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Let x̅1 and x̅2 (where x̅2 > x̅1) be the means of two sets comprising n1 and n2 (where n2 < n1) observations respectively. If x̅ is the mean when they are pooled, then which one of the following is correct?
If a complex number z, with integral real and imaginary parts, satisfies z2+ z̅2=16, then find the value of |z|.
Laplace transform of the function f(t) is given by $${\text{F}}\left( {\text{s}} \right) = {\text{L}}\left\{ {{\text{f}}\left( {\text{t}} \right)} \right\} = \int_0^\infty {{\text{f}}\left( {\text{t}} \right){{\text{e}}^{ - {\text{st}}}}{\text{dt}}{\text{.}}} $$       Laplace transform of the function shown below is given by
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Consider the following remarks pertaining to the irrotational flow: 1. The Laplace equation of stream function \(\frac{{{\delta ^2}{\rm{\Psi }}}}{{\delta {x^2}}} + \frac{{{\delta ^2}{\rm{\Psi }}}}{{\delta {y^2}}} = 0\) must be satisfied for the flow to be potential. 2. The Laplace equation for the velocity potential \(\frac{{{\delta ^2}{\rm{\varphi }}}}{{\delta {x^2}}} + \frac{{{\delta ^2}{\rm{\varphi }}}}{{\delta {y^2}}} = 0\) must be satisfied to fulfil the orate . of mass conservation i.e continuity equation.. Which of the above statements is/are correct?
The value of y which satisfies the equation 5(y + 3) + 7(3y + 2) = (30y + 17) Also satisfies the equation
The value of x which satisfies the equation 10 (x + 6) + 8(x - 3) = 5(5x - 4) Also satisfies the equation
Given the potential V = 25 sin θ, in free space, determine whether V satisfies Laplace’s equation.
The function f(t) satisfies the differential equation $$\frac{{{{\text{d}}^2}{\text{f}}}}{{{\text{d}}{{\text{t}}^2}}} + {\text{f}} = 0$$   and the auxiliary conditions, f(0) = 0, $$\frac{{{\text{df}}}}{{{\text{dt}}}}\left( 0 \right) = 4.$$  The Laplace transform of f(t) is given by
When a potential satisfies Laplace equation, then it is said to be
If Laplace equation satisfies, then which of the following statements will be true?