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Question Number 13501 Answers: 1 Comments: 0

Find x 10_C_x = 5_C_2

$$\mathrm{Find}\:\mathrm{x} \\ $$$$\mathrm{10}_{\mathrm{C}_{\mathrm{x}} } \:=\:\mathrm{5}_{\mathrm{C}_{\mathrm{2}} } \\ $$

Question Number 13548 Answers: 1 Comments: 11

Question Number 13447 Answers: 0 Comments: 0

Question Number 13434 Answers: 1 Comments: 1

ΔABC∼ΔDEF ΔABC=25 ΔDEF=35 ((ΣMadian^2 of ΔABC)/(ΣMadian^2 of ΔDEF))=?

$$\Delta{ABC}\sim\Delta{DEF}\: \\ $$$$\Delta{ABC}=\mathrm{25} \\ $$$$\Delta{DEF}=\mathrm{35} \\ $$$$\frac{\Sigma{Madian}^{\mathrm{2}} {of}\:\Delta{ABC}}{\Sigma{Madian}^{\mathrm{2}} \:{of}\:\Delta{DEF}}=? \\ $$

Question Number 13305 Answers: 1 Comments: 0

Does sin A=sin B imply sin (A/2)=sin(B/2)? For example A=π and B=−π?

$$\mathrm{Does} \\ $$$$\mathrm{sin}\:\mathrm{A}=\mathrm{sin}\:\mathrm{B} \\ $$$$\mathrm{imply}\:\mathrm{sin}\:\frac{\mathrm{A}}{\mathrm{2}}=\mathrm{sin}\frac{\mathrm{B}}{\mathrm{2}}? \\ $$$$\mathrm{For}\:\mathrm{example}\:\mathrm{A}=\pi\:\mathrm{and}\:\mathrm{B}=−\pi? \\ $$

Question Number 13888 Answers: 1 Comments: 3

Prove that if A′, B′ and C′ are the midpoints of the sides BC, CA and AB, respectively, then AA′ + BB′ + CC′ < AB + BC + CA

$$\mathrm{Prove}\:\mathrm{that}\:\mathrm{if}\:{A}',\:{B}'\:\mathrm{and}\:{C}'\:\mathrm{are}\:\mathrm{the} \\ $$$$\mathrm{midpoints}\:\mathrm{of}\:\mathrm{the}\:\mathrm{sides}\:{BC},\:{CA}\:\mathrm{and}\:{AB}, \\ $$$$\mathrm{respectively},\:\mathrm{then} \\ $$$${AA}'\:+\:{BB}'\:+\:{CC}'\:<\:{AB}\:+\:{BC}\:+\:{CA} \\ $$

Question Number 13236 Answers: 0 Comments: 16

For positive a,b,c such that a b c=1 show that a^(b+c) b^(c+a) c^(a+b) ≤1 solution: a^(b+c) b^(c+a) c^(a+b) =(a^b a^c b^c b^a c^a c^b ) =(b×c)^a (a×c)^b (a×b)^c =(a^0 ×b×c)^a (a×b^0 ×c)^b (a×b×c^0 )^c ≤(a×b×c)^(a ) (a×b^ × c)^b (a×b×c)^c ≤(1)^a (1)^b (1)^c ;since a b c=1 ≤1

$${For}\:{positive}\:\:{a},{b},{c}\:\:{such}\:{that}\:\:{a}\:{b}\:{c}=\mathrm{1} \\ $$$${show}\:{that}\:\:{a}^{{b}+{c}} \:\:{b}^{{c}+{a}} \:\:{c}^{{a}+{b}} \:\leqslant\mathrm{1} \\ $$$${solution}: \\ $$$${a}^{{b}+{c}} \:\:{b}^{{c}+{a}} \:\:{c}^{{a}+{b}} \:=\left({a}^{{b}} {a}^{{c}} \:{b}^{{c}} {b}^{{a}} \:\:{c}^{{a}} {c}^{{b}} \right) \\ $$$$\:\:\:\:\:\:=\left({b}×{c}\right)^{{a}} \:\left({a}×{c}\right)^{{b}} \:\left({a}×{b}\right)^{{c}} \\ $$$$\:\:\:\:\:\:\:=\left({a}^{\mathrm{0}} ×{b}×{c}\right)^{{a}} \:\left({a}×{b}^{\mathrm{0}} ×{c}\right)^{{b}} \left({a}×{b}×{c}^{\mathrm{0}} \right)^{{c}} \\ $$$$\:\:\:\:\:\:\:\leqslant\left({a}×{b}×{c}\right)^{{a}\:\:\:\:} \left({a}×{b}^{} ×\:{c}\right)^{{b}} \:\left({a}×{b}×{c}\right)^{{c}} \\ $$$$\:\:\:\:\:\:\:\leqslant\left(\mathrm{1}\right)^{{a}} \:\left(\mathrm{1}\right)^{{b}} \:\left(\mathrm{1}\right)^{{c}} \:\:\:\:;{since}\:\:{a}\:{b}\:{c}=\mathrm{1} \\ $$$$\:\:\:\:\:\:\:\:\leqslant\mathrm{1} \\ $$

Question Number 13228 Answers: 0 Comments: 5

Question Number 13127 Answers: 0 Comments: 0

Question Number 13067 Answers: 0 Comments: 4

Question Number 13005 Answers: 1 Comments: 0

using De Moivre theorem solve the equation (x+1)^5 +(x−1)^5 =0

$${using}\:{De}\:{Moivre}\:{theorem}\:{solve}\:{the}\:{equation}\:\left({x}+\mathrm{1}\right)^{\mathrm{5}} +\left({x}−\mathrm{1}\right)^{\mathrm{5}} =\mathrm{0} \\ $$

Question Number 12875 Answers: 0 Comments: 3

Question Number 12846 Answers: 2 Comments: 1

Question Number 12822 Answers: 1 Comments: 0

prove by contradiction 9+13(√(3 )) is irrational

$${prove}\:{by}\:{contradiction}\:\mathrm{9}+\mathrm{13}\sqrt{\mathrm{3}\:} \\ $$$${is}\:{irrational} \\ $$

Question Number 12725 Answers: 3 Comments: 4

Question Number 12569 Answers: 0 Comments: 0

tank you

$${tank}\:{you} \\ $$

Question Number 12566 Answers: 1 Comments: 0

we give U_1 ,U_2 ,U_3 the terms of a geometric sequence .Determine U_1 ,U_2 ,U_3 such that : { ((U_1 .U_2 .U_3 =64)),((U_1 ^2 +U_2 ^2 +U_3 ^2 =84)) :}

$${we}\:{give}\:{U}_{\mathrm{1}} ,{U}_{\mathrm{2}} ,{U}_{\mathrm{3}} \:{the}\:{terms}\:{of}\:{a}\:{geometric}\:{sequence} \\ $$$$.{Determine}\:{U}_{\mathrm{1}} ,{U}_{\mathrm{2}} ,{U}_{\mathrm{3}} \:{such}\:{that}\:: \\ $$$$ \\ $$$$\begin{cases}{{U}_{\mathrm{1}} .{U}_{\mathrm{2}} .{U}_{\mathrm{3}} =\mathrm{64}}\\{{U}_{\mathrm{1}} ^{\mathrm{2}} +{U}_{\mathrm{2}} ^{\mathrm{2}} +{U}_{\mathrm{3}} ^{\mathrm{2}} =\mathrm{84}}\end{cases} \\ $$$$ \\ $$

Question Number 12553 Answers: 0 Comments: 0

Using Laplace Transform, solve f(t) = ((sin 3t)/t)

$$\mathrm{Using}\:\mathrm{Laplace}\:\mathrm{Transform},\:\mathrm{solve} \\ $$$${f}\left({t}\right)\:=\:\frac{\mathrm{sin}\:\mathrm{3}{t}}{{t}} \\ $$

Question Number 12534 Answers: 1 Comments: 0

please help me .How can resolve this system? {_((1+(√2))x+y=1) ^(x^2 +y^2 =1)

$${please}\:{help}\:{me}\:.{How}\:{can}\:{resolve}\:{this}\:{system}? \\ $$$$\left\{_{\left(\mathrm{1}+\sqrt{\mathrm{2}}\right){x}+{y}=\mathrm{1}} ^{{x}^{\mathrm{2}} +{y}^{\mathrm{2}} =\mathrm{1}} \right. \\ $$

Question Number 12506 Answers: 2 Comments: 0

A wooden stick was broken randomly into three pieces. What is the probability that a triangle can be built from those three parts?

$$\mathrm{A}\:\mathrm{wooden}\:\mathrm{stick}\:\mathrm{was}\:\mathrm{broken}\:\mathrm{randomly}\:\mathrm{into} \\ $$$$\mathrm{three}\:\mathrm{pieces}.\:\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{probability}\:\mathrm{that}\:\mathrm{a}\:\mathrm{triangle} \\ $$$$\mathrm{can}\:\mathrm{be}\:\mathrm{built}\:\mathrm{from}\:\mathrm{those}\:\mathrm{three}\:\mathrm{parts}? \\ $$

Question Number 12490 Answers: 0 Comments: 1

328976/256

$$\mathrm{328976}/\mathrm{256} \\ $$

Question Number 12499 Answers: 1 Comments: 0

Water flows out of a tank through a hole of diameter 2cm above the hole (1) Determine the velocity of outflow (2) The rate of outflow when the level of the water in the tank is 2cm above the hole.

$$\mathrm{Water}\:\mathrm{flows}\:\mathrm{out}\:\mathrm{of}\:\mathrm{a}\:\mathrm{tank}\:\mathrm{through}\:\mathrm{a}\:\mathrm{hole}\:\mathrm{of}\:\mathrm{diameter}\:\mathrm{2cm}\:\mathrm{above}\:\mathrm{the}\:\mathrm{hole} \\ $$$$\left(\mathrm{1}\right)\:\mathrm{Determine}\:\mathrm{the}\:\mathrm{velocity}\:\mathrm{of}\:\mathrm{outflow} \\ $$$$\left(\mathrm{2}\right)\:\mathrm{The}\:\mathrm{rate}\:\mathrm{of}\:\mathrm{outflow}\:\mathrm{when}\:\mathrm{the}\:\mathrm{level}\:\mathrm{of}\:\mathrm{the}\:\mathrm{water}\:\mathrm{in}\:\mathrm{the}\:\mathrm{tank}\:\mathrm{is}\:\mathrm{2cm}\:\mathrm{above} \\ $$$$\mathrm{the}\:\mathrm{hole}.\: \\ $$

Question Number 12371 Answers: 0 Comments: 0

tank you

$${tank}\:{you} \\ $$$$ \\ $$

Question Number 12332 Answers: 2 Comments: 7

prove ; ((0/0))=2

$$\mathrm{prove}\:;\:\left(\frac{\mathrm{0}}{\mathrm{0}}\right)=\mathrm{2} \\ $$

Question Number 12267 Answers: 2 Comments: 0

Find the nth term of the sequence 1) (1/3) , (1/(15)) , (1/(35)) , (1/(63)) , (1/(99)) 2) (1/2), (1/6), (1/(12)), (1/(20)), (1/(30))

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{nth}\:\mathrm{term}\:\mathrm{of}\:\mathrm{the}\:\mathrm{sequence} \\ $$$$\left.\mathrm{1}\right)\:\:\:\frac{\mathrm{1}}{\mathrm{3}}\:,\:\frac{\mathrm{1}}{\mathrm{15}}\:,\:\frac{\mathrm{1}}{\mathrm{35}}\:,\:\frac{\mathrm{1}}{\mathrm{63}}\:,\:\frac{\mathrm{1}}{\mathrm{99}} \\ $$$$\left.\mathrm{2}\right)\:\:\:\:\frac{\mathrm{1}}{\mathrm{2}},\:\frac{\mathrm{1}}{\mathrm{6}},\:\frac{\mathrm{1}}{\mathrm{12}},\:\frac{\mathrm{1}}{\mathrm{20}},\:\frac{\mathrm{1}}{\mathrm{30}} \\ $$

Question Number 12265 Answers: 0 Comments: 2

Determinant method can be used to solve the system below?, if yes solve by determinant method and if no solve by another method x+y−z=8 2x+y−2z=3 (give clear reason for your answer)

$${Determinant}\:{method}\:{can}\:{be}\:{used}\:{to}\:{solve} \\ $$$${the}\:{system}\:{below}?,\:\mathrm{if}\:\mathrm{yes}\:\mathrm{solve}\:\mathrm{by}\:\mathrm{determinant}\:\mathrm{method}\:\mathrm{and} \\ $$$$\:\mathrm{if}\:\mathrm{no}\:\mathrm{solve}\:\mathrm{by}\:\mathrm{another}\:\mathrm{method} \\ $$$$\:\:\:\:\:\:\:\:\: \\ $$$${x}+{y}−{z}=\mathrm{8} \\ $$$$\mathrm{2}{x}+{y}−\mathrm{2}{z}=\mathrm{3} \\ $$$$\left({give}\:{clear}\:{reason}\:{for}\:{your}\:{answer}\right) \\ $$

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