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Question Number 182900 Answers: 1 Comments: 0

Determine the values of b so that the system of linear equations { ((x+2y+z=1)),((2x+by+2z=2)),((4x+8y+b^2 z=2b)) :} has (a) no solution (b) a unique solution (c) infinitely many solutions

$$\:{Determine}\:{the}\:{values}\:{of}\:{b}\:{so}\:{that} \\ $$$$\:{the}\:{system}\:{of}\:{linear}\:{equations} \\ $$$$\:\begin{cases}{{x}+\mathrm{2}{y}+{z}=\mathrm{1}}\\{\mathrm{2}{x}+{by}+\mathrm{2}{z}=\mathrm{2}}\\{\mathrm{4}{x}+\mathrm{8}{y}+{b}^{\mathrm{2}} \:{z}=\mathrm{2}{b}}\end{cases} \\ $$$$\:{has}\:\left({a}\right)\:{no}\:{solution}\: \\ $$$$\:\left({b}\right)\:{a}\:{unique}\:{solution} \\ $$$$\:\left({c}\right)\:{infinitely}\:{many}\:{solutions} \\ $$

Question Number 182896 Answers: 1 Comments: 1

Question Number 182895 Answers: 2 Comments: 0

Question Number 182902 Answers: 0 Comments: 0

∫ x^x dx

$$\int\:\boldsymbol{\mathrm{x}}^{\boldsymbol{\mathrm{x}}} \:\:\boldsymbol{\mathrm{dx}} \\ $$

Question Number 182891 Answers: 1 Comments: 0

∫_(0 ) ^∞ e^x ((sinmx)/x)dx=?

$$\int_{\mathrm{0}\:\:} ^{\infty} {e}^{{x}} \frac{{sinmx}}{{x}}{dx}=? \\ $$

Question Number 182890 Answers: 0 Comments: 0

Find the formula in terms of n S_n =Σ_(j=1) ^∞ (1/(Π_(k=0) ^n (j+k)))

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{formula}\:\mathrm{in}\:\mathrm{terms}\:\mathrm{of}\:{n} \\ $$$${S}_{{n}} =\underset{{j}=\mathrm{1}} {\overset{\infty} {\sum}}\:\frac{\mathrm{1}}{\underset{{k}=\mathrm{0}} {\overset{{n}} {\prod}}\:\left({j}+{k}\right)} \\ $$

Question Number 182888 Answers: 1 Comments: 0

A spring with length L and spring constant k is fixed on the ceiling. Hang a mass point m on the bottom of the spring. Find the relation between distsnce h from m to ceiling and time t. Ignore air resistance, friction and gravity of spring.

$$\mathrm{A}\:\mathrm{spring}\:\mathrm{with}\:\mathrm{length}\:{L}\:\mathrm{and}\:\mathrm{spring}\:\mathrm{constant}\:{k} \\ $$$$\mathrm{is}\:\mathrm{fixed}\:\mathrm{on}\:\mathrm{the}\:\mathrm{ceiling}.\:\mathrm{Hang}\:\mathrm{a}\:\mathrm{mass}\:\mathrm{point}\:{m} \\ $$$$\mathrm{on}\:\mathrm{the}\:\mathrm{bottom}\:\mathrm{of}\:\mathrm{the}\:\mathrm{spring}.\:\mathrm{Find}\:\mathrm{the} \\ $$$$\mathrm{relation}\:\mathrm{between}\:\mathrm{distsnce}\:{h}\:\mathrm{from}\:{m}\:\mathrm{to}\:\mathrm{ceiling} \\ $$$$\mathrm{and}\:\mathrm{time}\:{t}.\:\mathrm{Ignore}\:\mathrm{air}\:\mathrm{resistance},\:\mathrm{friction}\:\mathrm{and} \\ $$$$\mathrm{gravity}\:\mathrm{of}\:\mathrm{spring}. \\ $$

Question Number 182875 Answers: 2 Comments: 0

Find the value of S: S = 1 + (1/(1×2)) + (1/(2×3)) + (1/(3×4)) ...

$$ \\ $$$$\:{Find}\:{the}\:{value}\:{of}\:{S}: \\ $$$$\:{S}\:=\:\mathrm{1}\:+\:\frac{\mathrm{1}}{\mathrm{1}×\mathrm{2}}\:+\:\frac{\mathrm{1}}{\mathrm{2}×\mathrm{3}}\:+\:\frac{\mathrm{1}}{\mathrm{3}×\mathrm{4}}\:... \\ $$$$\: \\ $$

Question Number 182874 Answers: 1 Comments: 0

Question Number 182866 Answers: 1 Comments: 0

Question Number 184377 Answers: 1 Comments: 1

Question Number 182854 Answers: 0 Comments: 7

(sin54)^(10) =x_1 x_(1 ) is root ax^2 +bx+c=0 a,b,c is integer a=?

$$\left({sin}\mathrm{54}\right)^{\mathrm{10}} ={x}_{\mathrm{1}} \:\:\:\:{x}_{\mathrm{1}\:\:} {is}\:{root} \\ $$$${ax}^{\mathrm{2}} +{bx}+{c}=\mathrm{0} \\ $$$$\:\:{a},{b},{c}\:\:\:{is}\:{integer} \\ $$$${a}=? \\ $$

Question Number 182852 Answers: 3 Comments: 2

challanging question.. if , (1/( 1+(√(1−x+x^( 2) )))) −(x/(1+(√(1+x+x^( 2) ))))=1 find the value of : (x/(x^( 2) +1))

$$ \\ $$$$\:{challanging}\:{question}.. \\ $$$$\:\:{if}\:\:\:,\:\frac{\mathrm{1}}{\:\mathrm{1}+\sqrt{\mathrm{1}−{x}+{x}^{\:\mathrm{2}} }}\:−\frac{{x}}{\mathrm{1}+\sqrt{\mathrm{1}+{x}+{x}^{\:\mathrm{2}} }}=\mathrm{1} \\ $$$$\:\:\:{find}\:\:{the}\:\:{value}\:{of}\::\:\:\:\frac{{x}}{{x}^{\:\mathrm{2}} +\mathrm{1}} \\ $$$$ \\ $$

Question Number 182848 Answers: 3 Comments: 0

((sin^3 x−sin x+cos x)/(sin x))=cot x −cos^2 x prove this

$$\frac{{sin}^{\mathrm{3}} {x}−{sin}\:{x}+{cos}\:{x}}{{sin}\:{x}}={cot}\:{x}\:−{cos}^{\mathrm{2}} {x} \\ $$$${prove}\:{this} \\ $$$$ \\ $$$$ \\ $$

Question Number 182842 Answers: 3 Comments: 0

prove that sec(tan^(−1) x)=(√(x^2 +1))

$${prove}\:{that} \\ $$$${sec}\left({tan}^{−\mathrm{1}} {x}\right)=\sqrt{{x}^{\mathrm{2}} +\mathrm{1}} \\ $$

Question Number 182838 Answers: 0 Comments: 0

$$ \\ $$

Question Number 182836 Answers: 2 Comments: 0

Question Number 182835 Answers: 1 Comments: 0

s(n)=Σ_(n=1) ^(+oo) (((−1)^n +n^2 )/(n!))x^n =?

$${s}\left({n}\right)=\underset{{n}=\mathrm{1}} {\overset{+{oo}} {\sum}}\:\frac{\left(−\mathrm{1}\right)^{{n}} \:+{n}^{\mathrm{2}} }{{n}!}{x}^{{n}} \:=? \\ $$

Question Number 182829 Answers: 3 Comments: 0

Question Number 182811 Answers: 0 Comments: 0

Question Number 182810 Answers: 2 Comments: 0

What is the value of this infinite sum ((1/2)−(1/3))+((1/2^2 )−(1/3^2 ))+((1/2^3 )−(1/3^3 ))+...

$$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{this}\:\mathrm{infinite}\:\mathrm{sum} \\ $$$$\left(\frac{\mathrm{1}}{\mathrm{2}}−\frac{\mathrm{1}}{\mathrm{3}}\right)+\left(\frac{\mathrm{1}}{\mathrm{2}^{\mathrm{2}} }−\frac{\mathrm{1}}{\mathrm{3}^{\mathrm{2}} }\right)+\left(\frac{\mathrm{1}}{\mathrm{2}^{\mathrm{3}} }−\frac{\mathrm{1}}{\mathrm{3}^{\mathrm{3}} }\right)+... \\ $$$$ \\ $$$$ \\ $$

Question Number 182809 Answers: 0 Comments: 0

Question Number 182804 Answers: 2 Comments: 0

solve ⌊x_ ^ ⌋ − ⌊ (x/3) ⌋ = 3

$$ \\ $$$$\:\:\:\:{solve} \\ $$$$\:\:\:\:\lfloor\underset{} {\overset{} {{x}}}\:\rfloor\:−\:\lfloor\:\frac{{x}}{\mathrm{3}}\:\rfloor\:=\:\mathrm{3} \\ $$$$\:\:\:\:\:\:\: \\ $$

Question Number 182803 Answers: 0 Comments: 0

write an 8085 mp assembly language program to separate even numbers from a list of 10 numbers and store them in another list starting from (2300H). assume starting address of 10 numbers list is (2200H).

$${write}\:{an}\:\mathrm{8085}\:{mp}\:{assembly}\:{language}\:{program} \\ $$$${to}\:{separate}\:{even}\:{numbers}\:{from}\:{a}\:{list}\:{of} \\ $$$$\mathrm{10}\:{numbers}\:{and}\:{store}\:{them}\:{in}\:{another} \\ $$$${list}\:{starting}\:{from}\:\left(\mathrm{2300}{H}\right).\:{assume}\:{starting} \\ $$$${address}\:{of}\:\mathrm{10}\:{numbers}\:{list}\:{is}\:\left(\mathrm{2200}{H}\right). \\ $$

Question Number 182797 Answers: 0 Comments: 1

find the max and min value f(x,y,z) = x^3 +y^3 +z^3 −9xy−9xz+27x

$$\:\mathrm{find}\:\:\mathrm{the}\:\mathrm{max}\:\mathrm{and}\:\:\mathrm{min}\:\mathrm{value} \\ $$$$\:\mathrm{f}\left(\mathrm{x},\mathrm{y},\mathrm{z}\right)\:=\:\mathrm{x}^{\mathrm{3}} +\mathrm{y}^{\mathrm{3}} +\mathrm{z}^{\mathrm{3}} −\mathrm{9xy}−\mathrm{9xz}+\mathrm{27x} \\ $$

Question Number 182794 Answers: 1 Comments: 0

Ω = Σ_(n=1) ^∞ (( (−1_ ^ )^( n) )/(2^( n) .n(n+_ ^ 1)(n+_ ^ 2))) = ?

$$ \\ $$$$\:\:\:\:\:\:\:\Omega\:=\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\:\frac{\:\left(−\underset{} {\overset{} {\mathrm{1}}}\:\right)^{\:{n}} }{\mathrm{2}^{\:{n}} .{n}\left({n}\underset{} {\overset{} {+}}\mathrm{1}\right)\left({n}\underset{} {\overset{} {+}}\mathrm{2}\right)}\:=\:?\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\: \\ $$$$ \\ $$

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