Represent algebraically and graphically the set of values of z for which |z+3| = |2 – 2i|.

Q: Find the value of k such that A is singular. 1 0 5 3 -1 0 2 k k =

A:

Q: Find the value of k such that A is singular. 1 0 4 5 -1 0 3 3 k k =

A: Topic:- Matrix

Q: How do we prove a theorem of the form ∀x(P(x)->Q(x))?

A: To prove the theorem of the form ∀x(P(x)→Q(x)), we apply mainly two steps: 1: We take the arbitrary…

Q: Let f(x)=x2+8x+14. Find all values of c in the interval (−6,−2) such that f′(c)=0.

A:

Q: Letf(x)= (x - 1)(x - 2)(x - 3) Prove that there is more than one 'c' in (1, 3) such that f' (c) =0.…

A: We have to find the value of c

Q: Find the value of k such that A is singular 1 0 5 4 -1 0 L6 5 k k=

A: given isA=1054-1065kmatrix A is singular if |A|=01054-1065k=01(-k-0)-(4k-0)+5(20+6)=0

Q: The ________ ________ ________ states that if f(x) is a polynomial of degree n (n > 0), then f(x)…

A: Consider the statement, The ________ ________ ________ states that if f(x) is a polynomial of degree…

Q: For all real numbers x, cos (2x)= (a) 2 sin x cos x2 sin x cos x (b) sin (x2)sin x2…

A: SOLUTION- formulaconsider the addition formulacos (A+B)=cos A cos B-sin A sin B

Q: ·C) - G) + G)-G) + +-1 - Prove that for any positive integer n, 0.

A: Use simple property of combination.

Q: Find all (real) values of k for which A is diagonalizable

A:

Q: a. Solve b. Determine whether each of these functions is a bijection from Z to Z. f (n) = n² + 1

A: A function is said to be bijective, if it has both injective and surjective properties. Meaning the…

Q: The characteristic of Z5[x]/ is O 3 5

A:

Q: Find all the numbers z such that e^2iz= 5i.

A: We are given : e2iz=5i Now Using  Euler's equation: ( eix=cos x+i sinx) ⇒e2iz=cos (2z) +i sin(2z)…

Q: Solve the folowing equation on [0,2pi) 2sqrt2 +4cosx=0

A: In the given equation, the cosine function is the trigonometric function:   Rewrite the given…

Q: 1. The set of all pairs of real numbers of the form (x, 0) with the standard operations on R2.

A: 4. Given that the set of all pairs of real numbers of the form (x, 0) with the standard operation on…

Q: (2) Find all the numbers z such that elz = 10i.

A: Consider the given. eiz=10i

Q: Prove that x2 + 3x + 3 > 0 for all x.

A:

Q: |z+2i|=|z+1- 3i|

A:

Q: Determine the value(s) of x such that  [ x  2  1 ] [ 2   0  -2] [ x ]                 [ 0   3  3 ]…

A:

Q: Determine all values of x so that det(A) = 0, where

A: Determine all values of x so that det(A) = 0.

Q: if f (x) 9-x and g (x) = Vx, then the domain of (gof) (x) is: [-3,3] O [0, co0) O (-00, c0) O (-0,…

A: on solving this we get

Q: 7. (a) Find all the values of z such that e = 1+ i.

A:

Q: Let F(a) be Z2. Show that a2 and a2+a are zeros of x3+x+1.

A:

Q: Prove that x2 + 3x + 3 ≥ 0 for all x.

A: We have been given the quadratic equation  x2+3x+3

Q: 4. Let z = -4 + 3i and zw = -7 - 2i. By showing clear steps, find w in the form of | | a+bi.

A:

Q: 1. Find all values of z for which z5 -64. Write each of them in the form x + iy with x, Y e R.

A: Given that: z2=-64

Q: Find the sum of f(i) = 2i +2 over the integers 1, 2, 3, ..., 20.

A: Given,           The sum of fi=2i+2 over the integers 1,2,3,...,20

Q: Find the Domain (b) g(x) = In(x² –- x) %3D

A:

Q: Let x² – x – 2 h(x) = x² + 4x Find all the values of x that are NOT in the domain of h.

A: For a rational function, denominator should not be 0.

Q: b) Find the largest possible domain A, where all elements of A are non-negative and f: A → R, f(x) =…

A: Solution:-

Q: Find the value of a such that 1 0. 3 2 2 a- 2

A: I have solved the determinant

Q: (5.1,5.3) Let f(r) = Vx2 -4 and g(x) = 2r +2. Compute (gof)(x) and (fog)(z) and write down the…

A:

Q: (d) Let k(x) = h(g(x)). Find all values of x such that k'(x) 2

A: Here we use derivative of composition.

Q: Represent algebraically and graphically the set of values of z for which |z+3|=|z−2i|

A:

Q: Find the coefficient of x in (1+x'+x°).

A:

Q: -2 Find all the values of s €R such that A = -2 -2 is positive definite.

A:

Q: (ii) Prove that between any two zeroes of Jnx lie one and only one zero of J,n+1* as well as In-1x.

A: From the given information. The objective is to prove that between any two zeroes of lie one and…

Q: Find the value of k such that A is singular. 0 3 2 -1 0 L 3 3 k k =

A:

Q: a) The function m-x+e*,x=0 f(x)=- 2n, x>0 is x' -16x x<0 x - 4x continuous for all real values of x.…

A:

Q: Let f(x) = x4 − 2x2. Find all values of c in the interval (−2, 2) such that f′(c) = 0.

A:

Q: Letf(x) = (x - 1)(x - 2)(x - 3) Prove that there is more than one 'c' in (1, 3) such that f' (c) =…

A: We have to find the value of c

Q: a) If g(x) = 4x + 10 and h(x) = 3x - 2, %3D Find:- g[h(x)] = and express it in its simplest form %3D

A:

Q: find the value of ( ƒ ∘ g)' at the given value of x. ƒ(u) = 1 - 1/u, u = g(x) = 1/1 - x, x = -1

A:

Q: Determine a constant k such that (kA)" (kA) = 1, where -2 A = Is there more than one value of k that…

A: Given: kATkA=1 A=-21-1

Q: (a)] Show that 1+(1+z)/2 csch z In • [(b)] Use part (a) to find all the values of csch (-2i).

A: Let:

Q: Find the value(s) of k such that A is singular.

A: to find the value of k

Q: Determine the number a in Z5 so that (x - a) becomes a divisor of f (x) = x ^ 3 + 2x ^ 2 + 3x + 3 in…

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Q: {1 + x + x, x + x², for P2. Let >(x) = p(x)]B = 1 + 3x + 2x2. The

A: Here we have, B=1+x+x2, x+x2, x2  for P2. Let p(x)=1+3x+2x2 We have to find, p(x)B=?