Discrete Mathematics/combinatoric Please show your work  Question: Derangement is a permutation of π ∈ Sn that has none of the fixed points, or The components are still in their first placement. How many different derangements of [n] are possible?

Q: Considering a cube of side and a function vector B=√xi-y + zk calculate b)calculate VXB

A: Given B=xi-y1/5j+zk Here      Bx=xBy=-y1/5Bz=z We know that ∇×B =…

Q: 43. Choose the number q so that (if possible) the ranks are (a) 1, (b) 2, (c) 3: 6 4 2 -3 -2 -1 9 6…

A: 43. To Choose the number q so that (if possible) the ranks are (a) 1,  (b) 2, (c) 3   Given…

Q: Use the graph of f(x) = // below to find a number & such that f (x) -0.5| < 0.1 whenever 0 < x - 2|…

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Q: Let f RR be an increasing function. Suppose that there exist a, b R satisfy b> a and a ≤ f(a) and…

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Q: -6 -2 4 2 6 -2 4 -6 y 2 4 6 ww X

A: 1.As we can see the graph intersects only at the origin. Hence , x-intercept is (x,y)=(0,0) Also…

Q: d b i e a j f C 9 Complete the sequence of vertices printed by a post-order traversal:…

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Q: A vector field is given as G = (1/(√x² + xy))(e¯²ax +xzay), find the unit vector which is normal to…

A: The given vector fields are: G=1x2+xye-zax+xzayP=3x2ax-4yay We have to find the unit vector which is…

Q: Please, expert, I want to solve all these questions Homework: Evaluate the following integrals: 8.f…

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Q: S 18 What is the missing number? 30 1 S 3

A: Please comment if you need any clarification. If you find my answer useful please put thumbs up.…

Q: D²y(t) + 12Dy(t) + 36y(t) = 1t³ y (0) = 1; Dy(0) = 0

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Q: Show that the following argument with hypotheses on lines 1-3 and conclusion on line c is valid by…

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Q: The expression A=[(0)1³ de describes the area in polar coordinates bounded by the curve r=f(0) and…

A: Green's Theorem:  ∮C(Ldx+Mdy)=∬D∂M∂x-∂L∂ydxdy Let ∂M∂x-∂L∂y=1, then ∮C(Ldx+Mdy)=∬Ddxdy. We can find…

Q: (a) Graph the function f(x) = 1/x (b) Hence, using translations, reflections etc., obtain the graph…

A: Sol:- (a) First find the some information about f(x)=1/x Domain of  1x :  Solution:  x&lt;0  or…

Q: a. Show that x² + 2y² - 8z = 5 has no integral solutions. b. Use theory to determine if x² + 14x −…

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Q: Which of the following statements are equivalent? Proof your result. P→ (QR) (P→Q) ^ (P→ R) (PAQ) →…

A: Introduction: When identical statement variables are used to denote the component statements, two…

Q: Which of the following statements are equivalent? Proof your result. P→ (QR) ! (P→Q) ^ (P→ R) (PAQ)…

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Q: 2. Consider the following dynamical system on the plane: x = (x-3)(y-2), y = yx²-x. X. (a) Determine…

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Q: Let (X, T) topological space, where X = {a,b,c,d} and T = {X. Ø, {a}, {a,b}, {a,b,c}} Find a) Basic…

A: Given that X, T topological space, where X=a, b, c, d and T=X, ϕ, a, a, b, a, b, c.

Q: = i) x(t) = j) Στο 1-t, 0<t<1 otherwise 0, e-it-2n|

A: Given that x(t)=1-t2 , 0&lt;t&lt;10 , otherwiseFor 0&lt;t&lt;1X(ω)=∫01(1-t2) e-jωt dt…

Q: dy senx+y cos x = xsenx dx y(7/2)=2

A: Let us consider a differential equation of the form,  dydx+P(x)y=Q(x) Then solving the equation…

Q: Find the 4 by 3 matrix A that represents a right shift: (x₁,x2, x3) is transformed to (0, x₁, x2,…

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Q: 1. For r < 1, define fn(x) = ²x. (a) Prove that for x < 1, k=1 ƒ(x) = lim_ƒn(x) = 84x x(1+x) (1-x)³…

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Q: Question 3. 1. Let f: C\ {0, 1,2} → C be given by f(z) expansion of f in each of the following…

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Q: Considering B=√xi-y a) Sv B dv a cube of side and a function vector + zk calculate

A: Please comment if you need any clarification. If you find my answer useful please put thumbs up.…

Q: d: R²XR² → R₁+ d(x, y) = { x = (x₁, x₂), y = (y₁ - y₂) ER² 1 1 { 132₁_2₂1,1} if x₁=3₂₁ ; 1 otherwise…

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Q: If F=xi+yj, prove that JF.ñds equals [V.FdA, where R is the disk of radius C R "a" and centre at the…

A: Given Data: F =xi  +yjTo Prove:∫C F . n ds =∫R∇·F dA where R is the disk of radius ''a'' and centre…

Q: (b) Starting with the voltage divider rule, show that the power transmission coefficient T of an RC…

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Q: For both graphs drawn below, verify Euler's formula: (# of nodes) - (# of edges) + (# of loops) = 1.

A: Use the given information.

Q: what is the order of the method Uxx //₂2 [u/x+hgy) - 2x(my) +u/m_b₂y)] I 62

A: Using Taylors series expansion for first argument abou (x,y) For fixed y, u(x,y) as a function of x…

Q: 3. (a) If f:X→ Y and g: Y→ Z are functions and go f is one-to-one, must g be one-to- one? Justify…

A: Answer is NO  It is not necessary that if g∘f is one one then g must be one . But some time it may…

Q: Given a set of data that measured a diameter of a tube d1 = 1.65 mm, d2 = 1.66 mm, d3= 1.65 mm, d4 =…

A: The measured data are: d1=1.65 mm, d2=1.66 mm, d3=1.65 mm, d4=1.64 mm. We need to calculate the…

Q: The velocity potential o, (as defined in Question 6 (c)), for a fluid motion is specified in…

A: Given velocity potential,φ for a fluid motion is specified in spherical coordinates (r,θ,ψ)by…

Q: Consider the sets S = {1, 2, 3, 4, 5} and AC S x S given by A = {(1, 1), (1,4), (3, 1), (3, 4), (4,…

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Q: Which of the following statements is FALSE? a) The average rate of change is the slope of a secant…

A: Average rate of change of a function y=f(x) is  ∆f∆x

Q: Consider a physical system whose three-dimensional state space is spanned by the orthonormal basis…

A: Given Data: H^ =hω03i0-i30002 , B^ =b07i1-i-i71+i1+i1-i6D^= 002α02α02α0-3αψ0=e1ψ0e2ψ0e3ψ0=236

Q: Find two linearly independent solutions of 2x²y" - xy +(-3x+1)y=0, x > 0 of the form y₁ =…

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Q: Solve the differential equation of (A) In y=c Inx B x=clnx dx xlnx

A: Introduction: Any equation with a minimum of one normal or partial|derivative|differential…

Q: solve the following one-dimensional second-order partial differential equation. which is known as…

A: Given,          a2∂2u∂x2=∂2u∂t2, 0&lt;x&lt;L, t&gt;0…

Q: u² x(t = sin du 2 vit) = [coeds. y COS x(t) and y(t) are functions defined by integrating up to a…

A: It is provided that x(t)=∫0tsinu22du and y(t)=∫0tcosu22du. We need to verify if the curvature:…

Q: 3. The survival of two species depends on their mutual cooperation. For instance, a species of bee…

A: Given- The survival of two species depends on their mutual cooperation. For instance, a species of…

Q: Find all the values of x such that the given series would converge. (10x)" n3 The series is…

A: 1. Given ∑n=1∞10xnn3 By Ratio test limn→∞10xn3n &lt; 1⇒ |x| &lt; 110 = 0.1 Also the series is…

Q: please help with Question 2

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Q: 3. (a) If f: X→ Y and g: Y→ Z are functions and go f is one-to-one, must g be one-to- one? Justify…

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Q: Three sticks are arranged to form a right triangle. If the lengths of the three sticks are 0.88295…

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Q: Suppose we have n> 1 vectors in R" vector space where the ith element of the ith vector (for 1 ≤ i ≤…

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Q: Verify that the set C[a, b] of all continuous real-valued functions defined on the interval a ≤ x ≤…

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Q: The Euler totient function is defined as ϕ (m) = |{k : 1 ≤ k ≤ m gcd(k, m) = 1}|, or rather the…

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Q: f(x) = Co = C1 C₂ C3 = || = C4 = Represent the function 21n(9-x) as a power series (Maclaurin…

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Q: If the compound interest on P3, 000.00 in 2 years is P500.00, then the comcound interest on P3,…

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Q: Find (and simplify) the equation of the tangent line to the graph of y = 24 at x = 1.

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