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Question Number 46563    Answers: 1   Comments: 0

lim_(x→0) (((a^x +b^x +c^x )/3))^(1/x)

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\left(\frac{{a}^{{x}} +{b}^{{x}} +{c}^{{x}} }{\mathrm{3}}\right)^{\mathrm{1}/{x}} \\ $$

Question Number 46558    Answers: 1   Comments: 0

calculate the uncertainty in velocity of an electron which is confined in a 10^(−10 ) meter

$${calculate}\:{the}\:{uncertainty}\:{in}\:{velocity}\:{of}\:{an}\:{electron}\:{which}\:{is}\:{confined}\:{in}\:{a}\:\mathrm{10}^{−\mathrm{10}\:} {meter} \\ $$

Question Number 46553    Answers: 1   Comments: 0

Can someone please explain me how to solve a quadratic equation without the common formulas but with the sums and products method please ? Thank

$$\mathrm{Can}\:\mathrm{someone}\:\mathrm{please}\:\mathrm{explain}\:\mathrm{me}\:\mathrm{how}\:\mathrm{to} \\ $$$$\mathrm{solve}\:\mathrm{a}\:\mathrm{quadratic}\:\mathrm{equation}\:\mathrm{without}\:\mathrm{the}\: \\ $$$$\mathrm{common}\:\mathrm{formulas}\:\mathrm{but}\:\mathrm{with}\:\mathrm{the}\:\mathrm{sums}\:\mathrm{and} \\ $$$$\mathrm{products}\:\mathrm{method}\:\mathrm{please}\:? \\ $$$$\mathrm{Thank} \\ $$

Question Number 46552    Answers: 1   Comments: 2

Question Number 46549    Answers: 0   Comments: 3

is there any other maths forum apart from this?

$${is}\:{there}\:{any}\:{other}\:{maths}\:{forum}\:{apart}\:{from}\:{this}? \\ $$

Question Number 46546    Answers: 0   Comments: 7

Question Number 46542    Answers: 0   Comments: 5

pls help Find L(cos^2 t)

$${pls}\:{help}\: \\ $$$$\:\boldsymbol{{Find}}\:\boldsymbol{{L}}\left({cos}^{\mathrm{2}} {t}\right) \\ $$

Question Number 46534    Answers: 1   Comments: 0

using taylors expansion find find the value of a)tan45° 1′ b)sin30° 1′

$$\mathrm{using}\:\mathrm{taylors}\:\mathrm{expansion} \\ $$$$\mathrm{find}\:\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of} \\ $$$$\left.\mathrm{a}\right)\mathrm{tan45}°\:\mathrm{1}'\: \\ $$$$\left.\mathrm{b}\right)\mathrm{sin30}°\:\mathrm{1}' \\ $$

Question Number 46527    Answers: 0   Comments: 5

𝚺_(n= 1) ^∞ (((log n)/n))^2 Does the series converge or diverge, help find the sum ...

$$\underset{\mathrm{n}=\:\mathrm{1}} {\overset{\infty} {\boldsymbol{\sum}}}\:\left(\frac{\mathrm{log}\:\mathrm{n}}{\mathrm{n}}\right)^{\mathrm{2}} \\ $$$$\mathrm{Does}\:\mathrm{the}\:\mathrm{series}\:\mathrm{converge}\:\mathrm{or}\:\mathrm{diverge},\:\:\mathrm{help}\:\mathrm{find}\:\mathrm{the}\:\mathrm{sum}\:... \\ $$

Question Number 46522    Answers: 0   Comments: 0

∫ x cot^(−1) (3x^2 ) tan^(−1) (6x^2 )

$$\int\:\mathrm{x}\:\mathrm{cot}^{−\mathrm{1}} \left(\mathrm{3x}^{\mathrm{2}} \right)\:\mathrm{tan}^{−\mathrm{1}} \left(\mathrm{6x}^{\mathrm{2}} \right) \\ $$

Question Number 46502    Answers: 1   Comments: 1

∫_0 ^∞ (((sin (x))/x))dx

$$\int_{\mathrm{0}} ^{\infty} \left(\frac{\mathrm{sin}\:\left(\boldsymbol{\mathrm{x}}\right)}{\boldsymbol{\mathrm{x}}}\right)\boldsymbol{\mathrm{dx}} \\ $$

Question Number 46503    Answers: 0   Comments: 0

true or false ? θ_1 +θ_2 =90^° and m_1 ≠m_2 in elastic collision

$$\mathrm{true}\:\mathrm{or}\:\mathrm{false}\:? \\ $$$$\theta_{\mathrm{1}} +\theta_{\mathrm{2}} =\mathrm{90}^{°} \:\mathrm{and}\:\mathrm{m}_{\mathrm{1}} \neq\mathrm{m}_{\mathrm{2}} \\ $$$$\mathrm{in}\:\mathrm{elastic}\:\mathrm{collision} \\ $$

Question Number 46499    Answers: 2   Comments: 0

Question Number 46483    Answers: 1   Comments: 0

If tan^2 α tan^2 β+tan^2 β tan^2 γ+tan^2 γ tan^2 α +2tan^2 α tan^2 β tan^2 γ=1, then the value of sin^2 α+sin^2 β+sin^2 γ is

$$\mathrm{If}\:\:\mathrm{tan}^{\mathrm{2}} \alpha\:\mathrm{tan}^{\mathrm{2}} \beta+\mathrm{tan}^{\mathrm{2}} \beta\:\mathrm{tan}^{\mathrm{2}} \gamma+\mathrm{tan}^{\mathrm{2}} \gamma\:\mathrm{tan}^{\mathrm{2}} \alpha \\ $$$$+\mathrm{2tan}^{\mathrm{2}} \alpha\:\mathrm{tan}^{\mathrm{2}} \beta\:\mathrm{tan}^{\mathrm{2}} \gamma=\mathrm{1},\:\mathrm{then}\:\mathrm{the}\:\mathrm{value} \\ $$$$\mathrm{of}\:\mathrm{sin}^{\mathrm{2}} \alpha+\mathrm{sin}^{\mathrm{2}} \beta+\mathrm{sin}^{\mathrm{2}} \gamma\:\mathrm{is} \\ $$

Question Number 46482    Answers: 1   Comments: 1

Question Number 46481    Answers: 0   Comments: 3

Four spheres with radii a,b,c and d touch each other. Find the radii of their circumscribed sphere (R) and their inscribed sphere (r) in terms of a,b,c and d.

$${Four}\:{spheres}\:{with}\:{radii}\:{a},{b},{c}\:{and}\:{d} \\ $$$${touch}\:{each}\:{other}.\:{Find}\:{the}\:{radii}\:{of} \\ $$$${their}\:{circumscribed}\:{sphere}\:\left({R}\right)\:{and} \\ $$$${their}\:{inscribed}\:{sphere}\:\left({r}\right)\:{in}\:{terms}\:{of}\: \\ $$$${a},{b},{c}\:{and}\:{d}. \\ $$

Question Number 46478    Answers: 1   Comments: 1

If x^2 +y^2 +xy=1. Find range of E = x^3 y+xy^3 +4 .

$${If}\:{x}^{\mathrm{2}} +{y}^{\mathrm{2}} +{xy}=\mathrm{1}.\:{Find}\:{range}\:{of}\: \\ $$$${E}\:=\:{x}^{\mathrm{3}} {y}+{xy}^{\mathrm{3}} +\mathrm{4}\:. \\ $$

Question Number 46475    Answers: 1   Comments: 2

Question Number 46474    Answers: 2   Comments: 2

a)[If tan^(−1) a+tan^(−1) b+tan^(−1) c=π show that ((a+b+c)/(abc))=1 b)[ If tanx=((nsinycosy)/(1−nsin^2 y)) show that tan(y−x)=(1−n)tany

$$\left.\mathrm{a}\right)\left[\mathrm{If}\:\mathrm{tan}^{−\mathrm{1}} \mathrm{a}+\mathrm{tan}^{−\mathrm{1}} \mathrm{b}+\mathrm{tan}^{−\mathrm{1}} \mathrm{c}=\pi\:\:\mathrm{show}\:\mathrm{that}\:\frac{\mathrm{a}+\mathrm{b}+\mathrm{c}}{\mathrm{abc}}=\mathrm{1}\right. \\ $$$$\left.\mathrm{b}\right)\left[\:\:\mathrm{If}\:\:\mathrm{tanx}=\frac{\mathrm{nsinycosy}}{\mathrm{1}−\mathrm{nsin}^{\mathrm{2}} \mathrm{y}}\right. \\ $$$$\mathrm{show}\:\mathrm{that}\:\mathrm{tan}\left(\mathrm{y}−\mathrm{x}\right)=\left(\mathrm{1}−\mathrm{n}\right)\mathrm{tany} \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$

Question Number 46473    Answers: 1   Comments: 0

Find the value of θ which satisfy the equation cosθx+cos(x+2)θ=cosθ

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\theta \\ $$$$\mathrm{which}\:\mathrm{satisfy}\:\mathrm{the}\: \\ $$$$\mathrm{equation} \\ $$$$\mathrm{cos}\theta\mathrm{x}+\mathrm{cos}\left(\mathrm{x}+\mathrm{2}\right)\theta=\mathrm{cos}\theta \\ $$

Question Number 46472    Answers: 1   Comments: 0

Question Number 46467    Answers: 0   Comments: 2

Question Number 46465    Answers: 1   Comments: 0

If I=(1/2) ∫_0 ^∞ t^n e^(−t) dt = 360. Find n?

$${If}\:{I}=\frac{\mathrm{1}}{\mathrm{2}}\:\int_{\mathrm{0}} ^{\infty} {t}^{{n}} {e}^{−{t}} {dt}\:\:=\:\mathrm{360}. \\ $$$${Find}\:{n}? \\ $$

Question Number 46464    Answers: 0   Comments: 0

To this formula find the value of S when t=1 u=2 a=3 b=4 c=5 S=((tu)/((a+b+c))) [Answer]========================= S=0.1666666666666... ≈0.17 [Solution]======================== [S=((tu)/((a+b+c)))] =((1×2)/((3+4+5))) =(2/((3+4+5))) =(2/((7+5))) =(2/(12)) =0.1666666666666... ≈0.17 S=0.17

$${To}\:{this}\:{formula}\:{find}\:{the}\:{value}\:{of}\:{S}\:{when}\:{t}=\mathrm{1}\:{u}=\mathrm{2}\:{a}=\mathrm{3}\:{b}=\mathrm{4}\:{c}=\mathrm{5} \\ $$$${S}=\frac{{tu}}{\left({a}+{b}+{c}\right)} \\ $$$$\left[{Answer}\right]========================= \\ $$$$ \\ $$$$\:\:\:\:{S}=\mathrm{0}.\mathrm{1666666666666}... \\ $$$$\:\:\:\:\:\:\:\approx\mathrm{0}.\mathrm{17} \\ $$$$ \\ $$$$\left[{Solution}\right]======================== \\ $$$$ \\ $$$$\left[{S}=\frac{{tu}}{\left({a}+{b}+{c}\right)}\right] \\ $$$$\:\:\:\:\:=\frac{\mathrm{1}×\mathrm{2}}{\left(\mathrm{3}+\mathrm{4}+\mathrm{5}\right)} \\ $$$$\:\:\:\:\:=\frac{\mathrm{2}}{\left(\mathrm{3}+\mathrm{4}+\mathrm{5}\right)} \\ $$$$\:\:\:\:\:=\frac{\mathrm{2}}{\left(\mathrm{7}+\mathrm{5}\right)} \\ $$$$\:\:\:\:\:=\frac{\mathrm{2}}{\mathrm{12}} \\ $$$$\:\:\:\:\:=\mathrm{0}.\mathrm{1666666666666}... \\ $$$$\:\:\:\:\:\approx\mathrm{0}.\mathrm{17} \\ $$$$ \\ $$$${S}=\mathrm{0}.\mathrm{17} \\ $$

Question Number 46461    Answers: 1   Comments: 0

Find the sum of the nth term of the series: (1/2) + (3/4) + (7/8) + ((15)/(16)) + ...

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{nth}\:\mathrm{term}\:\mathrm{of}\:\mathrm{the}\:\mathrm{series}:\:\:\:\:\frac{\mathrm{1}}{\mathrm{2}}\:+\:\frac{\mathrm{3}}{\mathrm{4}}\:+\:\frac{\mathrm{7}}{\mathrm{8}}\:+\:\frac{\mathrm{15}}{\mathrm{16}}\:+\:... \\ $$

Question Number 46460    Answers: 0   Comments: 0

If k is odd, then show that 1^k + 2^k + 3^k + ... + n^k is divisible by 1 + 2 + 3 + ... + n, for every n ∈ N

$$\mathrm{If}\:\:\mathrm{k}\:\mathrm{is}\:\mathrm{odd},\:\mathrm{then}\:\mathrm{show}\:\mathrm{that}\:\:\:\:\mathrm{1}^{\mathrm{k}} \:+\:\mathrm{2}^{\mathrm{k}} \:+\:\mathrm{3}^{\mathrm{k}} \:+\:...\:+\:\mathrm{n}^{\mathrm{k}} \:\:\mathrm{is}\:\mathrm{divisible}\:\mathrm{by}\:\:\: \\ $$$$\mathrm{1}\:+\:\mathrm{2}\:+\:\mathrm{3}\:+\:...\:+\:\mathrm{n},\:\:\:\:\:\mathrm{for}\:\mathrm{every}\:\:\:\mathrm{n}\:\in\:\mathrm{N} \\ $$

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