find the center of mass of a thin plate of constantdensity d covering the given region. The region in the first and fourth quadrants enclosed by the curves y = 1/(1 + x2) and y = -1/(1 + x2) and by the lines x = 0 and x = 1

Q: use the given condition to write an equation for the line in slope int form  passing through (4,8)…

A: To write an equation for the line in slope int form  passing through (4,8) and (7,3)

Q: Find the distance between (1, 1/4, 1/2) and (1.5, 1/2, n).

A:

Q: y = 5t2 - 2t + 4 -'(t) =

A: The given function is y=t25t2-2t+4. We have to find the derivative of the given function. The…

Q: A farmer wants to repaint a thin, cylindrical water tank on their property. He only needs to paint…

A:

Q: Find the coordinates of the point/s on the curve y = 2x2 which are closest to the point ( 9, 0 ).

A:

Q: Find the area of the segment cut from the curve y=x (x-3) and the ordinates x=0 and x=5

A:

Q: a projectile launched at t=0 (t is measured in seconds) follows a path given by x=30t, y=-5t^2+80t,…

A: Given, a projectile launched at t = 0 second that follows a path x=30t, y=-5t^2+80t where x…

Q: What is the area of the largest triangle in the first quadrant with two sides on the axes and the…

A:

Q: Find the distance between the pointx1 =−1, y1 =1, z1 =3 and the point x2 =1, y2 =1, z2 =1.

A: The first point is (-1,1,3) and the second point is (1,1,1) We will use the distance formula:

Q: An inverted circular cone has a radius of 10 cm and a height of 15 cm. When water level in the cone…

A: GIVEN: radius of inverted circular cone = 10 CM Height = 15 cm

Q: f (x) = esin(x²), [0,3]

A:

Q: Find the area enclosed between the x-axis, the curve y= (x-15)(7-x)(x+12) and the lines x=-12 and…

A: We have to find the area enclosed between the x-axis, the curve y=(x-15)(7-x)(x+12) and the lines…

Q: Lake Ontario has a volume of approximately V =1600 km3. It is heavily polluted by a certain…

A: Rate of change of mas of pollutants in the Lake: dMdt=cinQin-cQout where c is concentration of…

Q: Find the distance between the line x + y + 2 = 0 and the point (1, 1).

A: The distance between the line ax+by+c=0 and the point x1,y1 is given as below. d=ax1+by1+ca2+b2

Q: Calculate the area of the segment cut from the curve y=x(3−x) by the line y=x. Also, sketch the…

A:

Q: Use cubic interpolation method with two points to find µ2 , where a = 0.6, h = 0. 1, ɛ = 0. 001 and…

A: Given: Let's determine μ2 using cubic interpolation method,  here a=0.6, h=0.1, ε=0.001,ϕι=-2.7

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.