Let A = {6, 8, 13, 15, 9, 16} and define a relation R on A as follows: xRy ⟺ 7 |(x – y) Draw a directed graph for R.

Q: Spring 2021 # 4. Let p(z) = 2+ 32 + 6. (a) Show that p(z) has three zeros (counting multiplicity) in…

A: Given :  It is given that,  p(z) = z4+3z3+6. To show :  We have to show the following statements ;…

Q: x +1 1. dx x* — 5х+6 dx 2. x(x² +1) X\x

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Q: aph each piecewise

A: d) Given,            f(x)=x+2,if x≤-1-x2+2,if x>-1

Q: (c) Consider the following ordinary differential equation (ODE): y"(1)+3y'(t)= 6e", subject to y(0)…

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Q: TRUE OR FALSE. Determine each of the following statements if it is true or false. If a^3 divides…

A: In 1st question given that a3 divides c2 so c2a3=k where is real number. Now c2a3=k…

Q: Activity #3 in Differential Equations Solve for GS/PS for the following differential equations.…

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Q: What is the general solution of the differential equation y" + 4y = cot 2x? Oy=G coe 2 +Gn 2-ain 2e…

A: variation of parameters, suppose it is desired to find a particular solution of the equation y″ +…

Q: Find the inverse of A= 1 1 1 Use any method. Show your solution 0 2 3 5 5 1

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Q: Given the plane † = (-2, 1,5) + s(3, – 2,0) + t(1, 1, 5), s, t e R. The plane cuts the x, y and…

A: Given the plane r→=-2,1,5+s3,-2,0+t1,1,5,s,t∈ℝ We have to find the volume of the pyramid.

Q: Is there a real number ______ whose square is -1? b. Does there exist _____ such that x 2 = −1?

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Q: 9. True or False? The interval of convergence is the same as the domain of the power series. 10.…

A: We need to answer 9th and 10th Questions using basic knowledge of convergence of power series.

Q: Find the mass of the solid with density p(x, y, 2) and the given shape. p(x, y, 2) - 48, solid…

A: Given ρ(x,y,z)=48, and solid bounded by z=x2+y2 and z=64We have to find Mass

Q: f(2022) (0) 3) Solve for the following equation: The Maclaurin series expansion of tan-r is given by…

A: We have to approximate the 1/2 arctan(1/2).

Q: 8s2 + 12 8. F(s) = (s – 2)(s – 4)4

A: As per bartleby guidelines we are supported to answer only first question when two or more are…

Q: Define L: Z → Z and M: Z → Z by the rules L(a) = a² and M(a) = a mod 5 for each integer a. (a) Find…

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Q: The temperature (T) at which water bols. varies inversely as the number of feet (h) above sea level.…

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Q: Let A = {a, b, c, d} and define a relation R on A. The directed graph of the relation is shown here.…

A: We have: The relation is: R=a,c,b,a,c,d,d,b

Q: Solve the differential equation with the appropriate method. Finalize the answer equated to ky^n 2.…

A: We have given a differential equation ,  dydx + y = y2 sinx This is Bernoulli equation of the form ,…

Q: 1. Find all solutions of u,+2u-3u- – 4u, +4u, Hint: Solve the characteristic equation (y)²-2y-3=

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Q: Find the area of the region bounded by the graphs of the equations. y = 5x2 + 3, x = 0, x = 2, y = 0

A: We have to find the area.

Q: The payment on a 15 year loan at 9.36% compounded weekly is $180.00. Calculate the amount of the…

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Q: Use the Right Endpoint approximation method to approximate the area under the graph of the function…

A: The given function is fx=4e-2x.

Q: Give the parametric and symmetric equations of the line that passes through the point (4, –3,5) and…

A: we have to find the equation of line which is passes through the given point and perpendicular to…

Q: Let x, y ∈ Z. Use a direct proof to show that if xy is even and x is odd, then y is even.

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Q: Let f:X→R be a Lipschitz continuous function defined on X. Show that f is uniformly continuous on X.

A: Given : function f:X -> R is a Lipschitz continuous function defined on X . To show : f is…

Q: Solve the given problems. 1. Determine the distance i to the center of mass of the homogeneous rod…

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Q: Given #= (1+--). dy 2 dx What is the value of k such that y is parallel to the curve y = 3x +1 at x…

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Q: In a fishery the long-run harvest function (harvest volume) is H(E) = aE – bE?, with a, b…

A: For relative maximum or minimum we will use following procedure  To maximize or minimize  a function…

Q: . Use Pascal's triangle to expand the binomial expression (1+x)^3 2.Use the binomial theorem to…

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Q: dx dy dx dy Use elimination to solve: + = e'; -= *+

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Q: Determine one real root of h (x) = In() = -3 between -0.9 and –0.2 using the Bisection Method.…

A: Given, h(x)=lnxx3-8=-3    ; -0.9,-0.2h(x)=lnxx3-8+3=0To find: One real root of h(x) between -0.9 and…

Q: . In one model of the changing population P(t) of a community, it is assumed that 4 = -, where and…

A: As we have to solve for p(t) in (a) so there is clearly  a misprint it should be dD/dt in place of…

Q: • b. Σ n =1 3n – 1 -

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Q: Find the inverse of laplace, f(t) if: 2s2 + 8 3. F(s) : ș3 – 7s2 + 14s - 8

A: Factorize the denominator of the given fraction.…

Q: Find the cubic function that models the data in the table below. - 2 - 1 1 2 3 4 y - 24 -5 - 3 - 8 -…

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Q: Given the vectors x and y',..., y™ in R". Our objective is to check whether x E conv{y', . , y™}.…

A: Given:vectors x and y1,...,ym in Rn

Q: 40. ƒ(x) sin x + 1, [-T, T] %3D

A: 40. Given that, the function is fx=sinx+1,-π,π. That is,∫abfxdx=∫-ππsinx+1dx. From the given…

Q: Find a basis for the nullspace of the matrix. (If there is no basis, enter NONE in any single cell.)…

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Q: 12. How much will a mother receive from her pension plan after paying P900 every month for 20 years…

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Q: Find the third order derivative of y = In(cos(2x))³. A. y' = -40sec² (2x)tan(2x) B. y' = -80sec?…

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Q: ind the inverse of laplace, f(t) if: 8s2 + 12 9. F(s) (s - 2)2(s – 4)4

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Q: Evaluate the iterated double integral: x+4 sin (y³ – 3y?) dy dx

A: Evaluation of the integrated Integral, bu using order of change of integrals

Q: (c) Justify the following statement and find the size of giant component in each case. "For a large…

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Q: Find the radius of convergence, R, of the series. (x – 9)^ n=1 R= Find the interval, I, of…

A: Interval of convergence and radius of convergence

Q: dlISwer. Use a separate pad paper for your solutions. 1. Michael saved P10 in January. Suppose for…

A: Since you have posted a multiple question according to guildlines I will solve first question for…

Q: (Refer to Exercise 2) A differential equation (see Exercise 2 above) and various initial conditions…

A: Disclaimer: Since you have posted a question with multiple sub-parts, we will solve first three…

Q: e, PQ//RS, find the value of x P. A Q 500 1230 R B

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Q: Provide NEAT and COMPLETE solutions for the following problems.  2. Prove by contraposition: Let x,…

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Q: Determine whether the set W is a subspace of R³ with the standard operations. If not, state why.…

A: The solution is given as

Q: 3 Write a limit using summations that would equal el+a dx. Answer: lim Submit Answer k=1 =WI

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