Let f(x) = 1-1 if 0 < x < 1 if 1

Q: Find the 3x3 homogeneous matrix for 2D-reflection across a line that goes through (B, C) and makes…

A: As per the question we have to to find the transformation matrix which reflects any point on 2d…

Q: (BACKWARD INDUCTION) Two players have to share 50 coins (of equal value). Players' payoffs are the…

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Q: Y OU (a) Find the least residue of 639 modulo 10. (b) Use Fermat's little theorem to find the least…

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Q: 6. Given a 2-unit factor of 0.87 find each of the following: (round answers to 4 decimal places) a)…

A: Given the 2−unit factor of 0.87. We have to find the value of: (a) The 4−unit facto, (b) The 1−unit…

Q: 1. Let X be the graph of f(x) = x²/3 given below that is, X is the subset of R x R satisfying the…

A: Sol

Q: 4. Find the absolute extrema of the function f(r, y) = ry -I-3y on the triangular region with…

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Q: 1. рV(~ р@9) p p (~p q) F F F F >

A: The truth table is given as follows :

Q: 7. If the rate of growth of a bacteria population is modeled by r(t) = 8e2t-1 thousand bacteria per…

A: Introduction: When a function is given, we determine the average value by integrating the function.…

Q: Verify Green's Theorem by evaluating both integrals dk + x° dy = /. / dA ду for the given path. C:…

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Q: Let T(x, y) = (5x – 3y, –7x + y) be a linear transformation. Find a basis B for R? with the property…

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Q: The length in meters of the four sides of a building are 3x, 6x - 5, 9x, and 4x + 1. (a) Calculate…

A: (a). Add 3x, 6x-5, 9x and 4x+1 to calculate the total length around the building.…

Q: Solve the initial value problem y"- 8y'+52y = 0, y(0) = 1, y'(0) = -3.

A: Note: We are allowed to solve one question at a time. Use the given differential equation.

Q: 00 Given that I* with convergence in (-1, 1), find the power series for with center 2. n=D0 Σ n=0…

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Q: Label each statement True or False. Not all circles are similar. There is only one transformation…

A: Below given clear answer

Q: 3. The position of an object that is moving along a straight line at t seconds is given by s(t) :…

A: This is a problem of dynamics.

Q: The relative error in reading a galvanometer is given by tanx + cotx, where x is the angular…

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Q: 4. The equation f (t) = models the bacterial count, in thousands, for a sample collected from pond…

A: solve when f(t)&gt; g(t)

Q: e) x·y= 0 iff x = 0 or y= 0. ) x<у iff — у < -х.

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Q: The slope of the surface z = ry in the r-direction at the point (2,3) is slope of this surface in…

A: The slope of the surface z=f(x, y) at x0, y0 in the x-direction is fxx0, y0. The slope of the…

Q: EXAMPLE 3-3 Show that ex is eigenfunction of the operator d" /dx". What is the eigenvalue? an

A: The solution is given as

Q: 2) Let Pz I 2 02 5 -2 ~s I -1 - -3341 360-72 A) write down al the colmns in P that form a basis for…

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Q: 3. LetR be the region shown in the accompanying figure. Fill in the missing limits of integration…

A: We have to fill the missing limit of integration .

Q: 5. SET-UP the double integral that solves for the volume of the solid: 3 3x+ 2y+ 4z 12

A: The solid is bounded by the triangle and the planes x=0,y=0, z=0

Q: nd the absolute extrema of the function f(r, y) = ry-I - 3y on the triangular region th vertices…

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Q: )4 in the Taylor -g x - log x2 abor

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Q: A curve has an equation of 9x2 + 25y2 = 225. Compute the second eccentricity of the curve. %3D 1.33…

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Q: Solve the initial value problem for transverse vibration of a taut string of length L which is…

A: Sol

Q: → M2x2 be the linear transformation defined by C T(ax? + bx + c) = ne matrix for T with respect to…

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Q: (a) (i) Use Euclid's algorithm to find a multiplicative inverse of 23 modulo 75, and hence solve the…

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Q: A. What is the specific volume of the five ice cubes in a glass if each is weighing 40,400 mg? Note…

A: Specific volume is defined as the volume (in cubic meters) occupied by one kilogram of a particular…

Q: Set up (but do not evaluate) an iterated triple integral for the volume of the solid enclosed…

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Q: So (b) dr centered at a = 0 (Use your answer to part (a)!) %3D

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Q: 4 Solve y" – y" – y' + y = 2e¬t + te' + 3 by using both the method of undetermined coefficients and…

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Q: This exercise uses the radioactive decay model. The half-life of cesium-137 is 30 years. Suppose we…

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Q: Find the following complex series. 2. Find the Mclaurin Series expansions of cos(x) + sin(x) up to…

A: Macluarin series expansion of the function

Q: A=18, B=22 Give a 2x2 matrix that will project any point (x, y) on to the line going through (0, 0)…

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Q: 99. How many full gallons of regular lead-free gas can Josie buy for $20? GAS PUMP Regular Lead-free…

A: Given in question,  Regular Lead free  = $1.69

Q: ... 4 B = (-1,4) A A = (1,0.25) %3D -4 -3 -2 -1 2 3 4 5 A y= - 4× y=4-x O f(x) =| D y=4•1*

A: We want to find the equation of given curve.

Q: Find the angle a, in radians, between the vectors -5 and 3

A: Use the formula of angle between the vectors to solve the question.

Q: (х-3) (х+1) f(x) = %| (х-2)(х+2)(х+1)

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Q: Assume that  dx1/dt= x1(10-2x1-x2) dx2/dt= x2(10-x1-2x2) a) Graph the zero isoclines. b) Show…

A: Given- Assume that  dx1dt = x110 - 2x1 - x2dx2dt = x210 - x1 - 2x2 To find-  Graph the zero…

Q: Question no. 2 Let A, B, C ben × n invertible matrices. When you simplify the expression:-…

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Q: Use proof by cases to prove that for any integer n, n² + 3n + 7 is even.

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Q: Find the following inverse laplace For simplification, you can use x = 22

A: Given that,Fs=xssx-s-xThe given value of x is 2Substituting x=2 in the given function, we…

Q: 2. Let X = R² – (0,0) and ~ be defined over X by setting x~y + y = tx Given a equivalence class [a]…

A: Sol

Q: Let X = R? – (0,0) and - be defined over X by setting X~y + y = tx for some non-zero t e R. (b)…

A: Sol

Q: Consider the following IVP: y"-3y'+2y = e3t; y(0) = 0, y'(0) = 0 Find the general solution. y(t) 31…

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Q: 8. Find the root of cos(x)-xe¬* using the Newton-Raphson method.(Use radians in solving)

A: Newton-Raphson method uses the formula: xn+1=xn-f(xn)f'(xn) to perform the iterations and to…

Q: 25.4 Solve the following problem with the fourth-order RK method: d'y dy + 0.6-+ 8y = 0 dx dx where…

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Q: If y is the solution to the initial value problem 9x? y(0) = 1 2y then y(2) =

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