Using the inner product (,): P₂ (R) × P₂ (R) → R, (p, q) = p(0)q(0) + p(1)q(1) + p(2)q(2) calculate (10x - 2x², 1 – 5x – 2x²).

Q: assume that Pr[A′]=0.55, Pr[B]=0.35 , and Pr[A′∩B]=0.2. (1) Pr[A∩B]=Pr[A∩B]=   (2)…

A: Solution : Given information; P(A')=0.55 P(A)=1-P(A')=0.45P(B)=0.35 and P(A'∩B)=0.2

Q: Find two functions f(x) and g(x) so that h(x) = (f og)(x) a) h(x) = (2x +3)².

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Q: Find the residues

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Q: Use the functions f and g in C[-1, 1] to find (f, g), ||f|, ||g||, and d(f, g) for the inner product…

A: According to the guidelines issued by the company We are supposed to answer only first three…

Q: Find f(x) and g(x) such that h(x) = (fo g)(x) and g(x) = Vx +9. h(x) = (Vx +9) * 4 f(x) = x

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Q: Find curl (9z i + 10x j + 5y k). curl (9z i + 10x j + 5y k) = ( i )i + ( i j + ( i

A: Curl

Q: (c) Write (V3+ i)" in the form of x+ iy.

A: Here I have applied De Moivre's Theorem. See the solution.

Q: factorise (c) x - - 3x - 4x + 12 (f) x'y – 4xy

A:

Q: Find the best quadratic approximation, Q(x, y) of √9 - 7x + 4y for (x, y) 7x+4y near (0,0), Q(x, y):…

A: Step 1:Step 2:Step 3:Step 4:

Q: If f(x, y) = 4x² – 7xy + 3x, then is given by: af - O 8x 8x – 7x + 7y + 3 - O 8x 8x – 7x – 7y + 3 -…

A: The solution of the problem is given in the next step.

Q: Find the coefficients a,b in the function f(x)=ax+b so that (f(x1)-y1)^2+(f(x2)-y2)^2+(f(x3)-y3)^2…

A: Given data: Function fx=ax+b so that fx1-y12+fx2-y22+fx3-y32 is as small as possible. Given table of…

Q: Find Vf at the given point. f(x,y,z) = x³ + y² − 2z² + z ln x, - = vf|(1,2,3) i++O* (Type exact…

A:

Q: Let f(x, y) = x² + y² - 4 2 y-2 Find fay(x, y).

A:

Q: 4. A) Factor f(x) into linear factors given that k is a zero of f(x). B) Find all roots of the…

A: f(x)=6x3+19x2+8x-5, k=-1To:a) Factor f(x) into linear factors b)Find all roots of the function

Q: Given m (x) = 3x - 9 and n(x) = - 4 +2x, find 2(x) – m (x). Do not include spaces in your answer.

A: By using direct subtraction rules we can   find n(x)-m(x)

Q: Find f(a), f(a + h), and the difference quotient la + h) na) where h * 0. f(x) = 5 - 6x + 2x2 f(a) =…

A: Given,            f(x) =5 - 6x + 2x2

Q: given that f(x)= 3X +2 and g(x)=2X squared + 4X and H(x)= - X squared - 1 develop an algebraic model…

A: Given

Q: Find the linearization L(x) of f(x) 5x2 5x + 5 at x х — 2. a) L(x) 15x 15 O b) L(x) 25x + 15 c) L(x)…

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Q: Find curl (9z i + 10x j+ 6y k). curl(9z i+ 10x j + 6y k) = ( i )i + (i j +( )k

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Q: Consider the polynomials a(x) = r' + x³ + x + 4 and b(x) = 2r³ + 4.x² + x + 2 from Z5[r]. a) Find…

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Q: (h) Write down the Lagrange's polynomial through (x), fo). (x1, f1), (x2, f2). Hence express 3x²…

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Q: help asap

A:

Q: Find β such that the equation βx 2 + x + β = 0 has a repeated real solution.

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Q: 3. Is the polynomial f(x) = 2x° + 30r – 150 € Q(r] reducible or irreducible over Q? In either case,…

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Q: Classify each of the following quadratic forms: (a) Q(x, y, z) = 3y² + 4z² (b) Q(x, y, z) = (c) Q(x,…

A: We have to classify the given quadratic function.

Q: Use the functions f and g in C[-1, 1] to find (f, g), ||f||, ||g||, and d(f, g) for the inner…

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Q: Determine the value of the coefficients  a, b, c, d and e such that the following f(x) is a natural…

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Q: 2. Determine whether the polynomial 1+ x + ? is a linear combination of P, = 2+x+x², p, = 1-x, p, =…

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Q: Perform convolution of h(t) and x(t) = (r(t) +r(-t)){u(t + 2) - ust - 2)1 %3D

A: Graph of x(t) is:

Q: Find and sketch the domain of f(x, y) = √√₁ - (x + 1)² − y² + 2ln(x − y + 1)

A: