1. Let S = {₁, 2, 3, 4, 5, 6, 7} be the set of 7 distinct integers. Use the Pigeonhole Principle to show that there exists a permutation €₁₂€€€€€7 of S such that €₁€₂ (€₂ + 1) (€₁+1) is odd.

Q: For the system of differential equations do the following. p' = -p² + q-1, q' = q (2 - p - q)

A:

Q: 2) Find an example of a continuous map between two metric spaces which is not uniformly continuous.

A:

Q: 3. A particle moves along the parabola y = x² in the first quadrant, in such a way that its…

A:

Q: The Science club is selecting its representative for a competition. The members rank the 4…

A: Voters 2 5 4 4 1st Berlin Antone  Charles Berlin 2nd Charles Berlin Berlin Charles 3rd Dianne…

Q: 5. (a) Find all singular points of (x³ + x² - 5x³x² + 8x - 4)y" + (5x + 10)y' + (10x − 10)y=0 -…

A:

Q: The function given is f(x) = x3 – x – ex – 2 between the interval [2, 3] and threshold of error is…

A:

Q: Let a 0 be a constant. Evaluate the curve Απα3 /3 πα? /2 Ο πα? /4 JIR dA where R is the region…

A: We have to evaluate the double integral  ∫∫RdAwhere R is the region given by  x=acost,y=asint 0≤t≤π

Q: If a = (z-i)/(z+i), show that, when z lies above the real axis, a will lie within the unit circle…

A:

Q: Solve the initial value problem below using the method of Laplace transforms. y" + 16y=96t² -32t +…

A: We have to find the solution of the given differential equation using Laplace transformation.

Q: 1. Let J₁ = {0, 1,2,3} and define f: J₁ J₁ and g: J₁ J₁ by f(x) = (x + 3)² mod 4 and g(x)=x²-3x +- 5…

A:

Q: ace transform of the f 1+ sin2t

A:

Q: Find the equations of the (a) tangent plane and (b) normal line to the surface x2 + y² = 4z at…

A: We have to solve given Questions.

Q: Change the order of integration to evaluate Love LV² sin x² dx dy.

A:

Q: Find a series solution of (x² - 4) d²y + dx² +3(x-2) + 5y = 0 in powers of x. dx

A:

Q: (c) (-1)"n! 2n (d) n=1 n=1 (x - 2)" n!

A:

Q: Question 8 If the standard matrix A of a linear transformation T: R5 → RS has a pivot in each row,…

A:

Q: Make the required change to the given equation. 1. r = 7 to spherical coordinates.

A:

Q: K The matrix associated with the solution to a system of linear equations in x, y, and z is given.…

A:

Q: 9. For n ΕΝ, find and prove a closed-form formula for Σ η 1 i(i + 1)

A:

Q: Prove that if p and q are distinct odd primes, then we have (p-1)(q-1) 4 25 52 TID = (-1) quadratic…

A:

Q: Find the isogonal trajectories cutting at an angle of arctan 4 to the family of curves y = Inx + C.

A:

Q: Problem 4: Consider a graph G with u, v E V(G). If there is no u v walk in G, can we say that there…

A: This is a question of Graph Theory.

Q: 39-44. Mean Value Theorem for Integrals Find or approximate all points at which the given function…

A:

Q: How many shortest lattice paths start at (2, 2) and a. end at (14, 14)? 8- b. end at (14, 14) and…

A:

Q: 9. For the linear operator LA R³ R³ defined by L₁(x) = Ax, for x column vectors in : R³, and 0 1 0 0…

A:

Q: 7. Let D be the region bounde Compute J1₁ x d.A.

A:

Q: 73-86. Derivatives of integrals Simplify the following expressions. 74. d dx ff et² dt

A: As per rule i uploaded 1st question  please mention if any specific

Q: of the congruences f(x) = 0 (m₂) has a solution. Moreover, if s(m) and s(1 the number of solutions…

A:

Q: SIA SIA SIA # 1 2x - Ty 5x - 10y + 4:

A: 8. The given system dxdt=2x-7ydydt=5x+10y+4zdzdt=5y+2z We have to find a general solution to this…

Q: 3. Let f(x, y) = zsin ry. Find: (a) f(x, y) (b) f(x,y) (c) Syy(x, y) (d) fyz(x, y)

A: Given function is f(x, y) = x sin(xy)

Q: The Noyes-Whitney equation for the dynamics of the drug concentration is dc = K(Cs - c) dt where k>…

A:

Q: Find the volume of the solid generated by revolving the region bounded by the following curves about…

A:

Q: 1. Find the general solution of ' 0 0 3 1 X. 0 0-1 1

A:

Q: A. Find the solution of the following differential equations. b4y=5x

A: This is a question of DE.

Q: Let (t)=(-5t2+4,t³-+4,2+³) 7 Find the line (L) tangent to (t) at the point (-1,0,2) L: (x,y,₁2)= +t

A: The given problem is to find the line tangent to the given parametric curve at the given point…

Q: Find the area between the graph of y = 5 - 5x³ and x-axis and −1 ≤ x ≤ 8 using Riemann sums.

A: The objective is to use Riemann sums to evaluate the area between y=5-5x23, x-axis and -1≤x≤8. For a…

Q: x'(t) = -2 4 1 -4 -6|x (t) x (0) = -2 t 0 1 -3 1 any 5-6 The only eigen value of this matrix is -3,…

A:

Q: In(5) S xed. Evaluate

A: Here we have to evaluate given integral.

Q: A farmer has land on which she plans to grow wheat and corn. Each acre of wheat requires 4 hours of…

A: A farmer has land on which she plans to grow wheat and corn. Each acre of wheat requires 4 hours of…

Q: 7. Let f {0, 1, 2, 3,..., 15} {0, 1, 2, 3,..., 15}, defined by f(x) = y = 5x + 2 (mod 16), where 0 ≤…

A: The function f:0, 1, 2, 3,....,15→0, 1, 2, 3,....,15, defined by fx=y≡5x+2mod 16, where 0≤y≤15. We…

Q: How long can a path be in the complete bipartite graph k(m,n)?

A:

Q: x' = y = y 4 x +. 1 2 2 xy xy

A: To find the non zero crical points for the given system

Q: What is most useful about mathematics for humankind?

A: The reasons for most useful about mathematics for humankind are given below.

Q: este ame of order 8. What are the possible homomorphisms P: S4→D4?

A:

Q: :// R Using дw V² wdxdy ди = -ds = i ф с дw ди w = 16ln (x² + y²) + 8xy³, R:1 < y < 5 - x², x ≥ 0. ф…

A:

Q: 14. Area functions The graph of f is shown in the figure. Let A(x) = f f(t) dt and F(x) = √₂ f(t) dt…

A:

Q: A manager wants to determine the number of kanbans to use in a new process for a part. The process…

A: Use the formula N=DT1+XC N is the number of kanbans, D is the usage of rate, T is the average time…

Q: (a) A type of lightbulb is labeled as having an average lifetime of 1,000 hours. It's reasonable to…

A:

Q: Find T(v) by using the standard matrix and the matrix relative to B and B'. T: R² R², T(x, y) = (2y,…

A:

Q: Question 22 A linear system with fewer unknowns than equations must have infinitely many solutions…

A: There are an infinite number of solutions to a system of M*N linear homogeneous equations with M =…