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Recent questions tagged p137

An open box with square base is to be made of a given quantity of card board of area $ 36 sq.metre.$ Find the maximum volume of the box.

asked Feb 4, 2014 by rvidyagovindarajan_1

1 answer

Find the equation of the curve passing through $(1 , 0 )$ and which has slope $1+\large\frac{y}{x}$ at $(x , y )$

asked Apr 15, 2013 by poojasapani_1

1 answer

Solve the following $(x^{2}+y^{2})dx+3xy dy$=$0$

asked Apr 15, 2013 by poojasapani_1

1 answer

Solve the following $x^{2}\large\frac{dy}{dx}$ =$ y^{2}+2xy$ given that $y=1,$ when $x=1$

asked Apr 15, 2013 by poojasapani_1

1 answer

Solve the following $\large\frac{dy}{dx}$=$\large\frac {y(x-2y)}{x(x-3y)}$

asked Apr 15, 2013 by poojasapani_1

1 answer

Solve the following $(x^{2}+y^{2})\;dy$ =$ xy \;dx$

asked Apr 15, 2013 by poojasapani_1

1 answer

Solve the following $\large\frac{dy}{dx}+\frac{y}{x}=\frac{y^{2}}{x^{2}}$

asked Apr 15, 2013 by poojasapani_1

1 answer

If $A = \begin{bmatrix} 2 & -3 & 5 \\ 3 & 2 & -4 \\ 1 & 1 & -2 \end{bmatrix} $ find \( A^{-1}\). Using \( A^{-1}\) solve the system of equations:\( 2x-3y+5z=11; 3x+2y-4z=-5; x+y-2z = -3\)

asked Feb 7, 2013 by thanvigandhi_1

0 answers

Find the dimentions of the rectangle of perimeter 36cm which will sweep out a volume as large as possible,when revolved about one of its sides.Also find the maximum volume.

asked Jan 11, 2013 by sreemathi.v

1 answer

An open box with square base is to be made of a given quantity of card board of area $ c^2$.Show that the maximum volume of the box is $\Large \frac{c^3}{6\sqrt 3}$ cubic units.

asked Jan 11, 2013 by sreemathi.v

1 answer

If the straight line $x\cos\alpha+y\sin\alpha=p$ touches the curve $\Large\frac{x^2}{a^2}\;\;\frac{y^2}{b^2}=\normalsize 1$,then prove that $a^2\cos^2\alpha+b^2\sin^2\alpha=p^2$.

asked Jan 11, 2013 by sreemathi.v

0 answers

A telephone company in a town has 500 subscribers on its list and collects fixed charges of Rs300/- per subscriber per year.The company proposes to increase the annual subscription and it is believed that for every increase of Re1/- one subscriber will discontinue the service.Find what increase will bring maximum profit?

asked Jan 11, 2013 by sreemathi.v

0 answers

Find the points of local maxima,local minima and the points of inflection of the function $f(x)=x^5-5x^4+5x^3-1$. Also find the corresponding local maximum and local minimum values.

asked Jan 11, 2013 by sreemathi.v

1 answer

If the sum of the lengths of the hypotenuse and a side of a right angled triangle is given,show that the area of the triangle is maximum when the angle between them is $\Large \frac{1}{3}$

asked Jan 11, 2013 by sreemathi.v

1 answer

Prove that $f(x)=\sin x+\sqrt 3\cos x$ has maximum value at $x=\Large\frac{1}{6}$.

asked Jan 11, 2013 by sreemathi.v

1 answer

At what point,the slope of the curve $y=-x^3+3x^2+9x-27$ is maximum?Also find the maximum slope.

asked Jan 11, 2013 by sreemathi.v

1 answer

Show that $f(x)=\tan^{-1}(\sin x+\cos x)$ is an increasing function in$\bigg(0,\Large \frac{1}{4}\normalsize \bigg).$

asked Jan 11, 2013 by sreemathi.v

1 answer

Show that for a$\quad 1,f(x)=\sqrt 3\sin x-\cos x-2ax+b$ is decreasing in R.

asked Jan 11, 2013 by sreemathi.v

1 answer

If \( A = \begin{bmatrix} 2 & -3 & 5 \\ 3 & 2 & -4 \\ 1 & 1 & -2 \end {bmatrix} \), find \( A^{-1} \) . Using \( A^{-1} \) , solve the system of equations : $ 2x – 3y + 5z = 11 ,3x + 2y – 4z = –5 ,x + y – 2x = –3. $

asked Dec 29, 2012 by thanvigandhi_1

0 answers

The cost of 4 kg onion, 3 kg wheat and 2 kg rice is Rs 60. The cost of 2 kg onion, 4 kg wheat and 6 kg rice is Rs 90. The cost of 6 kg onion 2 kg wheat and 3 kg rice is Rs 70. Find cost of each item per kg by matrix method.

asked Nov 29, 2012 by balaji.thirumalai

1 answer

If $A = \begin{bmatrix} 2 &-3 & 5\\ 3& 2 & -4\\ 1& 1& -2 \end{bmatrix}$, $\;$ find $A^{-1}.\;$ Using $ A^{-1}$ solve the system of equations: \[2x-3y+5z=11\] \[3x+2y-4z = -5\] \[x+y-2z = -3\]

asked Nov 29, 2012 by balaji.thirumalai

1 answer

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