18) (SAnn B anlogbro dtiv C AB = 12, BC = 3x + 6, and AC = 5x – 12 a) Find BC b) Find AC

Q: ) ydx + zedy-y'dy=o

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Q: value of ∑n=1∞(6an+9bn) if ∑n=1∞an=8 and ∑n=1∞bn=2.

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Q: (4) Evaluate 1 z² + 4z - 5 J -dz.

A:

Q: Solve for the following: a) Var(2X−5) when X ∼ U {1,2,…,20}. b) Var(3X−4) when X ∼ U {1,2,…,30}.

A: Given,X~U(1,2,.....20)minimum value=1maximum value=20f(x)=120-1f(x)=119         ; 1≤X≤20

Q: b) Heron's Formula Area = √5(5-a)(s-b)(s-c), where s = 1/(a+b+c) prove using the following steps.

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Q: Compute ATBT and BT AT by hand if possible. If not possible, describe why. A = 2 3 −1 0 B = 10 -1 0…

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Q: Show that T (1-i) cos- +isin- 40 40 (81-8√3) 6 10 = -√2

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Q: L[sih bt) 2.

A: From the definition of Laplace, L(f(t))=Fs=∫0∞fte-stdtSo,L(sin(bt))=∫0∞sin(bt)e-stdt Let,…

Q: bläi 4 * find each of a,& b 3 - i 2 – 2i - If a + ib = 2+ 3i then 1– 5i' -

A: Given :         a + ib = 3 - i2 + 3i + 2 - 2i1 - 5i   To find a and b.

Q: Show that we can have: (a) ANB = ANC without B = C. (b) AUB = AUC without B = C.

A:

Q: Evaluate (2i)3 a) 8 b) –8 с) -8i d) 8i

A: Let z=(2i)3

Q: 11 - d 18t7 dt dx 1 a) O 12x5 b) c) O 18x7/2 4 e) O 9x3

A: The correct option is (e).

Q: 2 let -27 Aslo -3 1470 -4 find AB+BA,AA"AA, (3A=2B)°C A'C..

A: "Since you have posted a question with multiple subparts, we will solve first three subparts for…

Q: Solve for x: a x 2 + b x- ct = 4tr + a x 2 O A) x = (47tr + ct) / b O B) x = 4tr + 2a x 2 - ct /b O…

A: we have to solve for xax2+bx-ct=4πr+ax2

Q: If A is 13×21 and dim(Col(A)) = 11, what can be said about dim(Nul(A))? Explain

A: Consider the given question,Here, A = [aij]13x21That means, the number of rows and columns in the…

Q: (x° – xº) (1+x³)5 Evaluate dr; Use B(m, n) = dr (1+x)m+n

A: Using the given result and

Q: Choose the right answer Given A =2x i- 42 j- 3xy k B = 2x i- 2zj (find A.B, AxB, div (A), div (B

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Q: If det (AB²) = 24 and det(AB) = 8, what is det (BT) equal to?

A: Note that, det(AB)=det(A)×det(B)

Q: 17) (12 – 8j)(4 + 3j) + 10

A: To expand by multiplying each term and adding them

Q: Evaluate e cosh 2t -3t s13 d) 4(s? - 6s-5) 3. s43 a) 4(s-6s + 5) b) 4(s? + 6s - 5) c) 4(s + 6s +5)

A:

Q: 4. If ā= 3i - 2j and b=-5i- j, express 3 a -b in terms of i and j.

A: This is a vector problem

Q: Even-degree polynomials can have how many absolute maximums or minimums? 1 2. 3. 1 2 3

A: Since you have posted multiple questions i can do first question as per our company guidelines…

Q: Sx³√4 - 2x² dx 3

A: We have to solve integration

Q: 6. Express in a + bi form: 2i(i + 3)

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Q: a) If Z1 = -3 + 3i and Z2 = 4i. Show that: i) Arg(Z,Z2) + Arg(Z,) + Arg(Z2) ii) Arg (2) = Arg(Z,) –…

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Q: д 1 Option 1 Option 3 1 1+ 3x2 2√3 9 2 3 3 dx Option 2 Option 4 √3л 9 √3л 3

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Q: Find the value of S in (3A +4Si)(6-7i) = 3+5i

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Q: V9x2+4 dx V9x2+4 +c V9x2+4 +c 3

A:

Q: -2/2] 2 3) If A= and B 2 2v21. Show that A and B commutative.

A: The two matrices A and B are said to be commutative if AB=BA. The given matrices are…

Q: Hiw: Find Eiqunhlues and Eig envac tors ofa 2x2 metrir If A-

A: Given A=01−2−3 The eigenvalues of A are the roots of the characteristic equation detA−λI=0…