q23- Suppose that P(M) = 0.6827, P(N) = 0.6437, and P(M υ N) = 0.6752, then P(M ∩ N) is: a. 0.3256 b. 0.4341 c. 0.6512 d. 0.7799

Q: ds if s = Find dt 7t + 3 ds dt II

A: We have given;

Q: Q3:- find the erea of the shap by the order 1- SS dydx 10

A: Please refer the attached image for complete solution.

Q: Evaluate I = √x+e²×¯¹dx 2x-1 a) By using Trapezoidal rule with 12 segments b) By using Simpson's one…

A: The given integral is I=∫17x+e2x-1dx. To Evaluate: (a) Using Trapezoidal Rule with 12 segments. (b)…

Q: Q3: Prove that Σ(y₁ - y) = 0 AND Σfi(y₁ - y) = 0

A: The question is about proving given equation. To prove : ∑ ( yi - y¯ ) = 0∑ fi ( yi - y¯ ) = 0

Q: Let x, y e Z. Prove that if 3x+7y is odd or 5x + 6y is even, then x or y is even.

A: We have given that for x,y belongs to integers. If 3x+7y is odd or 5x+6y is even then x or y is even…

Q: TQ residue of f(z) = e (z – 1) (z + 9) at z = -9 is 10e-9 :Select one True False

A:

Q: Consider a, = V4n² + 3n – 2n for n > 1. %3D -

A: Introduction: The sequence is a set of functions with the set of natural numbers as the domain of…

Q: Z1 is complementary to ZM 22 is complementary to ZM Z1 = 2 Given: Prove: M R 2

A: Given: ∠1 is complimentary to ∠M. ∠2 is complimentary to ∠M. To prove: ∠1≅∠2 According to the…

Q: 0 <m < n such that am = e. (Hin

A: Subgroup generated by any element in a finite group will have at most n element where n is order of…

Q: -145 2. find least 0అ కావులి Sంఖనాుంది spcave Axz b A z] 1 -4 1 1 2. 2. enter xas a Coloumn ve

A: Given that, AX=b A=1-4010012-1121,   b=3134 The least square solution to the system AX=b is the…

Q: Is it possible to find a number  n  such that is ∫0∞  xn dxconvergent?

A:

Q: 1 If z = 2 V3 -i, then find ()*

A: Given complex number is: z=-1-3i2 Find the conjugate of complex number: z¯=-1+3i2 Find z¯4?

Q: a²z If z = In(x² + y²)., find ax2 ay?

A: Here we have;  z=ln(x2+y2) ...................(1) partial derivative with respect to x

Q: Q1 (a) Calculate the coefficient of æ'yz in (r+y+2)13. (b) In her discrete math class, Karen was…

A:

Q: 1 Using Convolution theorem, find L' ,2 |(s² +a²)?

A:

Q: Q3: Prove that (9":n e Z} S {3":n Ee Z} but {9":n e Z} (3":n E Z}.

A: To prove:  {9n:n∈ℤ} ⊆{3n:n∈ℤ} but {9n:n∈ℤ} ≠{3n:n∈ℤ}

Q: for n>2, 5 . Deermine for whpch n, n2-2 let |anlく,

A: Given  an = 5nn2-2

Q: show that Ф (x, y, z) = аф PDE : агф дуг + дуг I х2 +у2 +Z2 024 072 satisfies the

A:

Q: Prove that i 224 s 2xP for xzO, y zo i and 1 t L-l with p>

A: Given that x,y≥0. And 1p+1q=1 with p&gt;1. Consider gx=xpp+1q-x. Then g'x=xp-1-1 and g'x&lt;0 when…

Q: Let P = {p:p=6x-1, for some x EZ} and Q= {q:6y+5, for some y EZ). Prove that P= Q

A:

Q: Q1 (a) Calculate the coefficient of a'y z in (r+y+2)13. (b) In her discrete math class, Karen was…

A:

Q: Q: Examine y (o.4), Using Runge - Kutta Order 4 method if X = 4n + 2

A: Given y′=4x2+2y,      y(0)=1,   h=0.1,   we have to find y(0.4).Forth order R-K…

Q: 5. (BH) Calculate det B, where 0. 4 1 1 В — 1 -2 4 -1 2 1 -1 0 7

A:

Q: a2 z a2z If z = In(x² + y²), find + 2 Əx2 ду?

A: The given function is z=ln(x2+y2).

Q: Show that Z, dv=2010 %3D if B= 2) : -1 Śn s3, ISySY,e

A:

Q: Prove indirectly: "V n E Z, 4 ł (n² – 2)."|

A: Ans:Let us assume that 4/n2-2;∀n∈zthen we have there exist a positive integer k such…

Q: Employ a suitable c 2n² +3n diverge (a) V5+n² n=1

A: ∑n=1∞2n2+3n5+n5limn→∞an+1an= limn→∞2(n+1)2+3(n+1)5+(n+1)52n2+3n5+n5= limn→∞…

Q: FOR N=195, by fermat's theorem an-2 =

A: Given: FOR N=195, by Fermat's theorem an-2

Q: Consider the following LP Min z= 3x, + 2.x, +7x, s.t - x, +x, =10 -2x, + x, - x, <-10 X,,X,,X, 2 0…

A: In the given LP problem when we solve it via simplex method, we use a series of tableaus.

Q: 1. For an = 5n2 + 9n3 + 1, an = n2, prove or disprove: rn = O(an) (n → o)?

A: We will use the standard definition.

Q: (b) Let z = x + iy = re?". Find |z| and z² first in terms of x and y and then in terms of r and 0.…

A: Given:

Q: Q4. Find guerel polution of following systens uning either method' of undetermind coefticients or…

A:

Q: 9. Let S- {xeZ| 3r.seZ,x=9r+6s) and T={xeZ| 3x} b) Prove that T Cs. a) Prove that SCT. Hint for (b):…

A: Part(a) We have S=x∈Z/ ∃r,s∈ℤ, x=9r+6s and T=x∈ℤ 3/x  Now, let a=9r+6s be an element in S. Then…

Q: What is the net crarop for fW={+5,05 as we qo from x=2 to X=5?

A: The given function  f(x) = x2 + 5

Q: In Euler's method, wk = y(tx) for k = 1, ..,n. Select one: O True O False

A:

Q: 08. Assyme that The fuyctign 4defined g defined femetionof ginen, egua jon. se the odhnique implig…

A: solution is given below

Q: 4. Show that V2 ¢ Q(v3) and Q(V2, v3) = Q(/2+v3). Hence find the mmp of V2+ V3 over Q.

A: We know that ,  ℚ2 = a + b2  / a , b ∈ ℚ ℚ3 = a + b3  / a , b ∈ ℚ  We need to prove that , 2 ∉ ℚ3 On…

Q: 03) find the ax en the sl abetwed wol y=J2-X, and y= 0

A:

Q: 4.By applying the Convolution Theorem to calculate L-1 is obtained: Determine the value of (a+b): a…

A: We have to find the solution.

Q: Then show that N(A) = R(AT)+ and N(AT) = R(A)+. %3D 11-1 02-3 -1 1-2 N(A) = N(AT) =

A:

Q: 4. Show that V2 ¢ Q(V3) and Q(/2, v3) = Q(/2+v3). Hence find the mmp of V2+ V3 over Q.

A:

Q: Prove that e“ p.w. on R. n! n=0 M8

A:

Q: (3b) Let n E Z. Prove that if 3|(2n² + 1), then 3 ł n

A:

Q: Consider the systenm o o-21 x + %3D 0 3 Frnel the ennit s tep esponse of the system.

A:

Q: In Euler's method, wr = y(tx) for k=1, · .., n. Select one: O True O False

A: if you find my answer helpful please put thumbs up. thank you. the required solution is given below…

Q: Let x, y e Z. Prove that if 3x + 7y is odd or 5x + 6y is even, then x or y is even.

A:

Q: Let f(n) = 2n – n? + 10n – 7. Show that f(n) is O(n³) using specific values of C and ng-

A: