12. Given vector p = 5i – 3j + 2k and vector i = i – 2j + 2k if ř is the orthogonal projection of the vector p on à and vector projection length i = 2i + j+ mk on † is 2, then the value of m that satisfies is. А.З В. 4 С.5 D. 6 E. 7

Q: 11. Given a quadratic equation (a – 2)x² – 6ax + 9a + 53 = 0 Where the roots are positive integers.…

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Q: 8. Given that a, b, c, d are positive integers that satisfy loga b = an log, d = if c – b = 23, then…

A: This is a problem related to fraction of the expression. Based on the general concept we will solve…

Q: Find the indicated derivative or integral a. D, (3** * ) c. D, log,, (x³ +9) –3x а. D, b. |x 2* dx…

A: We know that Dx ax = ax·ln(a) Dx af(x) = af(x)·ln(a)·f'(x)   ∫ax dx = axln(a)+C   Dx loga x =…

Q: -3 10. Given function f(x) = x3 – 3x² + x – 2. If matrix P 31 and matrix Q = f(P)i where i is the…

A: To find the determinant of a matrix . The given options are wrong  None of them is correct.

Q: cot? 3x lim (sec³ 2x) x→0 e O 2/3 e^2/3

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Q: 10. An education finance corporation claims that the average credit card debts carried by…

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Q: 2. If the polynomial f (x) divided by (x – 3) gives a remainder of -1, then the remainder of…

A: Solution is given below:

Q: 10- 8. 3 a 20 (a) Report a, accurate to 1 decimal place: a = 3.7 Report b, accurate to I decimal…

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Q: 9. If f (x) = sin 3x so lim f(x+2h)+f(x-2h)-2f(x) ... -18h2 А. —3 sin 3x В. —2 sin 3x C. sin 3x D. 2…

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Q: The Cholesky decomposition: Select one: а. is faster than the LU decomposition when solving a linear…

A: Solution:- the Cholesky decomposition is roughly twice as efficient as the LU decomposition for…

Q: 7. Given a cube ABCD.EFGH with side length 4. The points K, L, M, and N are the midpoints of the…

A: The solution is 3:16     The given cube ABCDEFGH is drawn below.

Q: Write the polynomial that has the 3 zeros at -2, -6, , and 1. 2'

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Q: /2 5b) What is ll xl)=(2 ²) if x= G,s%2;X3=--) toce where -n/2 2. and Xn = L?

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Q: a+vb So the value of a + b + c is. 4. If cos 36° A. 8 В. 10 С. 12 D. 15 Е. 18

A: Given PROBLEM:- cos(36°) =(a+√b)/c Find :- Value of a+b+c

Q: 3. Given the function y = [(x² +2x+ 1]/(x), (x0), find: (a) the limit of y as x approaches positive…

A: Given:  The function y=x2+2x+1x, x≠0 To Find:  a The limit of y as x approaches positive infinity.b…

Q: Show that any inner product satisfies the Cauch

A: Introduction: The Cauchy–Schwarz inequality asserts that if u and v are two vectors in an inner…

Q: 6. Given that f(x) is a continuous function for any real number with ff(x)dx = 18 and " f(x)dx = 6.…

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Q: 2. Given y = 2x + 1, find its inverse function? Then find dy/dx and dx/dy and verify the inverse…

A: The given function y=2x+1

Q: 3. Given p and q are real numbers such that p - Ja = 30. The maximum value of p – 4q is А. 1200 В.…

A: This question can be solved using the concept of maxima or minima.

Q: (vi) rot(fÃ) = f rot Ã+ grad(f) × rot à (vii) div(Ā× B) = B. rot à – Ã. rot Ē (viii) rot rot à =…

A: We know rot means rotational or curl.

Q: 1. (a) Let f: X → R be a subadditive function defined on a topological vector space. Prove that if f…

A: As you have asked more than one different/unreated to each other questions. We shall solve first…

Q: 14. It is known that the positive integer n is so that 9" = 20589113m094649 The correct value of m…

A: here we make find the n value  here we can try and find that n =15 92 =81 93 =729 .......... like…

Q: 3. If the ratio of a pair of corresponding altitudes of two similar triangles is 4:7, and the area…

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Q: 10) If x = -2 is a zero, what are the other zeros for 3x3 + 10x2 + 4x - 8 = 0? %3D

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Q: 7. Let X(s)=- 2s²-s+3 (s+2)(s+1)(s-2) ROC,{s:-1<Re(s) <2}. Determine x( t). be the Laplace transform…

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Q: The Set M, of all 2x2 matrices of the fom. where d's ß' fd EB denote the Conjugate of the Complex…

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Q: Find the Taylor polynomials of orders n = 0,1,2,3, and 4 about x = xo, and then find the nth Taylor…

A: Given f(x)=eax, x0=ln2

Q: 15. A bag contains nine balls which are numbered 1 to 9. Andi takes ball from the bag and returns it…

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Q: 1 2p 5. If f (x) %3D рх + q.g(x) %3D qx +p dan (fog)-1(x) %3D — х — With p and q as real numbers and…

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Q: Find the solution of the equation = e Cos y which tends to zero as x → 0o and has the value cos y…

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Q: 4) A box contains 10 red and 12 white rose flowers. Flowers are picked up at random one by one…

A: Given that there are 10 red and 12 white flowers. So, total (10+12)=22 flowers   i) We can draw the…