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Q: 1. Let A be an n x n matrix and x is a scaler. Show that det(x A)=x" det(A).

A: Solution:-          It is given that , A is any n×nmatrix and α is a scaler .…

Q: ¹9ƒ ( ² ) + Use the Master Theorem to give a big-O estimate for f(n) = 49f +2n².

A: Big-O notation is used to describe the rate of growth of functions. Consider an increasing function…

Q: 4. Consider a wave equation on an infinite line, J²u 2²u Ա 9 at² əx² = 0. Find the characteristics…

A: Comparing the given equations with the standard equation utt-c2uxx=0, we see that c=3. Also the…

Q: Which of the following degree sequences are possible for a simple graph? A. (9,7,7,7,7,6,5,4,4) B.…

A: To check that for which of the following degree sequences are possible for simple graph: A.…

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A: The cardinality of a set is the number of elements in the set. Consider two sets A and B. Then the…

Q: Consider the line which pases through the Parallel to the line X = 1 +7+₁₂y= 2 + + z=3+7+ find the…

A: Equation of line passing through the point x1,y1 and having direction ratio a,b,c x=x1+at , y=y1+bt…

Q: (c) (e) 0-3 2 3 along the second column -1 0 1+i 2 -2i 0 1-i 3 4i 0 along the third row (d) (f) (i 0…

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Q: If random variable X has the density function f(x)= e, -∞ <* < 0. 1 Show that M(t) = - 2 -1 < t < 1.

A: Definition of Moment is given below and conditions for that integral to exist(give a finite value)…

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Q: 6. Let f(x) = re. (a) Apply the composite trapezoid rule with m = 6 to approximate comparing with…

A: Given, f(x)=xex Three-point centred differnce formula is f'(x)=f(x+h)-f(x-h)2h

Q: In each of the following problems, use the method of undetermined coefficients to find the general…

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Q: On the measurable space (R, B(R)), let u: B (R) → IR be defined as: u(A) = The number of all…

A: A measure is said to be a finite measure if m takes only finite values. In other words, a measure m…

Q: Find the linearization of the function f(x, y) = √/54 — 1x² – 1y² at the point (5,-2). L(x, y) = Use…

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Q: 6. Prove that if M E Mnxn (F) can be written in the form A = - (68). where A and C are square…

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Q: 3. (Section 16.5) Consider √x² + y² + z² by √√32 = √² + y². Set-up the triple integral using: (a)…

A: Given integral ∫∫∫D1x2+y2+z2dV where solid D is bounded above by x2+y2+z2=4 and bounded below by…

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Q: Discount printers manufactures two types of inkjet printers, a consumer version and a business…

A: Make a table for the given data.   labor hours  profit Consumer Jet 1 35 Business Inkjet 3 60…

Q: 6. If (I, T) is a T.S., prove that A is dense in I iff every open subset of I intersects A, if at f

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Q: Let C(x) represent the centralizes of a. If x is an element of group G with the order of x be 5 (|x|…

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Q: Solve the Bernoulli equation for y. dy = 3y + y³. dt Use the following initial condition: y(0) = 1.…

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Q: Stephanie Carter has been gifted a sum of $50,000 by her grandparents on completing her graduation…

A: Q 6.   Reply:   Stocks:   Given information:   All out speculation of stocks = $59.77   Portions of…

Q: (1 point) Use a graph below of f(x) = ln(8x² + 1) to estimate the x-values of any critical points…

A: a) To find the inflexion point either by graph or derivatives, we will end up having the same…

Q: In the following exercises, consider linear systems whose augmented matrices reduce to the following…

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Q: Let a, b ∈ R with b ≠ 0. Show that R(a + bi) = C.

A: Given that a, b∈ℝ with b≠0. To prove that ℝa+ib=ℂ.

Q: 6. Subtract: a) 5 Reduce to lowest terms b) c) d) 15 6 10 2 3 2 4 15 -

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Q: The graph G₁ has 10 vertices, all of degree 9. How many edges does G₁ have? The graph G₂ has 7…

A: A graph G1 has 10 vertices, all of degree 9.  To Find: Number of Edges. A graph G2 has 7 vertices,…

Q: 3. (VP-1) Use the method of variation of parameters to find the general solution to the following…

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Q: Roberto bought a $210,000 house, paying 24% down, and financing the rest at 6.8% interest for 30…

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Q: You are given the graph of a function f. 1+ H -It -3-2-1 123 Determine the intervals where the graph…

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Q: You deposit $2000 each year into an account earning 8% interest compounded annually. How much will…

A: Annual payment (pmt) =$ 2000 Interest rate i=8 % = 8100=0.08 Time period n=30 years        Formula :…

Q: Solve by Gauuss

A: We have given that a system of equations, 7IP+6I+8W=100006IP+3I+5W=75008IP+9I+4W=9000 We will use…

Q: Construct a truth table for the statement p→~q

A: We construct Truth table for given statement. There are four columns for given statements and 22= 4…

Q: 2. Let f:1→ R, where is lim [f(x + h) + f(x-h) - 2f(r)] = 0. →0 Does this mean f is continuous at 2.…

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Q: Test the given data to see whether they are exponential, linear or neither. A Exponential data B…

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Q: f(x) = -5* b= 3 parent points (,), )( , ) Shift: New points: Asymptote: y= f(x)=3*-² b= 3 parent…

A: The given function are f(x)=-5x, f(x)=3x-2=3x9. To Find: (i) "b" (ii) three parent points. (iii)…

Q: 15. Write the other five possible orders of integration for the integral whose integration zone is…

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Q: A solid E lies within the cylinder x2 + y2 = 9, below the plane z = 21, and above the paraboloid z =…

A: The solid E lies within the cylinder x2+y2=9 and the plane z=21, and above the paraboloid z=9-x2-y2.…

Q: A = { 0, 2, 4, 6, 7, 8} B = 21, 3, 5, 6, 7, 93 c=20, 1, 2, 3, 4, 5, 7, 8, 93 Find A-CBUC) and (AUG)…

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Q: A clock is hung on a wall so that the center is 20 cm below the ceiling. The minute hand is 10 cm…

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Q: A woman wishes to save $20,000 for a down payment on a home. She can afford to set aside $1100 per…

A: Future value of ordinary annuity is  FV=R1+in-1i where R is regular deposit, 'i' is periodic…

Q: Suppose ʼn is a positive whole number. Simplify [n+1)! — n! × n. On! O 1 On + 1

A: 'n' is a positive whole number. We have to solve  (n+1)!-n!×n Remember : n!=n.(n-1)........3.2.1

Q: Use abbreviated truth tables to show that each of the following arguments is invalid: 2)    P ↔ Q,…

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Q: Solve the differential equation by variation of parameters. 1 9 + ex y(x) = y" + 3y' + 2y =

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Q: dy Solve = tan y cot x sec y cos x, simple dx substitution [Hint: Express the functions first in…

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Q: Using the concept of the Determination of Integrating Factors, find the particular solution of the…

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Q: 4. How many 6-digit numbers (using 1,2,3, ... ,9) are there if repetition is not allowed? How many…

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Q: Problem 1. If SC R is homotopy equivalent to a point, we say S is con- tractible. Which of the…

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Q: 1. Locate the centroid of the given areas. y ·b 06 PROB 05-06 (a) X 1 m 06 PROB 09-10 (b) =0.5e² y=…

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Q: Suppose that we use Euler's method to approximate the solution to the differential equation…

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Q: Find the least squares regression line for the data points. (Let x be the independent variable and y…

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