The equation of the curve is x=0.25y2. For the shaded area under the curve (from x=0 to x=9), considering the horizontal  strip shape below, the Moment of inertia around the x-axis e

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A: Apologies for the inconvenience. The correct solution is given below: Given that y=x2 Hence, dydx=2x

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A: Note: Since you have posted multiple sub parts. As per our policy we are allowed to solve the first…

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A: The given curve is r(t)=cos 8t i + sin 8t j + 8t k

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A: Given: a(t) = 3cost -2sint , s(0) =0, v(0)=4 We know that a(t) = ddtv(t) ⇒vt = ∫a(t) dt

Q: Given the velocity v = ds and the initial position of a body moving along a coordinate line, find…

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A: Note- according to bartleby guidelines I only have to solve first question from multiple question

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A: Given: The lateral surface area S of a right circular cone is related to the base radius r and…

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A: Given curve y=f(x)=x2,0≤x≤2 The objective is to find the length of the curve.

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A: Please see the below picture for detailed solution.

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A: NOTE: Refresh your page if you can't see any equations. . to find the inflection point, first, we…

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A: Given: fx,y=4lnx4-y We have to find the linear approximation in two variables.

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A: Given a particle is moving in a curve, r(t) = cos  7t i + sin 7t j +  8t k. To Find the tangential…

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A: This is a approximation problem

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A: Explained below

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A: Solution :

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A: NOTE: Refresh your page if you can't see any equations. . here we have

Q: -y=- coS I: dz

A: it is a first order differential equation and it is linear differential equation

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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.