}=\left({x}+\mathrm{2}\right)^{\mathrm{2}} −\mathrm{3} \\ $$$${Translation}\:{T}_{\mathrm{1}} =\begin{pmatrix}{{a}}\\{{b}}\end{pmatrix} \\ $$$${y}'={x}^{\mathrm{2}} \\ $$$${a}=?\:{b}=? \\ $$

Question Number 8325 Answers: 0 Comments: 0

In Δ ABC,∠A=90° , AD⊥BC, DE⊥AC, AF⊥FG,GH⊥FC. (a)How many triangles are there? (b)If AB=((16)/9) , ∠B=60°,find the length of GH.

$${In}\:\Delta\:{ABC},\angle{A}=\mathrm{90}°\:,\:{AD}\bot{BC},\:{DE}\bot{AC}, \\ $$$${AF}\bot{FG},{GH}\bot{FC}. \\ $$$$\left({a}\right){How}\:{many}\:{triangles}\:{are}\:{there}? \\ $$$$\left({b}\right){If}\:{AB}=\frac{\mathrm{16}}{\mathrm{9}}\:,\:\angle{B}=\mathrm{60}°,{find}\:{the}\:{length} \\ $$$$\:\:\:\:\:\:{of}\:{GH}. \\ $$

Question Number 8175 Answers: 0 Comments: 0

Prove (4^n /n)<^(2n) C_n for all n≥4 and n∈Z^+

$$\mathrm{Prove} \\ $$$$\frac{\mathrm{4}^{{n}} }{{n}}<\:^{\mathrm{2}{n}} {C}_{{n}} \:\mathrm{for}\:\mathrm{all}\:{n}\geqslant\mathrm{4}\:\mathrm{and}\:{n}\in\mathbb{Z}^{+} \\ $$

Question Number 8168 Answers: 0 Comments: 3

Find the coefficient of in the expansion of (1+x)(1+x^2 )(1+x^3 )...(1+x^n ).

$${Find}\:{the}\:{coefficient}\:{of}\:{in}\:{the}\:{expansion}\:{of} \\ $$$$\left(\mathrm{1}+{x}\right)\left(\mathrm{1}+{x}^{\mathrm{2}} \right)\left(\mathrm{1}+{x}^{\mathrm{3}} \right)...\left(\mathrm{1}+{x}^{{n}} \right). \\ $$

Question Number 8129 Answers: 0 Comments: 0

An ellipse having focii at (3 3)and (−4 4) and passing through origin has e??

$${An}\:{ellipse}\:{having}\:{focii}\:{at}\:\left(\mathrm{3}\:\mathrm{3}\right){and}\:\left(−\mathrm{4}\:\mathrm{4}\right)\:{and}\:{passing}\:{through}\:{origin}\:{has}\:{e}?? \\ $$

Question Number 8127 Answers: 1 Comments: 3

For ∣x∣<1, we have that (1+x)^(1/2) =1+(1/2)x+((((1/2))((1/2)−1))/(2!))x^2 +(((1/2)((1/2)−1)((1/2)−2))/(3!))x^3 +... (1+x)^(1/2) =1+Σ_(r=1) ^∞ ((Π_(k=0) ^(r−1) (0.5−k))/(r!))x^r . Let g(r)=Π_(k=0) ^(r−1) (0.5−k). Is it true that for x=(1/2)i⇒∣x∣=0.5<1 (1+(1/2)i)^(1/2) =1+Σ_(r=1) ^∞ ((g(r))/(r!))×(1/2^r )i^r ? (i=(√(−1)))

Question Number 8035 Answers: 0 Comments: 2

prove >> a^n +b^n =c^n [n>2] it has no integer roots

$${prove}\:>>\:{a}^{{n}} +{b}^{{n}} ={c}^{{n}} \:\:\left[{n}>\mathrm{2}\right] \\ $$$${it}\:{has}\:{no}\:{integer}\:{roots} \\ $$$$ \\ $$

Question Number 8032 Answers: 1 Comments: 0

find the real root: 99x^3 +297x^2 +594x−7867=0

$${find}\:{the}\:{real}\:{root}: \\ $$$$\mathrm{99}{x}^{\mathrm{3}} +\mathrm{297}{x}^{\mathrm{2}} +\mathrm{594}{x}−\mathrm{7867}=\mathrm{0} \\ $$

Question Number 8031 Answers: 1 Comments: 0

(√2) ≈((19601)/(13860))

$$\:\:\:\:\:\:\:\:\:\:\:\:\:\sqrt{\mathrm{2}}\:\approx\frac{\mathrm{19601}}{\mathrm{13860}} \\ $$

Question Number 8027 Answers: 1 Comments: 1

prove→ any prime number>2 can be written into( x^2 −y^(2 ) ) where (x,y)∈N

$${prove}\rightarrow\:{any}\:{prime}\:{number}>\mathrm{2}\: \\ $$$${can}\:{be}\:{written}\:{into}\left(\:{x}^{\mathrm{2}} −{y}^{\mathrm{2}\:} \right)\:{where} \\ $$$$\left({x},{y}\right)\in{N} \\ $$