Exercise 5.3 Transformation in curved space Find the coordinate transformation matrix [A] (showing its coordinate dependence) that changes the polar coordinates (0, ø) to the cylindrical coordinates (p, 4) on a 2-sphere: (2) - () dp de = [A] dø (5.13) dø

Q: What is the coefficient of x²wa³b in the expansion of (x+y+w+a+b)??

A: To determine the coefficient of x2wa3b in the expansion of x+y+w+a+b7.

Q: factors of 24 that add up to 10

A: factors of 24 that add up to 10

Q: Using the Binomial Theorem & Pascal's Triar expand the binomial, (a - b)* A. a -4ab3 + 6a?b? - 4a³b…

A:

Q: How many terms are there in the multinomial expansion of (x₁ + x₂ + ...........+xr)n?

A: Multinomial expansion :  (X1 + X2 + X3 + ......Xr)n  We have to calculate no. of terms in this…

Q: b. N(0)

A: Given,  r→t=sint, t, cost                   ...1

Q: a3-16a

A: a³−16a ⇒a(a²−16) ⇒a(a² −4²) ⇒a(a+4)(a−4)

Q: 10 8/10 + 9 7/12=

A:

Q: 12 Find the term of (a – 3b)" that has b in it.

A:

Q: Simplify.2 Express 0(3n° – 2n² + n) n) as:

A: Given that O(3n^3 - 2n^2 + n)

Q: Select and order the steps to prove the special product pattern for the square of a binomial. Step…

A: A square of a binomial is of the form (c+d)2  We first write it as a product (c+d)(c+d)Then we…

Q: 4n – 1

A:

Q: 7/2 + 3 4/6

A:

Q: 5/14+1/6

A: 514+16=15+742

Q: I. Find the general solution y = C₁91+C₂92 to the homogeneous equation y"-2y'+y = 0. II. Use the…

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Q: 1 7. 27 2.

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Q: Find the coefficient of x4 in the expansion of (2-3x)6

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Q: Use the binomial theorem (more than once) to expand (a+b+c)³.

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

Q: Factor 10k + 1 into a product of primes for k = 1, 2, 3, 4, 5.

A: The main objective is to factor p(k)=10k+1 into product of primes for k=1,2,3,4,5.

Q: In the expansion of (x + y)14 which term has the highest coefficient ? O a. x10y4 O b.x7y7 Oc x14 d.…

A:

Q: 7. How many terms are there in the multinomial expansion of (x₁ + x₂ + ... .+x)"? ******..

A: We want to find the number of terms in the multinomial expansion of x1 + x2 + ... + xrn

Q: factors of 20 that add up to 9

A:

Q: coefficient of variaton for given populaion   5,8,9,11,15,16,17,19

A:

Q: [ 8x³(4x² + 1)12dx

A:

Q: What is the 5th term in the expansion of (2x²y³ – ¹y)° O 14.25x7 y 20 15.75x10 y 19 15.05x¹0y17…

A: Given: 2x2y3-14y9=2x2y3-y49

Q: expansion of (1-2m)“

A:

Q: 57-24

A: Given that: 57-24

Q: (3) Find the prime factorization b. 180

A:

Q: 4. Find the 11th term in the expansion of 25 3x + 5xi

A:

Q: Find the nth term of  (– 4 3 14 29 ) and (4, 5, 8, 13)

A: Sequence

Q: (5/6)3

A: Cube means multiplying three times:   563=56×56×56=5×5×56×6×6=5363=125216

Q: 3 3/4 + 2 7/28

A:

Q: nvert

A: