The upward velocity of a rocket is given at three different times in the table below Time, (6) Velocity, v(m/s) S106.8 8177 2 12 279 2 The velocity data is approximated by a polynomial as v(t)at + at+a 551S 12 The coefficients a, ay and as for the above expression are given by 25 5 64 8 106 8 177.2 14 12 [279.2] n (a) i Find the values of a. da and ay tsing the Ganssian elimination method. a Find the velocity at t6.759 seconds

Q: 1. Find the polynomial of degree three for the following data. Also find P(-2). X 0 1 4 6 -1 1 y -1

A: We have,

Q: Table: t 0.2 0.4 0.6 0.8 1.0 1.2 v(t) 25 38 55 The second order Lagranges interpolating polynomial…

A: Here to=0.2, t1=0.4 & t2=0.6L1t=t-tot-t2t1-tot1-t2

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Q: Q-when fitting the data shown in the table with a second order polynomial Y=a+bx+cx? The value of a…

A: Make a table for the given data as follows                x y x2 x3 x4 xy x2y 1.2 1.5403 1.44…

Q: 22/By using Newton's backward difference formula, construct an interpolating polynomial from the…

A:

Q: From the given data, identify f(4) using Newton's polynomial. (2,10), (3,15), (5,25), (8,40)

A: Explanation of the solution is given below....

Q: The Lagrange polynomial that passes through the 3 data points (Xo,Vo) = (15,24), (x 1,V1) = (18,37),…

A:

Q: A third degree polynomial passes through the points (0,9), (1.14), (2,17), (3,24), (4,41), (5,74)…

A: The value of X1=∆y3=y4-y3=24-17⇒X1=7and value of ∆2y2=X2=∆y3-∆y2=7-3=4⇒X2=4

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Q: 32. The following data gives the melting points of an alloy of lead and zinc. Percentage of lead in…

A: Newton's farword diffrence formula

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A:

Q: Approximate  f′(2)f′(2) using the given data f(0)=−8,f(0)=−8, f(1)=−7,f(1)=−7, f(2)=0,f(2)=0,  and…

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Q: 1. Find the polynomial of degree three for the following data. Also find P(-2). X0 1 4 6 -1 1|-1 y 1

A: as per our guidelines we are supposed to answer?️ only one question. Kindly repost other question as…

Q: 13. a) Estimate the value of f (3.34) by approximating Lagrange interpolating polynomial for f(1) =…

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Q: c. Use the polynomials obtained in parts a. and b. to approximate the given quantity. 1 1 f(x) = a =…

A: Linear approximating polynomial means p1(x)=1-1(x-1) Given x=1.05

Q: Q1 Table below contains dataset of a robotic arm during a force measurement on a thigh phantom.…

A: given data  Time(s) 10.5 13.1 15.2 Force(N) 9.27 11.90 13.83 (A) lagrange interpolating…

Q: b) The following data gives the melting points of an alloy of lead and zinc. Percentage of lead in…

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Q: Q2: Use a Newton-Gregory polynomial (Forward & Backward) of degree 3 that fit table below, then find…

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Q: Using the given data, we see the largest change in Y is between X = -8 and X = -7. Y X 19.1 0 19.1…

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Q: Determine the 4th degree polynomial for the given set of data(x.y). 1. 1.3 2.4 3.7 3.8 5.1 y -6.3…

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Q: b) The following data gives the melting points of an alloy of lead and zinc. Percentage of lead in…

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Q: 1. The specific heat capacity Cp[J/mol/°C] is often correlated to temperature T[°C] in form of a…

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Q: 1. Find the polynomial of degree three for the following data. Also find P(-2). 1 4 6. y 1 -1 1 -1

A: For the given data points,we have to find out the third degree polynomial satisfying the given data.

Q: 2. Construct the interpolating polynomial of degree 4 using divided difference for the data given…

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Q: 2.3. Approximate fl1895) vising an interpolacting polynomial of degree & using Netu tons.…

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Q: 2. The voltage drop V across a resistor for a number of different values of current i is shown in…

A: (1) Given i V Vi , Vj Vi , Vj , Vk 0.75 -0.6         0.7-(-0.6)1.25-0.75 = 2.6   1.25 0.7…

Q: i155 Q-when fitting the data shown in the table with a second order polynomial Y=a+bx+cx? The value…

A: The quadratic regression technique uses a dataset to determine a quadratic function,: f(x)=a+bx+cx2…

Q: 13. a) Estimate the value of f(3.34) by approximating Lagrange interpolating polynomial for f(1) =…

A:

Q: th integral coefficients tha D4, 3+i

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A:

Q: 4. a) Let P3(x) (classical) be the interpolating polynomial for the data given in Table 1. Find y if…

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A: The graph of the polynomial is given by To evaluate: The equation of the polynomial.

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Q: a) Let P3(x) (classical) be the interpolating polynomial for the data given in Table 1. Find y if…

A: Since you have asked multiple questions, we will solve first one for you. If you want other question…

Q: b) The following data gives the melting points of an alloy of lead and zinc. Percentage of lead in…

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A: For this problem we use newton difference rule

Q: Q4 Table Q4 contains dataset of a robotic arm during a force measurement on a thigh phantom.…

A:

Q: 4. The upward velocity of a rocket is given as a function of time in Table 3. Table 3 Velocity as a…

A: The Lagrangian polynomial interpolation is given by,…

Q: 1. Find the polynomial of degree three for the following data. Also find P(-2). X01 4 6 -1 1 y 1 -1

A: This is a problem of Numerical Analysis.

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.