Discrete MAth Compute the chromatic polynomial of K3,3

Q: Prove that if every subgraph of G has a node of degree at most d, then G is (d + 1)-colorable.

A: We know that G is itself a sub graph of G, so G has maximum vertex degree d. A standard result in…

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Q: 21-3 -da it converges find this value

A: I have given the answer in the next step. Hope you understand that

Q: On a graphing paper, use the following individual vectors to GRAPHICALLY find the resultant vector…

A: I will solve first questionbif you want remainibgvthen repost it.

Q: a) 2xy dx+(1+x²)dy=0 b) y'+(4/x)y=x* ------by exact method ---by linear method

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Q: You bail out of the helicopter ripcord of your parachute. Now k = 1.6 your downward velocity…

A: Given that,                   dvdt=32-1.6v,    v(0)=0.

Q: Prove that if a polynomial function p(x)= a + ax + ₂x² is zero for x=-1, x-0, and x-1, then a - a₂…

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Q: Find the F. T of the following Signals X(t)=28(t + 2) - 28(t-2)-rect(+¹)+rect(²¹) -2 2 1 2 +t

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Q: 4. In fitting a straight line, the formula to find the sum of the squares of the residuals is (a) E…

A: 4. Hint: Here we need to just write the sum of the squares of the residuals.

Q: With respect to right-handed Cartesian coordinates, let a = [2, 1, 0], b = [-3, 2, 0], c = [1, 4,…

A: Given: The vectors are a=2,1,0, b=-3,2,0, c=1,4,-2 and d=5,-1,3. To find: The value of the following…

Q: F-1(- n+1 = -In( n+1 n+1-i Explain why, although A is not known, it suffices to use λ = 1 when…

A: We have given  F-1 (i/(n+1))= (1/lembda) ln(n+1/n+1-i)                     =  - (1/lembda)…

Q: 2. If the edge of a cube is 1.75 m, then how many square centimeters are there in its entire…

A: Sol:- Edge of Cube = a = 1.75m Entire surface area = 6a2

Q: Show that the function f(t) = sin(e*) is of exponential order as t → +oo but that its derivative is…

A: To show that the given function ft=sinet2 is of exponential order.

Q: Let Ø be the golden ratio. Write Ø8 in the form (a+b√5) where a, b are rational numbers.

A: What is Golden Ratio: If the ratio of two numbers is the same as the ratio of their sum to the…

Q: Angle of a line with the positive direction of the x-axis is 0 (0 is a cute). The line is rotated…

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Q: Let g(x) = f(t) dt, where f is the function whose graph is shown. Answer the following questions…

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Q: Show a graphing calculator computation of the eigenvalues and eigenvectors of the matrix?

A: Given matrix is A=-0.50.00.00.5-0.250.00.00.25-0.2 Since given matrix is in lower triangular form,…

Q: Q2:/ Sketch the region (R) of integration ſ x² dydx and evaluate the integration. Then reverse the…

A: The formula for iterated integrals with non-constant limits of integration is:…

Q: ILLUSTRATION 2.11 Let f(x) = x³ + x + 1 and P(x) be a cubic polynomial such that P (0) = -1 and…

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Q: First verify that the given vectors are solutions of the given system. Then use the Wronskian to…

A: Given : x'=1-40-201006-12-1-60-40-1x  ; x1=e-t1001  ; x2=e-t0010  ; x3=et010-2 ; x4=et 1030 (a) To…

Q: Determine the right most digit of 10000 the number 2 7x 137

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Q: 1- Given the waveform in Figure below, determine if the trigonometric Fourier coefficient has zero…

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Q: Q1:/Verify that the given function is harmonic and find it is harmonic conjugates so that f(z) = u +…

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Q: Q1) A Cylinder tank of radius 4m and height 10m is initially filled with water. At the bottom of the…

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Q: Sample Problem 1.9 Given the vectors A = 8i + 4j - 2k N B = 2j + 6k m C = 3i - 2j+ 4k m calculate…

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Q: The equation f(x) = x² - 6 = 0 has a root near x = 2. a) Apply four iterations of the Secant Method,…

A: Solution:- f(x)=x2-6Ist Iteration:-x0=1 and  x1=2f(x0)=f(1)=-5 and…

Q: Modular Arithmetic -  Find the class representaives in Z26 for the following: -1000 -30 -1 15 2001…

A: For any number n, the representative in Z26 is (n mod 26)  So, representative for -1000 is = -1000…

Q: In the following system Problem, categorize the eigenvalues and eigenvectors of the coefficient…

A: Given system of differential equation is x1'=2x1+3x2x2'=2x1+x2 We can write it in matrix form…

Q: A/ Show that as a half range series of cosine terms for 0 < x < 1, π² /cos 2x cos 4x cos 6x +- 6 +…

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Q: Apply Fourier transform, jw F(w) = F₁ (w) + F₂ (w)...... equation 2 F₁ (t) = −6(t + 2) +…

A: What is Dirac Delta Function: The unit impulse, sometimes referred to as the Dirac delta…

Q: Find the differential equations of the following primitives by eliminating the arbitrary constants.…

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Q: How many real solution the equation have? x^5+x=1

A: Sol:- Let's find the solution of the given equation:- x5+x=1x5+x-1=0Find one solution for x5+x-1=0…

Q: 3 Find the F.T. of the following Signals using differentiation prop. <-2 2 2 At 2 Ans FCw) =…

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Q: Angle of a line with the positive direction of the x-axis is 8 (8 is a cute). The line is rotated…

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Q: Find the F. T of the following Signals X(t)=28(t + 2) — 28(t-2)-rect(²+¹)+rect(^¯¹) 2 2 1 -i 2 At 2

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Q: Calculate the following double integrals and draw the region of integration.

A: Given: The integral is ∫12∫yy3exydxdy. To find: The value of the given integral. To sketch: The…

Q: 03/: Find the area over the region R that lies inside the cardioid r=1+cose and outside the circle…

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Q: A line OP makes equal angle with coordinate axes then find its direction cosines.

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Q: Name sets with cardinality (a) 365, (b) 12, (c) 7, (d) 11.5, (e) 0, (f) 1024. &#160;

A: Given: The cardinalities, (a) 365, (b) 12, (c) 7, (d) 11.5, (e) 0, (f) 1024. To name: The sets with…

Q: First verify that the given vectors are solutions of the given system. Then use the Wronskian to…

A: Given system is x'=3-20-13-20-13x First given vector is x1=et221 Now, x1'=et221 and,…

Q: Use the appropriate compound interest formula to compute the balarice in the account after the…

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Q: 3.) 12 sin ¹3t Note: a¹ = (a²)² 2

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Q: write these numbers in polar form for the complex setup: (1,-1,i,-i)

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Q: 5. Show that another approximation for log n! for large n is log n!=nlog(n)-n by expanding the log…

A: We will use property of log  log(ab) = loga-logb to expand log (n!) and then convert it into…

Q: 1/ Let (X₁T) and (Y₁J.) be top spaces and fix-x be a surjective and continuousmap, then y is Compact…

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Q: Estimate the volume of the following solids by Riemann sums m n v~ΣΣf(xi,3;)ΔΑ i=1 i=1 Estimate the…

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Q: Q4:A/ By using Exact equation solve the first order differential equation 2y²+ ye+ (4xy + xe +…

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Q: Solve each of the following by Laplace Transform: 1.) ď² y dt² +2 2 +y dy dt y (0) = = sinh 3t - 5…

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Q: In Problems 1-10, find a × b. 6. a = 4i + j − 5k, b = 2i + 3j – k In Problems 11 and 12, find P₁P₂ ×…

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Q: 8. One card is randomly drawn from a deck of cards. Let, A: The card is a face card (Jack, Queen or…

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