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Question Number 14145 Answers: 1 Comments: 1

Question Number 14104 Answers: 0 Comments: 0

Question Number 14071 Answers: 2 Comments: 1

Solve the Partial fraction ((3x^4 − 9x^3 + 16x^2 + 9x + 13)/((x − 1)^2 (x^2 + 2x − 2)^2 ))

$$\mathrm{Solve}\:\mathrm{the}\:\mathrm{Partial}\:\mathrm{fraction}\: \\ $$$$\frac{\mathrm{3x}^{\mathrm{4}} \:−\:\mathrm{9x}^{\mathrm{3}} \:+\:\mathrm{16x}^{\mathrm{2}} \:+\:\mathrm{9x}\:+\:\mathrm{13}}{\left(\mathrm{x}\:−\:\mathrm{1}\right)^{\mathrm{2}} \left(\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{2x}\:−\:\mathrm{2}\right)^{\mathrm{2}} } \\ $$

Question Number 13738 Answers: 1 Comments: 1

P,Q,R,S are four locations on the same horizontal plane.Q is on a bearing of 041° from P and the distance is 40km. S is 28km from R on a bearing 074°, R is directly due north of P and the distance between Q and R is 38km. (a)the bearing of R from Q (b)the distance between Q and S (c)the distance between P and R

$$\mathrm{P},\mathrm{Q},\mathrm{R},\mathrm{S}\:\mathrm{are}\:\mathrm{four}\:\mathrm{locations}\:\mathrm{on}\:\mathrm{the} \\ $$$$\mathrm{same}\:\mathrm{horizontal}\:\mathrm{plane}.\mathrm{Q}\:\mathrm{is}\:\mathrm{on}\:\mathrm{a}\: \\ $$$$\mathrm{bearing}\:\mathrm{of}\:\mathrm{041}°\:\mathrm{from}\:\mathrm{P}\:\mathrm{and}\:\mathrm{the} \\ $$$$\mathrm{distance}\:\mathrm{is}\:\mathrm{40km}. \\ $$$$\mathrm{S}\:\mathrm{is}\:\mathrm{28km}\:\mathrm{from}\:\mathrm{R}\:\mathrm{on}\:\mathrm{a}\:\mathrm{bearing}\:\mathrm{074}°, \\ $$$$\mathrm{R}\:\mathrm{is}\:\mathrm{directly}\:\mathrm{due}\:\mathrm{north}\:\mathrm{of}\:\mathrm{P}\:\mathrm{and} \\ $$$$\mathrm{the}\:\mathrm{distance}\:\mathrm{between}\:\mathrm{Q}\:\mathrm{and}\:\mathrm{R}\:\mathrm{is} \\ $$$$\mathrm{38km}. \\ $$$$\left(\mathrm{a}\right)\mathrm{the}\:\mathrm{bearing}\:\mathrm{of}\:\mathrm{R}\:\mathrm{from}\:\mathrm{Q} \\ $$$$\left(\mathrm{b}\right)\mathrm{the}\:\mathrm{distance}\:\mathrm{between}\:\mathrm{Q}\:\mathrm{and}\:\mathrm{S} \\ $$$$\left(\mathrm{c}\right)\mathrm{the}\:\mathrm{distance}\:\mathrm{between}\:\mathrm{P}\:\mathrm{and}\:\mathrm{R} \\ $$

Question Number 13735 Answers: 2 Comments: 6

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

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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

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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

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

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