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Question Number 37738 Answers: 0 Comments: 4

given a^2 <1 now a<(√1) or a<±1 ∴ a<1 and a<−1 but but its false we know if a^2 <1 so −1<a<1 so my question is why this is happening at all.

$$\mathrm{given}\:{a}^{\mathrm{2}} <\mathrm{1} \\ $$$$\mathrm{now} \\ $$$${a}<\sqrt{\mathrm{1}} \\ $$$$\mathrm{or}\:{a}<\pm\mathrm{1} \\ $$$$\therefore\:{a}<\mathrm{1}\:\mathrm{and}\:{a}<−\mathrm{1}\:\:\:\:\mathrm{but}\:\mathrm{but}\:\mathrm{its}\:\mathrm{false}\:\mathrm{we}\:\mathrm{know} \\ $$$${if}\:\mathrm{a}^{\mathrm{2}} <\mathrm{1}\:\mathrm{so}\:−\mathrm{1}<{a}<\mathrm{1}\: \\ $$$${so}\:{my}\:{question}\:{is}\:{why}\:{this}\:{is}\:{happening}\:{at}\:{all}. \\ $$

Question Number 37733 Answers: 1 Comments: 0

Prove that the equation sin θ = x + (1/x) is impossible if x be real.

$$\mathrm{Prove}\:\mathrm{that}\:\mathrm{the}\:\mathrm{equation}\:\mathrm{sin}\:\theta\:=\:{x}\:+\:\frac{\mathrm{1}}{{x}}\: \\ $$$$\mathrm{is}\:\mathrm{impossible}\:\mathrm{if}\:{x}\:\mathrm{be}\:\mathrm{real}. \\ $$

Question Number 37730 Answers: 1 Comments: 1

Differentiate x(1+x)^4

$$\:{Differentiate}\: \\ $$$${x}\left(\mathrm{1}+{x}\right)^{\mathrm{4}} \: \\ $$$$ \\ $$

Question Number 37728 Answers: 1 Comments: 0

1+n+((n(n−1))/(2!))+((n(n−1)(n−2))/(3!))+((n(n−1)(n−2)(n−3))/(4!))+........=

$$\mathrm{1}+\mathrm{n}+\frac{\mathrm{n}\left(\mathrm{n}−\mathrm{1}\right)}{\mathrm{2}!}+\frac{\mathrm{n}\left(\mathrm{n}−\mathrm{1}\right)\left(\mathrm{n}−\mathrm{2}\right)}{\mathrm{3}!}+\frac{\mathrm{n}\left(\mathrm{n}−\mathrm{1}\right)\left(\mathrm{n}−\mathrm{2}\right)\left(\mathrm{n}−\mathrm{3}\right)}{\mathrm{4}!}+........= \\ $$

Question Number 37712 Answers: 1 Comments: 1

Evaluate Σ_(r=0) ^∞ 2^(r−1)

$${Evaluate}\:\underset{{r}=\mathrm{0}} {\overset{\infty} {\sum}}\mathrm{2}^{{r}−\mathrm{1}} \\ $$

Question Number 37711 Answers: 1 Comments: 0

A commitee of 2 boys and 1 girl has to be formed from a class of 4 boys and 3 girls give the number of ways these can be done

$${A}\:{commitee}\:{of}\:\mathrm{2}\:{boys}\:{and}\:\mathrm{1}\:{girl} \\ $$$${has}\:{to}\:{be}\:{formed}\:{from}\:{a}\:{class} \\ $$$${of}\:\mathrm{4}\:{boys}\:{and}\:\mathrm{3}\:{girls}\:{give}\:{the}\:{number} \\ $$$${of}\:{ways}\:{these}\:{can}\:{be}\:{done} \\ $$

Question Number 37692 Answers: 2 Comments: 0

2+6+12+20+30+42+.........+n=(1/3)(n)(n−1)(n−2) is this true. if yes so please derive it from L.H.S hey I just noticed I got 15yrs and 5 months older

$$\mathrm{2}+\mathrm{6}+\mathrm{12}+\mathrm{20}+\mathrm{30}+\mathrm{42}+.........+\mathrm{n}=\frac{\mathrm{1}}{\mathrm{3}}\left(\mathrm{n}\right)\left(\mathrm{n}−\mathrm{1}\right)\left(\mathrm{n}−\mathrm{2}\right) \\ $$$$\mathrm{is}\:\mathrm{this}\:\mathrm{true}.\:\mathrm{if}\:\mathrm{yes}\:\mathrm{so}\:\mathrm{please}\:\mathrm{derive}\:\mathrm{it}\:\mathrm{from}\:\mathrm{L}.\mathrm{H}.\mathrm{S} \\ $$$$\mathrm{hey}\:\mathrm{I}\:\mathrm{just}\:\mathrm{noticed}\:\mathrm{I}\:\mathrm{got}\:\mathrm{15yrs}\:\mathrm{and}\:\:\mathrm{5}\:\mathrm{months}\:\mathrm{older} \\ $$

Question Number 37691 Answers: 0 Comments: 2

Sir Aifour, I just answered your question number 37209... greetings from a rainy Saturday evening in Vienna, Austria!

$$\mathrm{Sir}\:\mathrm{Aifour},\:\mathrm{I}\:\mathrm{just}\:\mathrm{answered}\:\mathrm{your}\:\mathrm{question} \\ $$$$\mathrm{number}\:\mathrm{37209}...\:\mathrm{greetings}\:\mathrm{from}\:\mathrm{a}\:\mathrm{rainy} \\ $$$$\mathrm{Saturday}\:\mathrm{evening}\:\mathrm{in}\:\mathrm{Vienna},\:\mathrm{Austria}! \\ $$

Question Number 37664 Answers: 1 Comments: 0

find ∫(1 + sinx)dx

$$\mathrm{find}\:\int\left(\mathrm{1}\:+\:{sinx}\right){dx} \\ $$

Question Number 37663 Answers: 3 Comments: 0

show that ((sin2A)/(1+cos2A)) = tanA.

$$\mathrm{show}\:\mathrm{that}\:\frac{{sin}\mathrm{2}{A}}{\mathrm{1}+{cos}\mathrm{2}{A}}\:=\:\mathrm{tanA}. \\ $$

Question Number 37662 Answers: 1 Comments: 0

Given that y=x^2 cosx, find (dy/(dx )), simplifying your answer as far as posible

$$\:\mathrm{Given}\:\mathrm{that}\:{y}={x}^{\mathrm{2}} {cosx}, \\ $$$$\mathrm{find}\:\frac{\boldsymbol{{dy}}}{\boldsymbol{{dx}}\:},\:\mathrm{simplifying}\:\mathrm{your}\:\mathrm{answer} \\ $$$$\mathrm{as}\:\mathrm{far}\:\mathrm{as}\:\mathrm{posible} \\ $$

Question Number 37661 Answers: 1 Comments: 0

Given the lines l_1 : r= −5i + 2j + s(3i−j) l_2 : r= −2i+j + t(2i+j) Find the cosine of the angle between l_1 and l_2 .

$$\mathrm{Given}\:\mathrm{the}\:\mathrm{lines}\: \\ $$$${l}_{\mathrm{1}} :\:\mathrm{r}=\:−\mathrm{5}{i}\:+\:\mathrm{2}{j}\:+\:{s}\left(\mathrm{3}{i}−{j}\right) \\ $$$${l}_{\mathrm{2}} :\:{r}=\:−\mathrm{2}{i}+{j}\:+\:{t}\left(\mathrm{2}{i}+{j}\right) \\ $$$${F}\mathrm{ind}\:\mathrm{the}\:\mathrm{cosine}\:\mathrm{of}\:\mathrm{the}\:\mathrm{angle} \\ $$$$\mathrm{between}\:{l}_{\mathrm{1}} \:{and}\:{l}_{\mathrm{2}} . \\ $$

Question Number 37658 Answers: 0 Comments: 0

Question Number 37652 Answers: 0 Comments: 0

A car,of mass 1000kg,has an engine capable of developing power of 15Kw against a constand Resistance R N.The maximum speed of the car on level road is ((100)/3) ms^(−1) Calculate the value of R. Given that the resistance and the power remain unchanged find the maximum speed of the car up a plane which is inclinded at an angle θ to the horizontal,where Sin θ= (1/(25)).

$$\mathrm{A}\:\mathrm{car},\mathrm{of}\:\mathrm{mass}\:\mathrm{1000kg},\mathrm{has}\:\mathrm{an}\:\mathrm{engine} \\ $$$$\mathrm{capable}\:\mathrm{of}\:\mathrm{developing}\:\mathrm{power}\:\mathrm{of}\: \\ $$$$\mathrm{15Kw}\:\mathrm{against}\:\mathrm{a}\:\mathrm{constand}\:\mathrm{Resistance} \\ $$$$\mathrm{R}\:\mathrm{N}.\mathrm{The}\:\mathrm{maximum}\:\mathrm{speed}\:\mathrm{of}\:\mathrm{the}\:\mathrm{car} \\ $$$$\mathrm{on}\:\mathrm{level}\:\mathrm{road}\:\mathrm{is}\:\frac{\mathrm{100}}{\mathrm{3}}\:{ms}^{−\mathrm{1}} \: \\ $$$$\mathrm{Calculate}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{R}. \\ $$$$\mathrm{Given}\:\mathrm{that}\:\mathrm{the}\:\mathrm{resistance}\:\mathrm{and}\:\mathrm{the}\:\mathrm{power} \\ $$$$\mathrm{remain}\:\mathrm{unchanged} \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{maximum}\:\mathrm{speed}\:\mathrm{of}\:\mathrm{the}\:\mathrm{car} \\ $$$$\mathrm{up}\:\mathrm{a}\:\mathrm{plane}\:\mathrm{which}\:\mathrm{is}\:\mathrm{inclinded}\:\mathrm{at}\:\mathrm{an} \\ $$$$\mathrm{angle}\:\theta\:\mathrm{to}\:\mathrm{the}\:\mathrm{horizontal},\mathrm{where}\: \\ $$$$\mathrm{Sin}\:\theta=\:\frac{\mathrm{1}}{\mathrm{25}}. \\ $$

Question Number 37649 Answers: 1 Comments: 0

Question Number 37648 Answers: 1 Comments: 0

A particle, of mass 5kg,moves in a straight line its displacement,x metres after t seconds is given by x = t^3 − 4t^2 +4t. Find the magnitude of the impulses exerted on the particle when t=2.

$$\mathrm{A}\:\mathrm{particle},\:\mathrm{of}\:\mathrm{mass}\:\mathrm{5kg},\mathrm{moves}\:\mathrm{in} \\ $$$$\mathrm{a}\:\mathrm{straight}\:\mathrm{line}\:\mathrm{its}\:\mathrm{displacement},\mathrm{x} \\ $$$$\mathrm{metres}\:\mathrm{after}\:\mathrm{t}\:\mathrm{seconds}\:\mathrm{is}\:\mathrm{given}\:\mathrm{by} \\ $$$${x}\:=\:{t}^{\mathrm{3}} −\:\mathrm{4}{t}^{\mathrm{2}} +\mathrm{4}{t}.\:{F}\mathrm{ind}\:\:\mathrm{the}\:\mathrm{magnitude} \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{impulses}\:\mathrm{exerted}\:\mathrm{on}\:\mathrm{the}\:\mathrm{particle} \\ $$$$\mathrm{when}\:\mathrm{t}=\mathrm{2}. \\ $$

Question Number 37645 Answers: 1 Comments: 0

Question Number 37642 Answers: 1 Comments: 0

3^(3(√(250))+7^(3(√(16))−4^(3(√(54))) ) )

$$\mathrm{3}^{\mathrm{3}\sqrt{\mathrm{250}}+\mathrm{7}^{\mathrm{3}\sqrt{\mathrm{16}}−\mathrm{4}^{\mathrm{3}\sqrt{\mathrm{54}}} } } \\ $$

Question Number 37636 Answers: 1 Comments: 1

find ∫_0 ^6 (x^2 −x+1)e^([−2x]) dx .

$${find}\:\:\int_{\mathrm{0}} ^{\mathrm{6}} \left({x}^{\mathrm{2}} −{x}+\mathrm{1}\right){e}^{\left[−\mathrm{2}{x}\right]} {dx}\:. \\ $$

Question Number 37635 Answers: 0 Comments: 1

let a>0 find the value of f(a) = ∫_0 ^(+∞) e^(−(t^2 +(a/t^2 ))) dt

$${let}\:{a}>\mathrm{0}\:\:{find}\:{the}\:{value}\:{of}\: \\ $$$${f}\left({a}\right)\:=\:\int_{\mathrm{0}} ^{+\infty} \:{e}^{−\left({t}^{\mathrm{2}} \:\:+\frac{{a}}{{t}^{\mathrm{2}} }\right)} {dt}\: \\ $$

Question Number 37634 Answers: 1 Comments: 1

find ∫_0 ^(+∞) e^(−(t^2 +(1/t^2 ))) dt

$${find}\:\int_{\mathrm{0}} ^{+\infty} \:\:{e}^{−\left({t}^{\mathrm{2}} \:+\frac{\mathrm{1}}{{t}^{\mathrm{2}} }\right)} {dt} \\ $$

Question Number 37633 Answers: 1 Comments: 0

find ∫_0 ^(+∞) [ x e^(−x) ]dx

$${find}\:\:\int_{\mathrm{0}} ^{+\infty} \left[\:\:{x}\:{e}^{−{x}} \right]{dx} \\ $$

Question Number 37632 Answers: 1 Comments: 1

Question Number 37627 Answers: 3 Comments: 0

Given {x} = x − ⌊x⌋ How many real solutions from equation {x} + {x^2 } = 1 with −10 ≤ x ≤ 10 ?

$$\mathrm{Given}\:\left\{{x}\right\}\:=\:{x}\:−\:\lfloor{x}\rfloor \\ $$$$\mathrm{How}\:\mathrm{many}\:\mathrm{real}\:\mathrm{solutions}\:\mathrm{from}\:\mathrm{equation} \\ $$$$\left\{{x}\right\}\:+\:\left\{{x}^{\mathrm{2}} \right\}\:=\:\mathrm{1} \\ $$$$\mathrm{with}\:−\mathrm{10}\:\leqslant\:{x}\:\leqslant\:\mathrm{10}\:? \\ $$

Question Number 37602 Answers: 0 Comments: 4

find the value of f(a)= ∫_0 ^∞ ((x^2 −1)/((x^4 +a^4 )^2 ))dx 2) calculate ∫_0 ^∞ ((x^2 −1)/((x^4 +1)^2 ))dx

$${find}\:{the}\:{value}\:{of} \\ $$$${f}\left({a}\right)=\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{x}^{\mathrm{2}} −\mathrm{1}}{\left({x}^{\mathrm{4}} \:\:\:+{a}^{\mathrm{4}} \right)^{\mathrm{2}} }{dx} \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\:\:\int_{\mathrm{0}} ^{\infty} \:\:\:\:\:\:\frac{{x}^{\mathrm{2}} \:−\mathrm{1}}{\left({x}^{\mathrm{4}} \:+\mathrm{1}\right)^{\mathrm{2}} }{dx} \\ $$

Question Number 37601 Answers: 0 Comments: 2

let give n inyehr natural≥1 find tbe value of A_n = ∫_0 ^∞ (dx/((x^2 +1)(x^(2 ) +2)....(x^2 +n)))

$${let}\:{give}\:{n}\:{inyehr}\:{natural}\geqslant\mathrm{1}\:{find}\:{tbe}\:{value}\:{of} \\ $$$${A}_{{n}} =\:\int_{\mathrm{0}} ^{\infty} \:\:\:\:\:\:\:\frac{{dx}}{\left({x}^{\mathrm{2}} +\mathrm{1}\right)\left({x}^{\mathrm{2}\:} +\mathrm{2}\right)....\left({x}^{\mathrm{2}} \:+{n}\right)} \\ $$

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