A tank is shaped like an upside-down square pyramid, with a base with sides that are 4 meters in length and a height of 12meters. If water is being pumped into the pyramid at a rate of 2/3  m3 /sec, at what rate is the height of the water increasing when the water is 2 meters deep? (The volume of a pyramid with height h and base area B is given by V=1/3 Bh.) Enter a fraction and do not include units.

Q: 2. Sand is being dropped at the rate of 10ft.3/min into a conical pile. If the height of the pile is…

A:

Q: The radius of a right circular cone is increasing at a rate of 1.2 in/s while its height is…

A: Differentiate volume wrt t

Q: If the radius of a sphere is increasing at a constant rate of 2 cm/sec, then the volume 3 is…

A:

Q: The side of an equilateral triangle is increasing at a rate of 2 m/sec, then the rate at which its…

A:

Q: A ladder of length 5 m rests against a vertical wall. If the base of the ladder is pulled away from…

A: Given:

Q: 11. If a snowball melts so that its surface area decreases at a rate of 1 cm/min, find the rate at…

A:

Q: 1. Oil is being pumped into a huge cylindrical oil drum with diameter 3 m and length 6 m at a rate…

A:

Q: The sides of a square increase in length at a rate of 3 m/sec. a. At what rate is the area of the…

A: lets the size of square is l so the rate of change of length = dl/dt = 3 m/sec area of square = l2…

Q: A solution is passing through a conical filter 24 in deep and 16 in across the top, into a…

A:

Q: If the volume of a cube is decreasing at a rate of 24 in sec, then find the rate at which the length…

A:

Q: A rectangular box has its height increasing at a rate of 1m/s while its volume is decreasing at a…

A: We have to find the  rate of change of length.

Q: A substance evaporates at a rate proportional to the exposed surface. If a sphericalmothball of…

A: The rate of evaporation is proportional to the exposed surface, and the exposed surface is that of a…

Q: The volume of a cone of radius r and height h is given by V=1/3pir^2h. If the radius increases at a…

A: Volume of a cone = πr2h3 , Where r= radius of a cone and h= height of a conedrdt= 0.5cm/sec , dhdt=…

Q: A conical tank with an upper radius of 4 m and a height of 5 m drains into a cylindrical tank with a…

A:

Q: A cylindrical column is (3m) high and (0.2m) radius, if the radius of the column increases at a rate…

A:

Q: A reservoir is 80m long and its cross section is an isosceles trapezoid having equal sides of 10m,…

A: Sol

Q: The width of a rectangle is increasing at a rate of 2 cm/sec, while the length increases at 3…

A: The rate of increase of the width of a rectangle i.e. dwdt=2 cm/sec The rate of increase of the…

Q: A rectangle is growing in such a way that when its length is 5 ft and its width is 2 ft, the length…

A: When length is:= 5 ft; When width is:= 2 ft; Rate of increasing length= 3 ft/s; Rate of increasing…

Q: How fast is the volume of the rind growing at the end of the fifth week?

A:

Q: A reservoir is 90m long and its cross section is an isosceles trapezoid having equal sides of 11m,…

A: Given that a reservoir is 90 m long whose cross section is an isosceles trapezoid. The dimensions…

Q: The width of a rectangle is increasing at a rate of 5 cm/sec, while the length increases at 6…

A:

Q: pherical balloon is to be deflated so that its radius decreases at a constant rate of 15 cm/min. At…

A: The radius of the balloon decreases at the rate of =15 cm/min let radius of balloon =r then…

Q: 1. If the radius of a spherical balloon is increasing at the rate of 3 cm/s, which of the following…

A: We are only allowed to solve one question at a time so we will answer only the first question.…

Q: 1. A spherical balloon is being inflated so that the volume is increasing at the rate of 5 ft.³ per…

A:

Q: A liquid solution is passing thru a conical filter 2 feet deep and 4/3 feet across the top, into a…

A: We have to find the rate at which the level of the solution in the cylinder rising.

Q: The volume of a cube increases at a constant rate of 135 ft°/ sec. The rate at which the side of the…

A:

Q: A reservoir is 80m long and its cross section is an isosceles trapezoid having equal sides of 10m,…

A: Given that the reservoir is 80m long whose cross-section is an isosceles trapezoid with sides of…

Q: A spherical balloon is inflated at a rate of 10 cm3>min. At what rate is the diameter of the…

A:

Q: The sides of a square increase in length at a rate of 3 m/sec. a. At what rate is the area of the…

A: let the side of the square is a meter, and the area is A given that da/dt=3m/sec a. a=15m area of…

Q: )1. A spherical balloon is being inflated so that the volume is increasing at the rate of 5 ft.' per…

A: according to our guidelines we can answer only first question and rest can be reposted.

Q: The side of a cube increases at the rate of 1 m/sec. The rate at which the volume of the cube…

A:

Q: If the radius of a sphere is increasing at a constant rate of 3 cm/sec, then the volume is…

A:

Q: A box has a length increasing at a rate of 2 in/s, a height decreasing at a rate of 3 in/s, and a…

A:

Q: At a constant pressure, what temperature must be reached to increase the volume of a 100mL samples…

A:

Q: 1. A spherical balloon is expanding. If the radius is increasing at the rate of 2 inches per minute,…

A: The given question can be solved as shown in step2.

Q: If a spherical balloon is being filled with air at a constant rate of 2 cm³/s, at what rate is the…

A: Let r be the radius of the balloon in cm and V be the volume in cm3. The variable t stands for time…

Q: 15. Water is being poured at the rate of 150 cm³/s into an inverted cone with a diameter of 3 meters…

A:

Q: If the radius of a sphere increases at a rate of 0.5 m/sec, then the rate at which the volume of the…

A: Let the radius of the sphere be r. Then the volume of the sphere is: V=43πr3…

Q: 1. Air is being pumped into a spherical balloon at a rate of 4 cm3/min. How fast is the radius of…

A: 1. Given:   The rate at which air is pumped into the spherical balloon = 4 cm3/min   Diameter of the…

Q: An inverted conical tank 10 m high and 3 m radius at the top fills with water at a constant rate. At…

A: Given: An inverted conical tank 10 m high and 3 m radius at the top fills with water at a constant…

Q: 4. Water is running out of a conical tank 3 m across the top and 4 m deep at the rate of 2 m3 /min.…

A: given  h = 4 m  (Note: measurement of h is always taken from bottom) r = (3 ÷ 2 ) = 1.5 m dVdt = 2…

Q: A ladder of length 5 m rests against a vertical wall. If the base of the ladder is pulled away from…

A:

Q: 18 Show that the volume V of a regular tetrahedron, all of whose side lengths are s, is V = s°V2…

A: Given that the volume of a tetrahedron is: 1442cm3 So, V=112s32 So, 112s32=1442⇒s3=123⇒s=12

Q: The radius of a sphere decreases at a rate of 4 m/s. when the radius is 7 m, then the rate at which…

A:

Q: 1. The width of a rectangle is increasing at a rate of 2 cm/sec, while the length increases at 3…

A: I have stated the used formulas in the solution

Q: 2. Air is leaking from a spherical-shaped advertising balloon at the rate of 26 cubic feet per…

A: Let r be the radius and v be the volume of balloon, Given dvdt=26 cf/minuteswe know…

Q: A circular pool of water is expanding at the rate of 16pi in^2/sec. At what rate is the radius…

A: expanding at the rate of 16pi in^2/sec of circular loop rate is the radius expanding if radius…

Q: A rectangle is growing in such a way that when its length is 5 ft and its width is 2 ft, the length…

A:

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.