How many numbers from 1-999 have: 1) all three digits the same? (assume that "1" is represented as "001" for this exercise) 2) exactly two digits the same? (assume that "1" is represented as "001" for this exercise)

Q: Let A be a complex normal matrix, and λ be a complex number: 1. Show A → λI is a normal matrix 2.…

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Q: Utt = 8urr x>0 u(0, t) = 0 u(x,0) = 1 u₁(x,0) = 0

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Q: Write in the form “if p then q” then write the converse, inverse and contrapositive of the…

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Q: Evaluate the integral 1/F. F. dr. F(x, y) = = (5x² + y) i+ (3x − cos y) j where C' is the boundary…

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Q: Use the Divergence Theorem to find the flux of across the surface of the solid bounded above by z =…

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Q: Let Q(x) be the statement “x hasn’t developed a program in JAVA”, where the domain consist of the…

A: We have to write each quantification in English statement.

Q: Match the solution curve with one of the differential equations. x y"- 7y' +12y = 0 Ⓒy" + 4y = 0 Ⓒy"…

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Q: Assume that the graph of y = f(x) consists of a semicircle of radius 2 and two line segments as…

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Q: For the graph shown find a spanning tree for it. Draw the spanning tree then scan or photograph it…

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Q: Find the general solution to the following equations. 1. x²y" — (y')² – 2xy' = 0

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Q: You have an opaque urn with three blue balls and two white balls. One by one, you draw (remove) a…

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Q: 1. Suppose that f(z) is analytic on 0 < |z| < ∞ and there exists a f(z) nonnegative integer m such…

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Q: Suppose that r1(t) and r2(t) are vector-valued functions in 2-space. Explain why solving the…

A: We will take an example to understand the situation better .

Q: 12. (a) Let R be a ring without zero divisors. Show that if ab = 1 then ba = 1 as well. Thus, a and…

A: Given that R is a ring without zero divisors. If ab=1, show that ba=1

Q: 5. Solve the following PDE: a. Ux= Uy + u

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Q: Let g(x) = x³ +px+q be the depressed cubic of f(x) = x³ + ax²+bx+c and suppose that S = 1 and p=-6.…

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Q: (c) Consider the system x'(t) =ay² - x, y' (t) = -y-ax². x' (t)-y-2x, y'(t)=2x-y-x³.

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Q: Let D = {0,1,c,d} be an integral domain. Explain why the following are true: (1) If 4.1=0 then 2.1 =…

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Q: 11-20 FOURIER SERIES Find the Fourier series of f(x) as given over one period. Sketch f(x). (Show…

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Q: (a). If G is an abelian group, then (b). If G an abelian group, and group. (c). If o(a) = n, then…

A: This is a problem of Group Theory.

Q: 3 Find the bounded Solution of o учу j²y аха = xt dt² sy( dy where y(x, 0) = and y (o₂t) = 0 (x,0)…

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Q: 15. Let (G, *) be a group, and let H₁, H₂,..., Hk be normal subgroups of G such that H₁ H₂0... Hk =…

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Q: Find the first quartile for this list of numbers 62 99 51 2 75 86 30 58 22 35 36 95 40 32 10

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Q: 34 The figure is not drawn to scale.

A: This is a right angel.

Q: You are given the sequence defined by a₁ = 4, a2 = 7 and for m≥ 3, am = am-1+am-2. Prove (using…

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Q: Evaluat the integral, dx dy y's зу

A: We have to find the double integral.

Q: A hole of radius 1 inch is drilled through the center of a spherical wooden ball of radius 3 inches.…

A: To find the volume of portion removed by drill.

Q: Use the Divergence Theorem to find the flux of F(x, y, z)=z³ i-x³j+y³ k across the sphere x² + y² +…

A: This is a problem of vector calculus.

Q: aws of logarithms to find the value of x log3 2+ log3 8 - log3 4 the value of x in the box below.…

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Q: Find the null space of the following matrix: A= [( 1,0,2,),(0,1,1),(0,0,0),(0,0,0)]

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Q: Given y₁ (t) = ² and y2(t) = t−¹ satisfy the corresponding homogeneous equation of t²y" - 2y = t³ –…

A: Variation parameter method is used

Q: Solve the PDE by using the Laplace transform: ay/ax + xəy/dt = 3x² хду/дт ду/дх Assume that y(x, 0)…

A: We are given the following system.          ∂y∂x+x∂y∂t=3x2y(x, 0)=0,   x&gt;0y(0, t)=0, t&gt;0 Let…

Q: f(x,y) = 3 a) what is the range of f? b) sketch the f for K = 0₁1₁2 c) Sketch the graph of f. x² +…

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Q: Find the points of inflection of the graph of the function. (If an answer does not exist, enter…

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Q: decimal places

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Q: Find the eigenvalues and eigenfunctions. 26. y" + Ay = 0, y (0) = 0, y' (π) = (

A: Given boundary value problem is y'' + λy = 0 ,   y(0) = 0, y'(π) = 0

Q: Use Newton's Method to approximate the zero(s) of the function. Continue the iterations until two…

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Q: Let T: R7 → M₂2 be a linear transformation. If the dimension of the kernel of T is 4, what is…

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Q: (You can click on the graph to enlarge the V The position function is the graph in Choose a Graph…

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Q: Ex/l let fi [1₂1]-> R be function f(x) = 3 x70 2 x < 0 Is the function integrable and Continuous?

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Q: Let F = be a vector field in space Find the potential function f(x,y,z) of F

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Q: In a mid-size company, the distribution of the number of phone calls answered each day by each of…

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Q: 19. (a) Evaluate the line integral F. dr, for F(x, y) = ex−¹ i + xy j and C is given by r(t) = t² i…

A: (a)F(x, y) = ex-1 i + xy j   And C: r(t) = t2i +t3j , 0≤t≤1.⇒drdt = 2t i + 3t2j and F(r(t)) = et2-1…

Q: Consider the following two ordered bases of R³: B = C = a. Find the change of basis matrix from the…

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Q: The graph of the function y = 4* does not pass through the origin. Which two of the following…

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Q: 1. 2. Solve the given differential equation and find the interval of definition: y' = x²/y Solve the…

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Q: f(x)=x(40-x)/(20+9cos(x)) Let the function and the set V=[10,15,20,25,30]. Consider the set W of…

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Q: 1. Solve the given differential equation and find the interval of definition: y' = x²/y

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Q: 1. Use the Improved Euler's method to integrate dx = t - sinx dt given x(0) = 1, using a step size…

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Q: Suppose A is a 2 × 2 real matrix with an eigenvalue λ = 3 + 5i and corresponding eigenvector * =…

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