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A fixed wire is in the shape of the cardioid $r = a(1+cos\theta)$, the initial line being the downward vertical.

asked Dec 23, 2017

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Consider the following system of equations in $x, y, z$ :

asked Dec 22, 2017

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Prove that distinct non-zero eigenvectors of a matrix are linearly independent.

asked Dec 22, 2017

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Find a basis and dimension of the image of $A$ and those of the kernel $A$.

asked Dec 22, 2017

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Find the possible dimensions of subspace $U \cap W$

asked Dec 22, 2017

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Assign the programs to the programmers in such a way that total computer time is least.

asked Dec 21, 2017

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Solve by simplex method the following LPP: Minimize $Z = x_1 - 3x_2 + 2x_3$

asked Dec 21, 2017

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Find the initial basic feasible solution of the following transportation problem using Vogel's approximation method.

asked Dec 21, 2017

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Solve the following linear programming problem by simplex method: Maximize $z= 3x_1+5x_2+4x_3$

asked Dec 21, 2017

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Show that the groups $Z_5 \times Z_7$ and $Z_{35}$ are isomorphic.

asked Nov 25, 2017

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Let $F$ be a field and $F[X]$ denote the ring of polynomials over $F$ in a single variable $X ... $.

asked Nov 25, 2017

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Using contour integral method, prove that $\int_{0}^{\infty} \frac{x \sin mx}{a^2 + x^2} dx = \frac{\pi}{2} e^{-ma}$.

asked Nov 25, 2017

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Let $f(t) = \int_{0}^{t} [x] dx$. Value of $t$ for continuity and differentiability?

asked Nov 25, 2017

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Using graphical method, find the maximum value of $2x+y$ subject to given constraints.

asked Nov 25, 2017

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Determine all entire functions $f(z)$ such that $0$ is a removable singularity of $f\left( \frac{1}{z} \right)$.

asked Nov 25, 2017

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Find the supremum and the infimum of $\frac{x}{\sin x}$ on the interval $\left (0, \frac{\pi}{2} \right ]$.

asked Nov 25, 2017

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Let $G$ be a group of order $n$. Show that $G$ is isomorphic to a subgroup of the permutation group $S_n$.

asked Nov 25, 2017

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Convergence of sequence: $x_1 = 2$ and $x_{n+1} = \sqrt{x_n+20}$

asked Nov 25, 2017

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How much bacteria after 4 weeks if they double in 1 week?

asked Nov 12, 2017

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Reduce the equation to $xyp^2 - (x^2+y^2-1)p+xy = 0$ Clairaut's form.

asked Nov 12, 2017

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