13.A particle moves in a straight line so that its distance x cm. from a fixed point O on the line is given by x = 9r- 2t where i is the time in seconds measured from 0. Find the speed of the particle when t= 3. Also find the distance from 0 of the particle when t = 4, and (ans.: 0. 16) %3D show that it is then moving towards 0.

Q: Differentiate the followings. (x+ (i) y =

A: If given an expression of a function which is a multiplication of two separate functions. In order…

Q: 5. y= cos™ -1 = COS (2²)

A:

Q: A tank initially contains 300 gallons of water with 50lbs of salt disolved in the water. A brine…

A:

Q: A particle moves along a line for time 20 such that its velocity is v(t) = 10e cost. What is the…

A:

Q: If ƒ (2) = 2.5 and f'(2) = −2.5, then ƒ(2.5) is approximately: OA. -2 OB. 1.25 OC. 2 OD. 2.5 O…

A:

Q: 2. Let y = x? 4x2 . LA. Find "dy". B. Find the value of "dy" when x = 4 and dæ = 0.01.

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Q: Sin 2x- Cos 2.x Sinh (u-v) = Sinh u.Cosh v - Cosh u.Sinh v %3D

A: See the attachment

Q: y= sin (0.25) + sinh (2).

A: According to the question, we need to evaluate the function: y = sin-1(0.25) + sinh(2)

Q: A 25-year old burns 150 80t calories per hour while walking on their treadmill. The caloric intake…

A: According to bartleby guidelines we supposed to do the first one of multiple questions kindly repost…

Q: If a baseball is thrown upward with a velocity of 45 m/s, its height in meters t seconds later is…

A: We know that, Average velocity          = change in position/time elapsed.

Q: Suppose that a particle moves along a straight line with velocity v(t) = 13 - 3t, where 0<t < 4 (in…

A:

Q: The displacement s (in metres) of a particle as a function of time t (in seconds) is given by s(t) =…

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Q: The acceleration (in ft/s2) of an object moving along a straight line is given by a(t) = 3t Find the…

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Q: d/dx (Vx)=1/vx.2 a. True b. False

A: using the differentiation  formula,       d/dx (xn )=nxn-1

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.