Advertisements
Advertisements
प्रश्न
The side of a square is increasing at the rate of 0.1 cm/sec. Find the rate of increase of its perimeter ?
Advertisements
उत्तर
\[\text { Let x be the side and P be the perimeter of the square at any time t. Then },\]
\[P = 4x\]
\[ \Rightarrow \frac{dP}{dt} = 4\frac{dx}{dt}\]
\[ \Rightarrow \frac{dP}{dt} = 4 \times 0 . 1 \left[ \because\frac{dx}{dt}=0.1 cm/sec \right]\]
\[ \Rightarrow \frac{dP}{dt} = 0 . 4 cm/\sec\]
APPEARS IN
संबंधित प्रश्न
If y = f (u) is a differential function of u and u = g(x) is a differential function of x, then prove that y = f [g(x)] is a differential function of x and `dy/dx=dy/(du) xx (du)/dx`
The radius of a circle is increasing at the rate of 0.7 cm/s. What is the rate of increase of its circumference?
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.
Sand is pouring from a pipe at the rate of 12 cm3/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?
The total cost C(x) in rupees associated with the production of x units of an item is given by C(x) = 0.007x3 – 0.003x2 + 15x + 4000. Find the marginal cost when 17 units are produced
The rate of change of the area of a circle with respect to its radius r at r = 6 cm is ______.
The total revenue in rupees received from the sale of x units of a product is given by R(x) = 3x2 + 36x + 5. The marginal revenue, when x = 15 is ______.
The two equal sides of an isosceles triangle with fixed base b are decreasing at the rate of 3 cm per second. How fast is the area decreasing when the two equal sides are equal to the base?
The sum of the perimeter of a circle and square is k, where k is some constant. Prove that the sum of their areas is least when the side of square is double the radius of the circle.
Find the rate of change of the area of a circle with respect to its radius r when r = 5 cm
Find an angle θ which increases twice as fast as its cosine ?
A kite is 120 m high and 130 m of string is out. If the kite is moving away horizontally at the rate of 52 m/sec, find the rate at which the string is being paid out.
A particle moves along the curve y = (2/3)x3 + 1. Find the points on the curve at which the y-coordinate is changing twice as fast as the x-coordinate ?
Find the point on the curve y2 = 8x for which the abscissa and ordinate change at the same rate ?
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 the perimeter.
The side of an equilateral triangle is increasing at the rate of \[\frac{1}{3}\] cm/sec. Find the rate of increase of its perimeter ?
Find the surface area of a sphere when its volume is changing at the same rate as its radius ?
The radius of a sphere is changing at the rate of 0.1 cm/sec. The rate of change of its surface area when the radius is 200 cm is
For what values of x is the rate of increase of x3 − 5x2 + 5x + 8 is twice the rate of increase of x ?
The radius of the base of a cone is increasing at the rate of 3 cm/minute and the altitude is decreasing at the rate of 4 cm/minute. The rate of change of lateral surface when the radius = 7 cm and altitude 24 cm is
The distance moved by a particle travelling in straight line in t seconds is given by s = 45t + 11t2 − t3. The time taken by the particle to come to rest is
The diameter of a circle is increasing at the rate of 1 cm/sec. When its radius is π, the rate of increase of its area is
A man of height 6 ft walks at a uniform speed of 9 ft/sec from a lamp fixed at 15 ft height. The length of his shadow is increasing at the rate of
A ladder 13 m long is leaning against a vertical wall. The bottom of the ladder is dragged away from the wall along the ground at the rate of 2 cm/sec. How fast is the height on the wall decreasing when the foot of the ladder is 5 m away from the wall?
For the curve y = 5x – 2x3, if x increases at the rate of 2 units/sec, then how fast is the slope of curve changing when x = 3?
Water is dripping out at a steady rate of 1 cu cm/sec through a tiny hole at the vertex of the conical vessel, whose axis is vertical. When the slant height of water in the vessel is 4 cm, find the rate of decrease of slant height, where the vertical angle of the conical vessel is `pi/6`
Two men A and B start with velocities v at the same time from the junction of two roads inclined at 45° to each other. If they travel by different roads, find the rate at which they are being seperated.
x and y are the sides of two squares such that y = x – x2. Find the rate of change of the area of second square with respect to the area of first square.
A ladder, 5 meter long, standing on a horizontal floor, leans against a vertical wall. If the top of the ladder slides downwards at the rate of 10 cm/sec, then the rate at which the angle between the floor and the ladder is decreasing when lower end of ladder is 2 metres from the wall is ______.
The radius of a cylinder is increasing at the rate of 3 m/s and its height is decreasing at the rate of 4 m/s. The rate of change of volume when the radius is 4 m and height is 6 m, is ____________.
If the rate of change of volume of a sphere is equal to the rate of change of its radius then the surface area of a sphere is ____________.
The radius of a circle is increasing uniformly at the rate of 3 cm per second. Find the rate at which the area of the circle is increasing when the radius is 10 cm.
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 2 cm/s. How fast is its height on the wall decreasing when the foot of the ladder is 4 m away from the wall?
A spherical balloon is being inflated at the rate of 35 cc/min. The rate of increase in the surface area (in cm2/min.) of the balloon when its diameter is 14 cm, is ______.
The median of an equilateral triangle is increasing at the ratio of `2sqrt(3)` cm/s. Find the rate at which its side is increasing.
An edge of a variable cube is increasing at the rate of 10 cm/sec. How fast will the volume of the cube increase if the edge is 5 cm long?
