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Question Number 27531    Answers: 0   Comments: 5

(√(1−cos θ/1+cos θ))=?

$$\sqrt{\mathrm{1}−\mathrm{cos}\:\theta/\mathrm{1}+\mathrm{cos}\:\theta}=? \\ $$

Question Number 27530    Answers: 0   Comments: 0

5/6.6/8.7/9.11/13.....asending order

$$\mathrm{5}/\mathrm{6}.\mathrm{6}/\mathrm{8}.\mathrm{7}/\mathrm{9}.\mathrm{11}/\mathrm{13}.....{asending}\:{order} \\ $$

Question Number 27525    Answers: 1   Comments: 1

x=7×4(√(3 ))thenx+1/x=?

$${x}=\mathrm{7}×\mathrm{4}\sqrt{\mathrm{3}\:}{thenx}+\mathrm{1}/{x}=? \\ $$

Question Number 27524    Answers: 1   Comments: 0

If x is real, the maximum value of ((3x^2 +9x+17)/(3x^2 +9x+7)) is

$$\mathrm{If}\:{x}\:\mathrm{is}\:\mathrm{real},\:\mathrm{the}\:\mathrm{maximum}\:\mathrm{value}\:\mathrm{of} \\ $$$$\frac{\mathrm{3}{x}^{\mathrm{2}} +\mathrm{9}{x}+\mathrm{17}}{\mathrm{3}{x}^{\mathrm{2}} +\mathrm{9}{x}+\mathrm{7}}\:\:\mathrm{is} \\ $$

Question Number 27520    Answers: 0   Comments: 0

Question Number 27539    Answers: 2   Comments: 1

Question Number 27517    Answers: 0   Comments: 0

Question Number 27557    Answers: 0   Comments: 1

proove that π = 3.142

$${proove}\:{that}\:\pi\:=\:\mathrm{3}.\mathrm{142} \\ $$

Question Number 27514    Answers: 1   Comments: 0

The president of a republic wishes to assign the premiership,the vice-premiership,and six other cabinet posts to a selected group of 8,comprising of 6 career diplomats and 2 business men.If none of the business men can be made premier or vice premier,in how many ways can the 8 posts be assigned to the 8 people?

$${The}\:{president}\:{of}\:{a}\:{republic}\:{wishes} \\ $$$${to}\:{assign}\:{the}\:{premiership},{the}\: \\ $$$${vice}-{premiership},{and}\:{six}\:{other} \\ $$$${cabinet}\:{posts}\:{to}\:{a}\:{selected}\:{group} \\ $$$${of}\:\mathrm{8},{comprising}\:{of}\:\mathrm{6}\:{career} \\ $$$${diplomats}\:{and}\:\mathrm{2}\:{business}\:{men}.{If} \\ $$$${none}\:{of}\:{the}\:{business}\:{men}\:{can}\:{be} \\ $$$${made}\:{premier}\:{or}\:{vice}\:{premier},{in} \\ $$$${how}\:{many}\:{ways}\:{can}\:{the}\:\mathrm{8}\:{posts} \\ $$$${be}\:{assigned}\:{to}\:{the}\:\mathrm{8}\:{people}? \\ $$

Question Number 27513    Answers: 1   Comments: 0

Using only the integers 4 to 8, how many even numbers can be formed if each must lie between 4000 and 9000?

$${Using}\:{only}\:{the}\:{integers}\:\mathrm{4}\:{to}\:\mathrm{8}, \\ $$$${how}\:{many}\:{even}\:{numbers}\:{can}\:{be} \\ $$$${formed}\:{if}\:{each}\:{must}\:{lie}\:{between} \\ $$$$\mathrm{4000}\:{and}\:\:\mathrm{9000}? \\ $$$$ \\ $$

Question Number 27555    Answers: 0   Comments: 0

Question Number 27507    Answers: 1   Comments: 4

2(√(x ))+y=9....(1) x+ 2(√y)=3....(2) solve the simultaneous equation

$$\mathrm{2}\sqrt{{x}\:}+{y}=\mathrm{9}....\left(\mathrm{1}\right) \\ $$$${x}+\:\mathrm{2}\sqrt{{y}}=\mathrm{3}....\left(\mathrm{2}\right) \\ $$$$ \\ $$$${solve}\:{the}\:{simultaneous}\:{equation} \\ $$

Question Number 27503    Answers: 1   Comments: 0

If x=cy+bz ,y=az+cx & z=bx+ay prove that(x^2 /(1−a^2 ))=(y^2 /(1−b^2 ))=(z^2 /(1−c^2 )) .

$$\mathrm{If}\:\mathrm{x}=\mathrm{cy}+\mathrm{bz}\:,\mathrm{y}=\mathrm{az}+\mathrm{cx}\:\&\:\mathrm{z}=\mathrm{bx}+\mathrm{ay} \\ $$$$\mathrm{prove}\:\mathrm{that}\frac{\mathrm{x}^{\mathrm{2}} }{\mathrm{1}−\mathrm{a}^{\mathrm{2}} }=\frac{\mathrm{y}^{\mathrm{2}} }{\mathrm{1}−\mathrm{b}^{\mathrm{2}} }=\frac{\mathrm{z}^{\mathrm{2}} }{\mathrm{1}−\mathrm{c}^{\mathrm{2}} }\:. \\ $$

Question Number 27502    Answers: 0   Comments: 1

find ∫_0 ^(π/2) ((ln(1+xsin^2 t))/(sin^2 t))dt with −1<x<1 .

$${find}\:\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\:\:\frac{{ln}\left(\mathrm{1}+{xsin}^{\mathrm{2}} {t}\right)}{{sin}^{\mathrm{2}} {t}}{dt}\:{with}\:−\mathrm{1}<{x}<\mathrm{1}\:. \\ $$

Question Number 27500    Answers: 0   Comments: 2

find ∫∫_Δ (√(4 −x^2 −y^2 )) dxdy with Δ={(x,y) ∈R^2 / x^2 +y^2 ≤2x}

$${find}\:\int\int_{\Delta} \sqrt{\mathrm{4}\:−{x}^{\mathrm{2}} −{y}^{\mathrm{2}} \:}\:\:{dxdy}\:{with} \\ $$$$\Delta=\left\{\left({x},{y}\right)\:\in\mathbb{R}^{\mathrm{2}} /\:{x}^{\mathrm{2}} \:+{y}^{\mathrm{2}} \:\leqslant\mathrm{2}{x}\right\} \\ $$

Question Number 27498    Answers: 0   Comments: 0

find S_n = (C_n ^0 )^3 +( C_n ^1 )^3 +....(C_n ^n )^3 .

$${find}\:\:{S}_{{n}} \:=\:\:\left({C}_{{n}} ^{\mathrm{0}} \:\right)^{\mathrm{3}} \:\:+\left(\:{C}_{{n}} ^{\mathrm{1}} \right)^{\mathrm{3}} +....\left({C}_{{n}} ^{{n}} \right)^{\mathrm{3}} \:\:. \\ $$

Question Number 27497    Answers: 0   Comments: 0

let give I_n = n ∫_1 ^(1+(1/n)) f(x^n )dx with f is numerical function integrable on[1,e] .prove that lim_(n−>∝) I_n = ∫_1 ^e ((f(t))/t) dt.

$${let}\:{give}\:{I}_{{n}} =\:{n}\:\int_{\mathrm{1}} ^{\mathrm{1}+\frac{\mathrm{1}}{{n}}} {f}\left({x}^{{n}} \right){dx}\:{with}\:{f}\:{is}\:{numerical} \\ $$$${function}\:{integrable}\:{on}\left[\mathrm{1},{e}\right]\:.{prove}\:{that} \\ $$$${lim}_{{n}−>\propto} \:\:{I}_{{n}} \:=\:\int_{\mathrm{1}} ^{{e}} \:\:\frac{{f}\left({t}\right)}{{t}}\:{dt}. \\ $$

Question Number 27496    Answers: 0   Comments: 0

let give f(x)= ∫_0 ^∝ (1/(√t)) e^(−(1+ix)t) dt calculate f^′ (x) prove that ∃λ∈R/(x+i)^2 (f(x))^2 = λ then find ∫_0 ^∝ e^(−t^2 ) dt .

$${let}\:{give}\:{f}\left({x}\right)=\:\int_{\mathrm{0}} ^{\propto} \:\:\frac{\mathrm{1}}{\sqrt{{t}}}\:{e}^{−\left(\mathrm{1}+{ix}\right){t}} {dt} \\ $$$${calculate}\:{f}^{'} \left({x}\right)\:{prove}\:{that}\:\exists\lambda\in{R}/\left({x}+{i}\right)^{\mathrm{2}} \:\left({f}\left({x}\right)\right)^{\mathrm{2}} =\:\lambda \\ $$$${then}\:{find}\:\:\int_{\mathrm{0}} ^{\propto} \:\:{e}^{−{t}^{\mathrm{2}} } {dt}\:. \\ $$

Question Number 27495    Answers: 0   Comments: 1

find α and β from R /∫_0 ^π (αt^2 +βt)cos(nt)dt= (1/n^2 ) for all number n from N^(∗ ) then find Σ_(n=1) ^∝ (1/n^2 ) .

$${find}\:\alpha\:{and}\:\beta\:{from}\:{R}\:/\int_{\mathrm{0}} ^{\pi} \left(\alpha{t}^{\mathrm{2}} +\beta{t}\right){cos}\left({nt}\right){dt}=\:\frac{\mathrm{1}}{{n}^{\mathrm{2}} } \\ $$$${for}\:{all}\:{number}\:{n}\:{from}\:{N}^{\ast\:} \:{then}\:{find} \\ $$$$\sum_{{n}=\mathrm{1}} ^{\propto} \:\:\frac{\mathrm{1}}{{n}^{\mathrm{2}} }\:. \\ $$

Question Number 27492    Answers: 0   Comments: 1

Question Number 27486    Answers: 0   Comments: 0

Question Number 27481    Answers: 0   Comments: 1

find the value of ∫_0 ^∝ ((√x)/(e^x −1))dx .

$${find}\:{the}\:{value}\:{of}\:\int_{\mathrm{0}} ^{\propto} \:\frac{\sqrt{{x}}}{{e}^{{x}} −\mathrm{1}}{dx}\:. \\ $$

Question Number 27467    Answers: 0   Comments: 0

Question Number 27464    Answers: 0   Comments: 5

Show that: ∫_( 0) ^( 2π) ((cos(3x))/(5 − 4cos(x))) dx = (π/(12))

$$\mathrm{Show}\:\mathrm{that}:\:\:\:\:\int_{\:\mathrm{0}} ^{\:\mathrm{2}\pi} \:\frac{\mathrm{cos}\left(\mathrm{3x}\right)}{\mathrm{5}\:−\:\mathrm{4cos}\left(\mathrm{x}\right)}\:\mathrm{dx}\:\:=\:\:\frac{\pi}{\mathrm{12}} \\ $$

Question Number 27449    Answers: 2   Comments: 0

factorise a^4 −(b+c)^4

$${factorise}\:{a}^{\mathrm{4}} −\left({b}+{c}\right)^{\mathrm{4}} \\ $$

Question Number 27447    Answers: 1   Comments: 0

∫^∞ _0 v^(4 ) e ((−mv^2 )/(2KT))dv solve it

$$\underset{\mathrm{0}} {\int}^{\infty} \:\mathrm{v}^{\mathrm{4}\:} \:\mathrm{e}\:\frac{−\mathrm{mv}^{\mathrm{2}} }{\mathrm{2KT}}\mathrm{dv}\: \\ $$$$\mathrm{solve}\:\mathrm{it} \\ $$

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