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Question Number 182949 Answers: 0 Comments: 0

if z(z^2 +3x)+xy=0 show that (d^2 z/dx^2 )+(d^2 z/dy^2 ) = ((2x(x−1))/((z^2 +3)^3 ))

$$\mathrm{if}\:\mathrm{z}\left(\mathrm{z}^{\mathrm{2}} +\mathrm{3x}\right)+\mathrm{xy}=\mathrm{0}\:\mathrm{show}\:\mathrm{that} \\ $$$$\frac{\mathrm{d}^{\mathrm{2}} \mathrm{z}}{\mathrm{dx}^{\mathrm{2}} }+\frac{\mathrm{d}^{\mathrm{2}} \mathrm{z}}{\mathrm{dy}^{\mathrm{2}} }\:=\:\frac{\mathrm{2x}\left(\mathrm{x}−\mathrm{1}\right)}{\left(\mathrm{z}^{\mathrm{2}} +\mathrm{3}\right)^{\mathrm{3}} } \\ $$

Question Number 182947 Answers: 1 Comments: 1

If a< b<0, then ∣a−b∣ + ∣a+b∣ + ∣ab∣=

$$\mathrm{If}\:\:\mathrm{a}<\:\mathrm{b}<\mathrm{0},\:\:\mathrm{then}\:\:\mid\mathrm{a}−\mathrm{b}\mid\:+\:\mid\mathrm{a}+\mathrm{b}\mid\:+\:\mid\mathrm{ab}\mid= \\ $$

Question Number 182946 Answers: 1 Comments: 1

If 0 < x <1 , then ∣ x −1 ∣ + ∣2x−4∣ + ∣2x+1∣=

$$\mathrm{If}\:\:\mathrm{0}\:<\:\mathrm{x}\:<\mathrm{1}\:,\:\:\mathrm{then}\:\:\mid\:\mathrm{x}\:−\mathrm{1}\:\mid\:+\:\mid\mathrm{2x}−\mathrm{4}\mid\:+\:\mid\mathrm{2x}+\mathrm{1}\mid= \\ $$

Question Number 182941 Answers: 0 Comments: 0

Solve: [x^2 +(xy^2 )^(1/3) ](dy/dx)=y M.m

$$\mathrm{Solve}: \\ $$$$\left[\mathrm{x}^{\mathrm{2}} +\left(\mathrm{xy}^{\mathrm{2}} \right)^{\frac{\mathrm{1}}{\mathrm{3}}} \right]\frac{\mathrm{dy}}{\mathrm{dx}}=\mathrm{y} \\ $$$$ \\ $$$$ \\ $$$$\mathrm{M}.\mathrm{m} \\ $$

Question Number 182940 Answers: 2 Comments: 0

Are Σ_(n≥1) (1/(4n^2 −1)) and Σ_(n≥1) (1/(n(n+1)(n+2))) convergent?

$${Are}\:\underset{{n}\geqslant\mathrm{1}} {\sum}\frac{\mathrm{1}}{\mathrm{4}{n}^{\mathrm{2}} −\mathrm{1}}\:{and}\: \\ $$$$\underset{{n}\geqslant\mathrm{1}} {\sum}\:\:\frac{\mathrm{1}}{{n}\left({n}+\mathrm{1}\right)\left({n}+\mathrm{2}\right)}\:\:{convergent}? \\ $$

Question Number 182936 Answers: 0 Comments: 0

Question Number 182934 Answers: 1 Comments: 0

Is that right ! IF : Σ_(k = 1) ^n (⌊(n/k)⌋−⌊((n−1)/k)⌋) = 2 so n is a prime number .

$$\:\:\:\:\:\:\:\:{Is}\:{that}\:{right}\:! \\ $$$$\:\:\:\:{IF}\:\::\: \\ $$$$\underset{{k}\:=\:\mathrm{1}} {\overset{{n}} {\sum}}\:\left(\lfloor\frac{{n}}{{k}}\rfloor−\lfloor\frac{{n}−\mathrm{1}}{{k}}\rfloor\right)\:=\:\mathrm{2} \\ $$$$\:\:\:{so}\:{n}\:{is}\:{a}\:{prime}\:{number}\:. \\ $$

Question Number 182928 Answers: 6 Comments: 0

Question Number 182923 Answers: 0 Comments: 3

diameter of concave mirror=60cm p=10.5cm q=?

$${diameter}\:{of}\:{concave}\:{mirror}=\mathrm{60}{cm} \\ $$$${p}=\mathrm{10}.\mathrm{5}{cm} \\ $$$${q}=? \\ $$

Question Number 182922 Answers: 1 Comments: 0

solve ⌊ x ⌋ + ⌊ 2x ⌋ + ⌊ 3x ⌋ =1

$$ \\ $$$$\:\:\:{solve} \\ $$$$ \\ $$$$\:\:\:\lfloor\:{x}\:\rfloor\:+\:\lfloor\:\mathrm{2}{x}\:\rfloor\:+\:\lfloor\:\mathrm{3}{x}\:\rfloor\:=\mathrm{1} \\ $$$$ \\ $$

Question Number 182921 Answers: 0 Comments: 1

what are the examples of microscopic and macroscopic in physics?

$${what}\:{are}\:{the}\:{examples}\:{of}\:{microscopic} \\ $$$${and}\:{macroscopic}\:{in}\:{physics}? \\ $$

Question Number 194056 Answers: 2 Comments: 0

Question Number 182910 Answers: 1 Comments: 0

Question Number 182909 Answers: 0 Comments: 0

xε]−1,1[ calcul: Σ_(n=1) ^(+oo) (x^n /((1−x^n )(1−x^(n+1) )))

$$\left.{x}\epsilon\right]−\mathrm{1},\mathrm{1}\left[\:{calcul}:\right. \\ $$$$\underset{{n}=\mathrm{1}} {\overset{+{oo}} {\sum}}\frac{{x}^{{n}} }{\left(\mathrm{1}−{x}^{{n}} \right)\left(\mathrm{1}−{x}^{{n}+\mathrm{1}} \right)} \\ $$

Question Number 182907 Answers: 0 Comments: 0

2, 3, 5, 7, 11

$$\mathrm{2},\:\mathrm{3},\:\mathrm{5},\:\mathrm{7},\:\mathrm{11} \\ $$

Question Number 182906 Answers: 0 Comments: 0

2^(−1) =(1/2)

$$\mathrm{2}^{−\mathrm{1}} =\frac{\mathrm{1}}{\mathrm{2}} \\ $$

Question Number 182905 Answers: 0 Comments: 0

33

$$\mathrm{33} \\ $$

Question Number 182904 Answers: 1 Comments: 0

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)) ...

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

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