Let R be the triangle with vertices (0,0), (1,2), and (3,0). Find the average value of the function f (x, y) = y +1 over the region.

Q: show that the matrix П (I2 + 03) ® I2 is a projection matrix.

A: A matrix is a set of numbers organized into a predetermined number of rows and columns. The numbers ...

Q: 6. Write the rule to describe the rotation. I' A I A'

A: Any point in the cartesian coordinate system is represented by the ordered pair: x, y. Start from th...

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Q: Let A 1B = 5 l, and C-1 = If X is a matrix that satisfies: %3D %3D 2B = Al2 - XC then X is

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Q: 5. Find the volume of the solid formed by revolving the region bounded by the graphs of y = 3 – x² a...

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Q: sinh(5) =

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Q: The arc length re-parameterization of the line l: F(t) = (1,1, 1) + t(1,2, 3) with 0 <t < 1 is given...

A: This is a problem of curve parametrization.

Q: 2 If 15 is one of the then sum of the c

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Q: Factor T623000 Compretely. Wrie,o0suwer in canonical form.

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Q: Determine the upper bound on the error in the approximation – 16x5 + 256x° if |x| < 0.2 - 1+16x4

A: Given:x1+16x4 ≈x-16x5 + 256x9  

Q: Round 234 to the nearest ten and hundred.

A: The hundreds place, tens place and unit place of a number can be represented as:

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Q: 1. Determine the following: a. Given a sector with an arc length of 4.5 cm and a radius of 3 cm, fin...

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Q: Change the Cartesian integral to an equivalent polar integral and then evaluate: 15 N" (x² +y²) dx d...

A: We have to convert the integral I=∫015∫0225-y2x2+y2dxdy to an equivalent polar integral. For this, w...

Q: Jonathon needs at least an 89 on his test to keep his essay in math what inequality matches Jonathon...

A: The inequalities are represented by the symbols: &lt;, &gt;, ≥, ≤, ≠.

Q: the Laplace transform of f(t) find F(4s) %3D

A: Laplace transform of the function

Q: 1. Fibonacci Numbers Recall that the Fibonacci numbers f(n) can be be defined recursively by letting...

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Q: 2- Solve the following system of equations using the Gauss and Gauss-Jordan elimination methods. 2x1...

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Q: For the following primitives, identify the number of essential constants.(x and y are the variables)...

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Q: Sketch the graph of the function f(x) = 3x 4 + 4x 3 .

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Q: Make 1 problem solving regarding AREA. The area can be from a triangle, polygon, circles, rectangles...

A: Question:-  A basketball court with length 90 m and width 50 m is going to be painted. It costs $1.6...

Q: 1. Fill in the table for each parabola equation. BE CAREFUL Some information is not given by certain...

A: "Since you have asked multiple questions, we will solve the first question for you. If you want any ...

Q: A waste management company is designing a rectangular construction dumpster that will be twice as lo...

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Q: Let A={a.b.c.de) and S, T, U and V relations on A where S= {(a.a), (ab), (bea), (bd), (Ge), (ed), (a...

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Q: dy Consider the differential equation ty-1. ) Explain why you cannot solve this differential equatio...

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Q: 5х — 3 dx = 2 ln |æ + 1| + 3 ln |x – 3| + c J (x + 1)(x – 3) -

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Q: Find the particular solution of the differential equation that satisfies the initial condition. (Ent...

A: Introduction: The separation of variables method is the basic method to solve a first order differen...

Q: Prove that V3 is irrational

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Q: Obtain the differential equation of the family of plane curves and kindly described and sketch sever...

A: Introduction: Every differential equation dydx=fx,y represents a family of curves. The family of cur...

Q: 1. Let f(x, y) = x³ – 3.xy + y3. Find all critical points of f and at each critical point, use the S...

A: We have to find the saddle point, relative maxima or minima of f(x,y).

Q: If tan then 1– 2 1+ z2 COS X 8 |N

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Q: cos(2x) dx 1 In |1 – sin(2x)|+c 2 - 1 – sin(2x)

A: Note: It is assumed that the question is asking to test of the validity of the given equation.   It ...

Q: Use the Laplace transform to solve the given initial-value problem. У"+6у'+5у %3D0, у (0) %31, у'(0)...

A: Given differential equation is y'' + 6y' + 5y = 0 with y(0) = 1 , y'(0) = 0

Q: The Taylor series expansion is given by: 00 (-1)" sin x= 2 x2n +1 (2n + 1)! n= 0 Evaluate sin 44° us...

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Q: Apply the Extended Euclidian Algorithm to find 1/21 modulo 59 with a table

A: We will apply Extended Euclidian Algorithm to find 121 modulo 59 i.e., multiplicative inverse of 21 ...

Q: Problem 4. Let w, y, z E Z[i] such that wyz, and let d be a gcd of w and z, show that w|yd.

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Q: Let B= {b, ,b2} and C= {c,,c2} be bases for R?. Find the change-of-coordinates matrix from B to C an...

A: Change of coordinate matrix 

Q: Let g : N Z be defined by g(0) = 2 and Sa(n – 1) 29(n- 2) if n > 2 and n is even. if n >1 and n is o...

A: This is a problem of recurrence and counting.

Q: 1 dx 7х — 2 1 In(7a — 2) + с 7 -

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Q: Consider the three systems of linear equations: 4х1 + 6х2 + 2х3 + 8х4 2 4x1 + 6x2 + 2x3 + 8x4 2 2x1 ...

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Q: Match the vocab work with the correct definition Line Choices a line that extends indefinitely in on...

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Q: B. Prove that the given equation is a solution to the given DE: 1. = C,e3* + C2e²* + C3e* ; y"" – 6y...

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Q: f(t) = 2e3t sin 2t 3e3t cos 2t

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Q: For the following matrices, find all eigenvalues and eigenvectors. [3 4

A: Given matrix is 3−24−1. We have to find the eigenvalues and eigenvectors. Let A=3−24−1 The eigenvalu...

Q: Solve for w where u (1, 1, –1, 0) and v = (2, 3, 0, –1). 5w = u – 4v w =

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Q: 22 23 24 25 26 3 2.32 - 3.33 4.34 5.35 .. 6.36

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Q: cos? x sin x | cos“ x dr 3 + 4 COs x sin x 1 COS4 + 4 + c 2

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Q: f(x) - f(1) If f(x) = log2(x), then lim x-1 (A) In(2) (B) In(2) (C) 0 (D) 2 8:4A R (E) 1

A: If limx→af(x)g(x) takes the form of 00 or ∞∞, then using the L'Hospital's Rule, it can be written th...