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Recent questions tagged p198

The length $x$ of a rectangle is decreasing at the rate of 5 cm/minute and the width y is increasing at the rate of 4 cm/minute. When $x = 8$ cm and $y = 6$ cm, find the rates of change of (b) the area of the triangle.

asked Jul 5, 2013 by sreemathi.v

1 answer

The solution of $x \large\frac{dy}{dx}$$+y=e^x$ is:\[(A)\;y=\frac{e^x}{x}+\frac{k}{x} \quad (B)\;y=xe^x+cx \quad (C)\;y=xe^x+k \quad (D)\;x=\frac{e^y}{y}-\frac{k}{y}\]

asked Jan 19, 2013 by sreemathi.v

1 answer

The solution of the differential equation $\cos x\sin y\;dx+\sin x\cos y\;dy=0$ is:

asked Jan 19, 2013 by sreemathi.v

1 answer

$y=ae^{mx}+be^{-mx}$ satisfies which of the following differential equation?

asked Jan 18, 2013 by sreemathi.v

1 answer

The integrating factor of the differential equation $\Large \frac{dy}{dx}\normalsize+y=\Large \frac{1+y}{x}$ is

asked Jan 18, 2013 by sreemathi.v

1 answer

The solution of the differential equation $\Large \frac{dy}{dx}=\frac{1-y^2}{1-x^2}$ is:\begin{array}{1 1}(A)\;y=\tan^{-1}x & (B)\;y-x=k(1+xy)\\(C)\;x=tan^{-1}y & (D)\;\tan (xy)=k\end{array}

asked Jan 18, 2013 by sreemathi.v

1 answer

Integrating factor of the differential equation $\large\frac{dy}{dx}$$+y\tan x-\sec x=0$ is \begin{array}{1 1}(A)\;\cos x & (B)\;sec x\\(C)\;e^{\cos x} & (D)\;e^{\sec x} \end{array}

asked Jan 18, 2013 by sreemathi.v

1 answer

Choose the correct answer in the rate of change of the area of a circle with respect to its radius $r$ at $r = 6$ cm is

asked Nov 23, 2012 by thanvigandhi_1

1 answer

The total revenue in Rupees received from the sale of $x$ units of a product is given by $ R(x) = 13x^2 + 26x + 15.$ Find the marginal revenue when $x = 7$.

asked Nov 23, 2012 by thanvigandhi_1

1 answer

The total cost $C(x)$ in Rupees associated with the production of $x$ units of an item is given by $ C(x) = 0.007x^3 - 0.003x^2 + 15x + 4000.$ Find the marginal cost when 17 units are produced.

asked Nov 23, 2012 by thanvigandhi_1

1 answer

Sand is pouring from a pipe at the rate of $12 cm^3/s$. The falling sand forms a cone on the ground in such a way that the height of the cone is always one-sixth of the radius of the base. How fast is the height of the sand cone increasing when the height is 4 cm?

asked Nov 23, 2012 by thanvigandhi_1

1 answer

A balloon, which always remains spherical, has a variable diameter $\large\frac{3}{2}$$(2x+1)$. Find the rate of change of its volume with respect to $x.$

asked Nov 23, 2012 by thanvigandhi_1

1 answer

The radius of an air bubble is increasing at the rate of $ \large\frac{1}{2}$ cm/s. At what rate is the volume of the bubble increasing when the radius is $1\; cm$?

asked Nov 23, 2012 by thanvigandhi_1

1 answer

A particle moves along the curve $ 6y = x^3 +2$. Find the points on the curve at which the $y$-coordinate is changing $8$ times as fast as the $x$-coordinate.

asked Nov 23, 2012 by thanvigandhi_1

1 answer

A ladder 5 m long is leaning against a wall. The bottom of the ladder is pulled along the ground, away from the wall, at the rate of 2cm/s. How fast is its height on the wall decreasing when the foot of the ladder is 4 m away from the wall ?

asked Nov 23, 2012 by thanvigandhi_1

1 answer

A balloon, which always remains spherical has a variable radius. Find the rate at which its volume is increasing with the radius when the later is $10\; cm$.

asked Nov 22, 2012 by thanvigandhi_1

1 answer

A balloon, which always remains spherical on inflation, is being inflated by pumping in $900$ cubic centimetres of gas per second. Find the rate at which the radius of the balloon increases when the radius is $15\; cm$.

asked Nov 22, 2012 by thanvigandhi_1

1 answer

The length $x$ of a rectangle is decreasing at the rate of $5\; cm/minute$ and the width y is increasing at the rate of $4\; cm/minute$. When $x = 8$ cm and $y = 6$ cm, find the rates of change of (a) the perimeter

asked Nov 22, 2012 by thanvigandhi_1

1 answer

The radius of a circle is increasing at the rate of $0.7\; cm/s$. What is the rate of increase of its circumference?

asked Nov 22, 2012 by thanvigandhi_1

1 answer

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