The turbine fan blade of a turbojet engine is 1.2 m in diameter and rotates at 250r/s. How fast is the tip of a blade moving?

Q: Can the distance traveled by a particle ever be less than its displacement? When are they equal?

A: No, the magnitude of the displacement is always less than or equal to the distance traveled.

Q: A water tank is in the form of an inverted right circular cone h feet deep and d feet wide across…

A: Consider the following:

Q: A pulley having a diameter of 36 cm is turned by a belt that moves at the rate of 5 m/sec. How many…

A: In one revolution the pulley will rotate by an angle of 360°. Hence, the belt will cover a distance…

Q: A Ferris wheel with a radius of 10 m is rotating at a rate of one revolution every 2 minutes. How…

A: the height is given byh = 10 sin (pi * t) + 10dh/dt = 10 cos (pi * t) * pi

Q: A ladder 10 ft long rests against a vertical wall. If the bottom of the ladder slides away from the…

A: Given: Length of a ladder which rests against a vertical wall is 10 ft. Let the distance between…

Q: A spherical balloon is inflated with air at a rate of 32 cm3/ min. At what rate does the radius…

A: Find dr/dr.

Q: Sugar is poured into a conical tank at the rate of 15cm3/sec whose bottom radius is always quarter…

A: The volume of a cone is given by the formula V=13πr2h. Where, V-volume, r-radius and h is the height…

Q: Find the rate at which the water level is rising when the water level is 2 cm.

A:

Q: A ladder 10 ft long rests against a vertical wall. If the bottom of the ladder slides away from the…

A: To find: The rate at which the angle between the ladder and the ground  is changing

Q: If a ball of candy is covered in chocolate and is melting so that its surface area decreases at a…

A: To find: The rate at which diameter decreases when diameter is 10 cm. Given: The rate of surface…

Q: Water is flowing at the rate of 9 ft3/min into a tank that is in the shape of a right circular…

A: Let r be the radius of base of cylinder, then r=2 ft .Let h be the height of water level at any time…

Q: Each side of a square is increasing at a rate of 6 cm/s. At what is the area of the square…

A: Given that, Area of square is  25cm2    Area A = x2 Where x is the side length. The area of square…

Q: A stone is thrown vertically upwards, from the edge of a 5 m tall cliff with an initial velocity of…

A:

Q: A thread is being pulled off a spool at the rate of 56.3cm per sec. Find the radius of the spool if…

A:

Q: Rain is falling into a cylindrical barrel at the rate of 20 cm3/min. If the radius of the base is 18…

A: Given,            Rain is falling into a cylindrical barrel at the rate of 20 cm3/min.…

Q: Question 4

A: Let a be the acceleration, v be the velocity, s be the position and t be the time of braking.

Q: Water is pouring from a hole at the rate of 25 cu. m per minute and is forming a conical pile on the…

A: This question can be solved by applying the concept of rate of change of physical quantities.

Q: An egg is thrown off the roof of a 60ft. building with an initial velocity of 6.5 ft/s. How long…

A: Given initial velocity = 6.5fts

Q: Water is flowing into a vertical cylindrical tank at the rate of 5 cu ft/min. If the radius of the…

A: Given, water is flowing into a vertical cylindrical tank at the rate of 5 cu ft/min (ie) Volume is…

Q: A snowball is melting at a rate of 2.4ft^3 hr^-1 – if the snowball remains a sphere throughout the…

A: given: A snowball is melting at a rate of 2.4ft3/hr. that implies dVdt=-2.4ft3/hr where V is the…

Q: A kite 100 ft above the ground moves horizontally at aspeed of 8 ft/s. At what rate is the angle…

A:

Q: A water trough is 10m long and a cross-section has the shape of an isosceles trapezoid that is 30cm…

A:

Q: 1000 liters of water per second is filled into the square prism-shaped tank with a base edge of 10…

A: We have to find the relating equation of volume with height and then differentiate it with respect…

Q: A rocket lifts off the surface of Earth with a constant acceleration of 20 m/sec2. How fast will the…

A:

Q: the tires of a bicycle have a radius of 14inches and are turning at the rate of 230 revolutions per…

A: Given that the tires of a bicycle have a radius of 14inches and are turning at the rate of 230…

Q: A trough is 10 ft long and its ends have the shape of isosceles triangles that are 3 ft across at…

A: We have to find how fast is the water level rising when the water is 6 inches deep.

Q: Rain is falling into a cylindrical barrel at the rate of 20 cm3 /min. If the radius of the base is…

A:

Q: a of 3 inche tall and has a radius of 2 inches How fast does the water level rise when the water is…

A:

Q: A Fluid flows in an inverted conical tank, 14 in diameter on top and 24in deep at a rate of…

A:

Q: The volume of a cube is increasing at the rate of 8 cm /sec.How fast is the surface area in creasing…

A: We can find the answer as below

Q: A trapezoidal trough is 10 ft long, 4 ft wide at the top, 2 ft wide at the bottom and 2 ft deep. If…

A:

Q: On the moon, the acceleration due to gravity is 1.6 m/sec2. If a rock is dropped into a crevasse,…

A: Consider the given value of acceleration due to gravity 1.6 m/sec2.

Q: A person with a mass of 75 kg is accelerated to 3 m/s2 How much force was applied to him?

A:

Q: A trough is 12 ft long and its ends have the shape of isosceles triangles that are 2 ft across at…

A: Given data:   The length of the trough is L=12 ft. The side of the isosceles triangle is b=2 ft. The…

Q: A ladder 10 ft long rests against a vertical wall. If the bottom of the ladder slides away from the…

A: To determine the rate of change of angle between the ladder and the ground.

Q: ) A snowball is melting at a rate of 1 cm3 per second. If it remains spherical, how fast is the…

A:

Q: A paper cup has the shape of a cone with height 10 cm and radius 3 cm (at the top). If water is…

A: From the given problem the representative diagram is shown as below: Let the radius of the cone be…

Q: A computerized spin balance machine rotates a 25-inch-diameter tire at 480 revolutions per minute.…

A:

Q: A kite 100 ft above the ground moves horizontally at a speed of 8 ft/s. At which rate is the angle…

A: Given,  Consider the height of the lite from the ground is 100 ft. The speed is dxdt=8 ft/s. To find…

Q: The radius of the tires of a car is 18 inches, and they are revolving at the rate of 673 revolutions…

A: To find the circumference of the tyre.

Q: A trough is 14 ft long and its ends have the shape of isosceles triangles that are 4 ft across at…

A: Given that: A trough is 14 feet long and its ends have the shape of isosceles triangles that are 4…

Q: A car braked with a constant deceleration of 16 fts 2 , producing skid marks measuring 200 ft…

A: Given, deceleration a(t) = 16 ft/sec2. s(0) = 0 ft and s(T) = 200 ft and v(T) = 0. Where T is the…

Q: A 90 kg man lying on a surface of negligible friction shoves a 81 g stone away from himself, giving…

A: Explanation of the answer is as follows

Q: A trough is 12 ft long and its ends have the shape of isosceles triangles that are 2 ft across at…

A:

Q: A gas line-driven lawnmower has a blade that extends out 1 foot from its center. The tip of the…

A:

Q: . A kite 100 ft above the ground moves horizontally at aspeed of 8 fts. At what rate is the angle…

A: At what rate is the angle between the stringand the horizontal decreasing when 200 ft of string has…

Q: How fast is the surface area of a cu

A: Given that : Edge of a cube = 30 cm Th edge changing at the rate of 3 mm per second.

Q: Rain is falling into a cylindrical barrel at the rate of 20 cm3/min. If the radius of the base is 18…

A:

Q: A trough is 10 ft long and its ends have the shape of isosceles triangles that are 4 ft across at…

A: Let V be the volume of the water inside the trough and h be the height of the water inside the…

Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.