dx x dyx+(1+x7y}=12

Q: 4 Let x € [0, 1]. Show that ge 2 satisfying f(x)= 5 FC f(t) gx (t) dt & feu

A:

Q: Given that A1,A2,A3,... An are n points in a plane whose coordinates are (xl,yl), (x2,y2), (xn,yn),…

A:

Q: Let p be a prime in an integral domain. If p | a1a2 .....an, prove thatp divides some ai.

A: There is prime p in the integral domain. Our aim is to show that if  p | a1a2 .....an, then p…

Q: Let f: IR be a convex fun Theorem x1,x2,.. , are points in I and A₁, A2,..., An are real numbers [0,…

A:

Q: Show that every element of GF(pn) can be written in the form ap forsome unique a in GF( pn).

A: Given: GFpn. To show: Every element of GFpn can be written in the form ap for some unique a in GFpn.

Q: [an] 2. If A is similar to a diagonal matrix D then A is similar to AT.

A:

Q: The sides of a triangle lie on the 3x+y-5-0, x-3y-1=0, and x+3y+7=0. Find the equation of the circle…

A:

Q: x=x++(x-1 =x++ (x-1) for all x in R then find the value of a Let If f(0) = 100 And (5). let a…

A: a

Q: Prove that Z[√5] is not a unique factorization domain.

A: To Prove: Z5 is not a Unique factorization domain.

Q: The characteristic polynomial of A 1 -2 1 € M3(R) is p(A) = −X(X+3)². 1-2 1. Find the set of…

A: A=-2111-2111-2pλ=-λλ+32=0

Q: A connected graph with 7 nodes and 7 edges has how many loops?

A: Given: The nodes of a connected graph=7 and the edges of a connected graph=7To find: The number of…

Q: A. y =q₁z+₂√7 D. y=+ 2. ( ) Let Y(t) At+ A₁t+ A, be a solution to y" + 4y = 4² where (A, A₁, A₂) are…

A:

Q: First part of the question is that convert the following Cartesian coordinates to the corresponding…

A:

Q: Show that a regular 9-gon cannot be constructed with an unmarkedstraightedge and a compass.

A: To show that a regular 9-gon cannot be constructed with an unmarked straightedge and a compass. Here…

Q: Use cylindrical shells to find the volume of the solid obtained by rotating the region bounded on…

A: Given that solid obtained by rotating the region bounded on the right by  the graph of g(y)=7y and…

Q: tan-1 X a+√a²-x² = 2 X sin-¹ *, -a< a

A: To prove tan-1xa+a2-x2=12sin-1xa, -a&lt;x&lt;a Let x=asinθ

Q: Question 4 The inverse tan can be calculated using the integral n = ²(x)=√√₁²² tan -dz 01+2² a Use…

A:

Q: Circle the best answer in each of the following questions, and fill answers into the table below:…

A: Q1 asked and answered.

Q: Find the splitting field x4 - x2 - 2 over Z3.

A: In mathematics, a splitting field is a field extension that contains all of the roots of a given…

Q: 3. Determine the Jordan Canonical Form of A if the characteristic polynomial (1-A)²(2-A)³ with…

A: Given that the characteristic polynomial of A is 1-λ22-λ3 with dimKerA-I=1 and dimKerA-2I=2. We have…

Q: (b) (i) Solve the following system of linear equations by reducing its augmented matrix to…

A: The given problem is to find the solution for the given system of linear equations by using the row…

Q: 1. Let a, b, c be positive real numbers, and let p, q, r be [0,1/2]. Suppose a+b+c= p + q + r = 1.…

A:

Q: Step 5 We have found the following derivatives of the functions u₁(x) and u₂(x). U₁= (4+ e*) Find…

A:

Q: 4. The following Differential, du = yx dx - yx dy, is a. Second order b. Inexact C. Exact d. None

A: Given Differential equation du=yxdx-yxdy Comparing with  M(x,y)dx+N(x,y)dy=0 Here…

Q: Suppose that f (x) and g(x) are irreducible over F and that deg f (x)and deg g(x) are relatively…

A: Given: Two polynomials f(x), and g(x) which are irreducible over F. deg(f(x)) and deg(g(x)) are…

Q: ow using partitions that the function f(x) = r² is Riemann integrable on 1], and that

A: Let f:[0,1]→R be a function given by f(x)=x2 .The uniform partitionPn of [0,1] is defined as 0,1n…

Q: 1. Evaluate the determinant of the matrix -3 4 P = 2-3 -4 -4 -3-4, -1 -2 3 1 -2 3 12

A: As per the guidelines I am answering only one question at a time. 1] P=12-34-1-23-41-23-412-3-4

Q: 3. If is subject to f(x, y) = 7xy x² + y² - 14(x + y) = 49 find a global maximum stationary point…

A:

Q: Determine a Green function for the equation x²y"(x) + 2xy'(x)-2y(x) = f(x), with boundary conditions…

A:

Q: 1. Let B = (B₁)tzo be a standard Brownian motion started at zero, and let (FB)zo denote the natural…

A: note : Since you have posted multiple questions with multiple sub parts, we will provide the…

Q: 23+13 23+1 :

A:

Q: Determine a Green function for the equation x²y"(x) + 2xy'(x)-2y(x) = f(x), with boundary conditions…

A:

Q: Given P(A) = 0.86, P(B) = 0.08, and the fact that events A and B are independent, What is P(A and…

A:

Q: Find one series solution of the 'modified Bessel equation' x²y" + xy' - x²y = 0.

A: The given problem is to find the general solution for the given modified bessel equation ODE. Given…

Q: 7. Let P(x) be the propositional function "x>2" .The domain of discourse of the propositional…

A:

Q: Let Show f is defined for all x &gt; 0. Is f continuous on (0,∞)? How aboutdifferentiable?

A: Given: fx=1x-1x+1+1x+2-1x+3+1x+4-... To Show: Function is defined for all x&gt;0 also explain…

Q: Find the Fourier series of the sign function f(x)=signx={−1,−π≤x≤01,0&lt;x≤π, knowing that the…

A: Given: fx=signx=-1-π≤x≤010&lt;x≤π We have to find the Fourier series of the given function.

Q: 6. Let P(n, k) denote the number of partitions of n into exactly k parts. Prove that P(n, k) = P(n −…

A: Solution:The permutation of a set is represented by                           P(n,k) = n!(n-k)!Now…

Q: If G is a group of odd order and x ∈ G, show that x-1 is not in cl(x).

A: As per the question we are given a group G of odd order, and for any non-identity element x ∈ G we…

Q: The velocity of a falling rain is illustrated in Figure 1. Determine how far the raindrop travel,…

A: t 0 0.5 1 2.5 4.5 vt 0 4.51 7.34 9.33 9.43

Q: Show that a &gt; -1  if and b&gt; a+1  , then the followingintegral is convergent. integral 0 to…

A: Given that a&gt;-1 and b&gt;a+1. To show that the improper integral ∫0∞xa1+xbdx is convergent. Here…

Q: The dynamic model for a process is given by d2y/dt2+6dy/dt+8y=3u(t) where u(t) is the input function…

A: Given:  d2ydy2+6dydt+8y=3ut, y0=dydt0=0. We have to find ut=be-2tthe solution when a ut=be-2t, b…

Q: A. Eliminate the arbitrary constants. Show your solutions. 1. x³y² - xtan²y = C C 2r c 3r 2

A:

Q: Find a basis for and the dimension of the solution space of the homogeneous system of linear…

A:

Q: 10. Assume the economy consists of 3 sectors namely agriculture (A), manufacturing (M) and energy…

A: Given Matrix 0.20.20.10.20.40.10.10.20.3 The total production if the final consumer demand is 80…

Q: Apply the method of undetermined coefficients to find a particular solution of each of the following…

A:

Q: Prove Z(G) = 1⇒ Z (AutG) = 1 and show an example of how this theorem works.

A:

Q: An important example of an infinite series is the geometric series a+a r+a r^{2}+a r^{3}+\dots+a…

A: A geometric series is a type of infinite series in which each term is obtained by multiplying the…

Q: Let a be a complex number that is algebraic over Q and let r be arational number. Show that ar is…

A: Given: a is algebraic over Q and r is any rational number. To Show: ar is algebraic over Q.

Q: Find the equations of the tangent and normal to the equation: y (15-3x²)Inx when x = 1.

A: