7. In ABCD, AC and BD divide each other in half at E. (a) Prove that ZDBC ZBDA. (b) Prove that ADBC ABDA.

Q: 16 Tt 2c) Compute tan 3

A:

Q: 7. (a) V.(V4) = V²¢ (b) (4× R) _ (2-n).A n(A.R)R %3D E,r =|R|

A: a)

Q: Transform triangle ABC with vertices A (4,0), B(0, 2), and C(-2, -1) as shown. RO. 1800(ABC) A'. В'…

A:

Q: Multiply and simplify: 4r°y* (5x² – 5æy + 4y?) Submit Question

A: Given expression, 4x3y4(5x2 - 5xy + 4y2)

Q: Theorem mDF : 52' D 162

A:

Q: •2πT 2 cos³ t + 3 cos² t dt

A:

Q: 14. Show that p q and (paq)V-PA) are equiv- alent.

A:

Q: 77 Vo +1 dydr

A: we have to change order of integration

Q: 3Tt ) Determine; [cos (4t +) 4

A: solution given below..

Q: A Show that : tan" [ ica-a)' (2ta)) -i 2

A: Let ax=eiθ. So: tan-1ix-ax+a=tan-1i1-ax1+ax                         =tan-1i1-eiθ1+eiθ…

Q: 2- Let z=x+iy. Find a) Img(1/2) b) Re z c) Img (1/z')

A:

Q: If u = x²/(x² + y²), find ou/ox, du/dy.

A: # As per the guidelines we are entitled to solve one question at a time, please resubmit the other…

Q: iii) modulus of complex z = e"H equal to а. 3 b.2 С. 1 d. 0

A:

Q: Show that the following relationships hold. a) (1+i)™sn[ = Sn+m[ ¯ Sm| b) än+1] = 1+ an] (m) (m), c)…

A: Considering the LHS (Left hand Side) : LHS=(1+i)mSn|¯ RHS=Sn+m|¯-Sm|¯ ( Right Hand Side)…

Q: Evaluate "(ti + tj + tk) dt. 10 (ti + tj + t'k)dt

A:

Q: 4.] Find PIAJ if A = Co,bicd)

A:

Q: 3 of u(a,9) = Cof"( 4y Cof' (+y then provethat ace +4u + Sin2ce=0

A:

Q: 18 In(z – 3) Question 10) Find I = -dz, where C = Iz - 2 + 4i| = 4, Ccw z2 + (4 + 4i)z + 3+ 4i

A:

Q: Given that z = cos + isin and u-iv-(1+z)(1-22). Show that 30 v = utan 2 r = 4² cos² (2). where r is…

A:

Q: Prove that eie ei(0+2K) ,where k = 0,±1, +2,...., = D

A:

Q: 4. This question has two parts. a) Compute the value of eln 2020+3xi/4 b) Find all complex numbers z…

A:

Q: b) Consider the second-order DE. y" +25y = 0 rE (-00, 00) Show the zero’s of the solutions separate…

A: The given differential equation is y''+25y=0 If D=dydx then equation will be D2+25y=0 Now Auxilliary…

Q: . Example: shew that -at? e ayo 1, | a a?+p? Hindin ĕ dy Fis fourier -00

A:

Q: Find the Lapla C and x²y"- xy'

A: Given : second-order differential equation    x2y''-xy'=11-x-1 To find : Laplace transform of given…

Q: tr(AA') = (tr(A))* There exist square matrices A and B such that AB-BA=I.

A:

Q: du u = ek sin-¹ m. m = sinx.k = 2² Iny,l == then at mv2 In 2 4 In 2 b) 2√2 rv2In 2 # In 2

A:

Q: 1. Do not use a theorem to find the ff. Z if yz? + z = 5xy – 1. %3D

A: In the multivariable function, if we have to find the partial derivative of one variable with…

Q: f (て) be a top. space 3.ト X-Tab, cidiel (xて) be top space %3D %3D et A= {bj. FindO A Tb,d] %3D 2.…

A:

Q: Using the prove by contradiction, show that a. A'U B'UC = AUBUC %3D b. AOB = ANB 109 %3D

A: Proof by contradiction : ¬P→Q⇔P∧¬Q Assume both P and ¬Q are true. Hence, P∧¬Q cannot be true and P→Q…

Q: Q6A)If y = cos ¹) prove Zyy + z = 0.

A: See this solution in below

Q: [2 1] 1 3 l3 4] 4 Q2) Assume A %3D and B show that (AB)' = B' A' 6. %3D

A: