2. Let T: P2- P2 be defined by T(a+ bx + c?) = a - 2b+ (2b – 4c)x+3ca². Find a basis C for P2 such that [T]c is a diagonal matrix. %3D

Q: Check whether the following differential equation is exact. (6ye-3z + 3x)dx + (5y – 2e3")dy = 0 Then...

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Q: 2 then the m 3.

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Q: if xo = 2, x1 = 3 and x2 = 4 the second degree %3| polynomial for f(x) = using Lagrange Interpolatio...

A: Given function is f(x)=12and the nodes are x0=2, x1=3 and x2=4. We have to find second degree Lagran...

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Q: 9. (a) f(t) = cos (at + B) (b) f(t) = sin (at + B) %3D 10. f(t) = sin 2t 3 Hint: sin' a = 1 -sin a 4...

A: 9(a). Use the identity cosA+B=cosA·cosB-sinA·sinB to expand the expression cosαt+β.  

Q: Scos -de cos

A: We have to evaluate the integral ∫cos3θ3dθ.

Q: Find the root of the following using the method indicated. E < 0.0001 1. f (z) = sin I +e - 2, xo = ...

A: Use the following formulae, to find the root of the function fx. Fixed Point Iteration Method: Rewr...

Q: a) Write sin(3 - i) in the form of a+ bi . b) Find all the values of (3)-in .

A: (a) sin3-i we have to write this in form of a+ib. (b)We have to find the value of  3-iπ. The formula...

Q: 5. -5 -5 5 -5- -5

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Q: (Practice on Logarithmic functions) What is log264? What is log100.1? Is log2ab = log2a + log2b? ...

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Q: 2s - 1 43. s2 - 6s + 18

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Q: Determine the volume of the solid formed by revolving the area bounded by 9x2 + 36x + 4y2 + 24y + 36...

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Q: answer d & e only

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Q: а. Show that the set S of all symmetries of an equilateral triangle form a group under composition o...

A: We will be solving part (c) and (d) as mentioned. let S be the group of all symmetries of an equilat...

Q: tan-1(z3)

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Q: Convert each equation from polar to rectangular form. 9) r= 4csc 0 10) r= 2sin (0 +") 11) r² = 5sec ...

A: We have to use relation between cartesian and polar co ordinate system  x = r cosθ  , y= r sinθ Squa...

Q: Use the sequential runoff method to determine the winner if a majority cannot be determined. Votes 3...

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Q: Find an explicit formula for the sequence of the form a1, a2, a3, . . . with the initial terms given...

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Q: Ingrid wants to buy a $20,000 car in 5 years. How much money must she deposit at the end of each qua...

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Q: What are the end behaviours of f(x) = –3x6 +2x + 1? Tell me how you know. As x > 0, y → As x > Tell ...

A: Given,  f(x) = -3x6+2x+1 We have to find the end behavior of f(x). 

Q: Permutations Use the permutations to solve the given problem. Explain your answer. Show your solutio...

A: Total no. Of options = Number of options for 1×no. Of options for 2nd and goes on

Q: Bonita obtained 22/30 for a Geography test and 18/25 for a history test In which subjects did she ob...

A: Marks obtained in Geography is 2230 marks obtained in history is 1825 we need to compare two fractio...

Q: f) If you approximate 0.60167084 using chopping to 4 digits, what will be the approximated value? g)...

A: (f) Approximation of 0.60167084 using chopping to 4 digit will be 0.6016  ( considering only 4 digit...

Q: Let G be a group with |G|=187 then every proper subgroup of G is: Non abelian O Non cyclic O Cyclic ...

A: We will use basic knowledge of group theory to answer this question.

Q: Find the Taylor polynomial of degree 4 for the function f(x) = In(x), centered at a = the sums of po...

A: The derivative of the function is the measure of how fast the function is changing with respect to x...

Q: The point P (,=) lies on the unit circle

A: The Point P45, -15 lies on the unit circle ________?_______

Q: umber of linearly i: 1 0

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Q: Consider the following table of values of f(x) = e". 0.0 0.2 0.6 f(x) 1.0 1.22140 1.82212 (a) Approx...

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Q: Use the plurality method to determine the winner of the election of the school president. There are ...

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Q: 4) r= 2cos 0 + 2sin 0

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Q: 1. You have two vests, three hats and 14 buttons. How many outfits can you make if each outfit has a...

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Q: 6. Find all tu roots for each espression. (a) (-2+ 2i) (b) (-3) (c) (2i)

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Q: Check the DE if it is exact or not then solve it. (If it is not exact use the method by using integr...

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Q: (b) Find the LU factorization of the matrix: 1 -1 A= 3 -4 -2 | 2 -3 -2

A: The given matrix is                                A=1-1-13-4-22-3-2 We have to find the LU factoriz...

Q: b) Find the inverse ztransform of the following: i z's zl2|sin 3 2(2/2/cos 3)z+|2/F] zz(z*+4z+1) 1 (...

A: We will use the basic knowledge of the theory of z-transforms to answer all the three subparts of th...

Q: Q1: Solve (x – 1)(x – 2) + y = x2 dx

A: Write the equation in the standard form. dydx+1x-1x-2y=x2x-1x-2               ...1

Q: ce matrix. locate a logistics build

A: Given as,

Q: 30-35. Given L = {0, –2,2, –1,2,3, –4,1, –3} A = {-100, ... 99, 100, .. 201} B = {3,2,1,6,5,4] Write...

A: The given sets are:L=0,-2,2,-1,2,3,-4,1,-3A=-100, . . . , 99, 100, . . . , 201B=3,2,1,6,5,4We have t...

Q: (a) the boy con only make UP pnd Right moves anly he de food? the How many parths (b) If he mandemly...

A: We will use basic logic to answer both parts. Note that in the question post, only two parts named (...

Q: we consider the initial value problem above. When applying the midpoint method, what is the largest ...

A: We can  solve this using midpoint method of ode

Q: Σ (-1)" Vn Inn Σ 1-n0.5 2n0.5+1

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Q: Zmax = 3x1 + Subject to 2x1 + X1 +:

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Q: Show that the substitution 1- x a = -1, b = l+ 1, c = 1 2 converts the hypergeometric equation into ...

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Q: Topic: Graphing on Intervals (-8, 8)  Instructions: 1.) Using any graphical app, construct three d...

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Q: Verify that the given function is a solution of the given differential equation. y" + 2y'–3y = 0; y1...

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Q: Question 3. Let u = (1, 1, 1) E R³ and denote U = span(u). Let W = {(x1, X2, 13) E R³ : ¤1+ x2 + x3 ...

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Q: 2. It is desired to obtain the real-valued roots of S(2) = 0, f(z)= (x*. 8. - 6z - 5z2 + 6r - 4VT+10...

A: We will use basic knowledge of set theory and real-valued functions to answer the first two subparts...

Q: You are asigned by your groue leader for the gathering of Important doata for your project in Mathem...

A: Given: At 1:00 pm, the angle of elevation of the sun is 80 degrees. Here the Length of the shadow s...

Q: Solve the following  complex numbers in their rectangular form. Use  4

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Q: A palindrome number is a number that remains the same when its digits are reversed. For example, the...

A: We will be solving Q.4 as mentioned. A Palindrome number is a number that remains the same when its ...