5) A spherical storage tank has a radius of 3 feet, and half of it is underground: The equation of the curve in this drawing is x2+y²=9. The tank is full of a fluid having a weight density of w . How much Ib work is required to pump all the fluid up to the top of the tank? [The answer will be an expression containing w.]

Q: 2. Find an equation for the line through the point P(1, 0, -3) and perpendicular xy-plane. to the

A: Answer

Q: Water is poured into a conical paper cup at the rate of 3 cubic centimeters (cm) per second (s). The…

A: Given that, water is poured into a conical paper cup at the rate of 3cm3/s. The paper cup is 8 cm…

Q: 8. At what angle do the parabolas, y = ax and = 8 ay intersect? Ans. At (0, 0), 90°; at another…

A: According to question,Given equation of parabolas,y2 = ax,andx2 = 8ay

Q: 3. Find the dimension of the largest rectangle (in terms of area) that can be inscribed in a circle…

A:

Q: 3. Use calculus (derivative and C.N.) to find the area of the largest rectangle that can be…

A: This question is related to conic section .solve in step 2.

Q: Solve the problem. Find the length of the curve y = In(csc x), 7/4 T/2 VI E

A:

Q: 1. The three points A = (-2, -4), B= (6,2) and C = (-3,3) are taken as the vertices of a triangle T.…

A: Given that: A=(-2, -4), B=(6, 2), C=(-3, 3)

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.