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Question Number 180396 Answers: 0 Comments: 0

The difference between the ages of Sammy and Cindy is half the difference between the ages of their parents. Their father is 6 years older than twice the age of Cindy. Their mother is twice as old as Cindy and 12 years older than Sammy. By how many years is Sammy younger than Cindy?

$$\mathrm{The}\:\mathrm{difference}\:\mathrm{between}\:\mathrm{the}\:\mathrm{ages}\:\mathrm{of} \\ $$$$\mathrm{Sammy}\:\mathrm{and}\:\mathrm{Cindy}\:\mathrm{is}\:\mathrm{half}\:\mathrm{the}\: \\ $$$$\mathrm{difference}\:\mathrm{between}\:\mathrm{the}\:\mathrm{ages}\:\mathrm{of}\: \\ $$$$\mathrm{their}\:\mathrm{parents}.\:\mathrm{Their}\:\mathrm{father}\:\mathrm{is}\:\mathrm{6} \\ $$$$\mathrm{years}\:\mathrm{older}\:\mathrm{than}\:\mathrm{twice}\:\mathrm{the}\:\mathrm{age}\:\mathrm{of}\: \\ $$$$\mathrm{Cindy}.\:\mathrm{Their}\:\mathrm{mother}\:\mathrm{is}\:\mathrm{twice}\:\mathrm{as}\:\mathrm{old} \\ $$$$\mathrm{as}\:\mathrm{Cindy}\:\mathrm{and}\:\mathrm{12}\:\mathrm{years}\:\mathrm{older}\:\mathrm{than}\: \\ $$$$\mathrm{Sammy}.\:\mathrm{By}\:\mathrm{how}\:\mathrm{many}\:\mathrm{years}\:\mathrm{is}\: \\ $$$$\mathrm{Sammy}\:\mathrm{younger}\:\mathrm{than}\:\mathrm{Cindy}? \\ $$

Question Number 180391 Answers: 1 Comments: 1

y = x − (2/x) Find the set of values of the function.

$$\mathrm{y}\:=\:\mathrm{x}\:−\:\frac{\mathrm{2}}{\mathrm{x}} \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{set}\:\mathrm{of}\:\mathrm{values}\:\mathrm{of}\:\mathrm{the}\:\mathrm{function}. \\ $$

Question Number 180388 Answers: 1 Comments: 0

Question Number 180381 Answers: 2 Comments: 0

(√((8^(12) +4^(13) )/(8^6 +4^(14) )))

$$\sqrt{\frac{\mathrm{8}^{\mathrm{12}} +\mathrm{4}^{\mathrm{13}} }{\mathrm{8}^{\mathrm{6}} +\mathrm{4}^{\mathrm{14}} }} \\ $$

Question Number 180379 Answers: 1 Comments: 0

∫ x^2 ((x^6 +5))^(1/6) dx =?

$$\:\:\:\:\int\:{x}^{\mathrm{2}} \:\sqrt[{\mathrm{6}}]{{x}^{\mathrm{6}} +\mathrm{5}}\:{dx}\:=? \\ $$

Question Number 180378 Answers: 1 Comments: 0

Question Number 180368 Answers: 2 Comments: 5

Question Number 180365 Answers: 1 Comments: 0

Question Number 180364 Answers: 1 Comments: 0

Question Number 180363 Answers: 1 Comments: 0

Question Number 180362 Answers: 0 Comments: 0

Question Number 180351 Answers: 0 Comments: 0

solve the differential equation y′′ +2 y′ + y = 0 using power series method that is, assume y = Σ_(n=0) ^∞ c_n x^n is a solution

$$\mathrm{solve}\:\mathrm{the}\:\mathrm{differential}\:\mathrm{equation}\:\:{y}''\:+\mathrm{2}\:{y}'\:+\:{y}\:=\:\mathrm{0} \\ $$$$\mathrm{using}\:\mathrm{power}\:\mathrm{series}\:\mathrm{method}\:\mathrm{that}\:\mathrm{is},\:\mathrm{assume} \\ $$$${y}\:=\:\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}{c}_{{n}} {x}^{{n}} \:\mathrm{is}\:\mathrm{a}\:\mathrm{solution} \\ $$

Question Number 180350 Answers: 1 Comments: 0

Question Number 180348 Answers: 0 Comments: 0

Question Number 180343 Answers: 1 Comments: 1

Question Number 180340 Answers: 1 Comments: 1

please answer this question i have no idea to post an image. it is sent by mistke.

$${please}\:{answer}\:{this}\:{question} \\ $$$${i}\:{have}\:{no}\:{idea}\:{to}\:{post}\:{an}\:{image}.\:{it}\:{is}\: \\ $$$${sent}\:{by}\:{mistke}. \\ $$

Question Number 180335 Answers: 2 Comments: 1

The integers between 1 to 10^4 contain exactly one 8 and one 9 is? I got 1160 but one is arguing 1154only..kindly help me out

$${The}\:{integers}\:{between}\:\mathrm{1}\:{to}\:\mathrm{10}^{\mathrm{4}} \\ $$$${contain}\:{exactly}\:{one}\:\mathrm{8}\:\:{and}\:{one}\:\mathrm{9} \\ $$$${is}?\:{I}\:{got}\:\mathrm{1160}\:{but}\:{one}\:\:{is}\:{arguing} \\ $$$$\mathrm{1154}{only}..{kindly}\:{help}\:{me}\:{out} \\ $$

Question Number 180301 Answers: 3 Comments: 1

Question Number 180300 Answers: 3 Comments: 0

Question Number 180299 Answers: 1 Comments: 0

Question Number 180298 Answers: 1 Comments: 0

Question Number 180295 Answers: 0 Comments: 2

Express these both Cartesian and polar form (1) f(z)=3z^2 −2z+(1/z) (2) f(z)=z+(1/z) Thanks

$$\mathrm{Express}\:\mathrm{these}\:\mathrm{both}\:\mathrm{Cartesian}\:\mathrm{and}\: \\ $$$$\mathrm{polar}\:\mathrm{form} \\ $$$$\left(\mathrm{1}\right)\:\mathrm{f}\left(\mathrm{z}\right)=\mathrm{3z}^{\mathrm{2}} −\mathrm{2z}+\frac{\mathrm{1}}{\mathrm{z}} \\ $$$$\left(\mathrm{2}\right)\:\mathrm{f}\left(\mathrm{z}\right)=\mathrm{z}+\frac{\mathrm{1}}{\mathrm{z}} \\ $$$$ \\ $$$$ \\ $$$$\mathrm{Thanks} \\ $$

Question Number 180285 Answers: 0 Comments: 3

Express this f(z)=((2z+i)/(z+i)) in polar form where z=re^(iθ) (polar form)

$$\mathrm{Express}\:\mathrm{this}\:\mathrm{f}\left(\mathrm{z}\right)=\frac{\mathrm{2z}+\mathrm{i}}{\mathrm{z}+\mathrm{i}}\:\mathrm{in}\:\mathrm{polar}\:\mathrm{form} \\ $$$$\mathrm{where}\:\mathrm{z}=\mathrm{re}^{\mathrm{i}\theta} \:\left(\mathrm{polar}\:\mathrm{form}\right) \\ $$$$ \\ $$

Question Number 180277 Answers: 0 Comments: 4

Express the function f(z)=ze^(iz) into cartesian form and separate it into Real and Imaginary part. M.m

$$\mathrm{Express}\:\mathrm{the}\:\mathrm{function}\:\mathrm{f}\left(\mathrm{z}\right)=\mathrm{ze}^{\mathrm{iz}} \:\mathrm{into} \\ $$$$\mathrm{cartesian}\:\mathrm{form}\:\mathrm{and}\:\mathrm{separate}\:\mathrm{it}\:\mathrm{into} \\ $$$$\mathrm{Real}\:\mathrm{and}\:\mathrm{Imaginary}\:\mathrm{part}. \\ $$$$ \\ $$$$\mathrm{M}.\mathrm{m} \\ $$

Question Number 180274 Answers: 1 Comments: 0

Solve in C the equation z^4 +(7−i)z^3 +(12−15i)z^2 +(4+4i)z+16+192i=0 Knowing that it has one real root and a purely imaginary root of equal magnitude.

$$\mathrm{Solve}\:\mathrm{in}\:\mathbb{C}\:\mathrm{the}\:\mathrm{equation}\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:{z}^{\mathrm{4}} +\left(\mathrm{7}−{i}\right){z}^{\mathrm{3}} +\left(\mathrm{12}−\mathrm{15}{i}\right){z}^{\mathrm{2}} +\left(\mathrm{4}+\mathrm{4}{i}\right){z}+\mathrm{16}+\mathrm{192}{i}=\mathrm{0} \\ $$$$\mathrm{Knowing}\:\mathrm{that}\:\mathrm{it}\:\mathrm{has}\:\mathrm{one}\:\mathrm{real}\:\mathrm{root}\:\mathrm{and}\:\mathrm{a}\:\mathrm{purely}\:\mathrm{imaginary}\:\mathrm{root} \\ $$$$\mathrm{of}\:\mathrm{equal}\:\mathrm{magnitude}. \\ $$

Question Number 180273 Answers: 0 Comments: 0

In triangle ABC with angles α , β , γ correspondently , Euler′s line interescts BC at point P. Ite′s put δ is angle between Euler′s line and BC (∠BPH). Then the following is true tan δ = ((2 cos β cos γ − cos α)/(sin (β − γ)))

$$\mathrm{In}\:\mathrm{triangle}\:\:\mathrm{ABC}\:\:\mathrm{with}\:\mathrm{angles}\:\:\alpha\:,\:\beta\:,\:\gamma \\ $$$$\mathrm{correspondently}\:,\:\mathrm{Euler}'\mathrm{s}\:\mathrm{line}\:\mathrm{interescts} \\ $$$$\mathrm{BC}\:\:\mathrm{at}\:\mathrm{point}\:\:\mathrm{P}.\:\mathrm{Ite}'\mathrm{s}\:\mathrm{put}\:\:\delta\:\:\mathrm{is}\:\mathrm{angle} \\ $$$$\mathrm{between}\:\mathrm{Euler}'\mathrm{s}\:\mathrm{line}\:\mathrm{and}\:\:\mathrm{BC}\:\left(\angle\mathrm{BPH}\right). \\ $$$$\mathrm{Then}\:\mathrm{the}\:\mathrm{following}\:\mathrm{is}\:\mathrm{true} \\ $$$$\mathrm{tan}\:\delta\:=\:\frac{\mathrm{2}\:\mathrm{cos}\:\beta\:\mathrm{cos}\:\gamma\:−\:\mathrm{cos}\:\alpha}{\mathrm{sin}\:\left(\beta\:−\:\gamma\right)} \\ $$

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