Use long division to divide the first polynomial by the second. x12x² + 11x - 1, x - 3

Q: What are the critical points of f? On what open intervals is f increasing or decreasing? At what…

A: Note - Since you have posted multiple question we will solve first 3 sub parts as per…

Q: 2. now clearly sketch as well as indicate your angle and you may assume you know the points on the…

A: Reference angle is the positive acute angle between the terminal side of the angle and the x-axis.

Q: 3. Assume that the annual rate of inflation will average 3.8% over the next 10 years. a) Write an…

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Q: Use the divergence theorem to evaluate the surface integral F. N dS where F = xy²i+yz²j + zx²k, S is…

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Q: Laplace transform to solve th-

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Q: pply the theorem L(f* g) = L(f)L(g) to find the inverse Laplace transform; also do it in mother way…

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Q: Approximately how much material is needed to make the tent illustrated in the following figure (both…

A: A graph of the tent is given, the aim is to find the amount of material needed to make the tent.

Q: 29 Desde un cierto punto, que dista 20 m del pie de una torre de 10 m de altura, vemos el punto más…

A: This is height & distance problem. We use the trigonometric identity relation of tan(x).

Q: Vector field F is given by F(r) = (x, y, z + 1) and surface A is the locus of points satisfying z +…

A: The given vector field is .The given surface  is the locus of points satisfying  for .We need to…

Q: Consider the vector space V over the real numbers, consisting of all polynomials of degree less than…

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Q: 2 east one of the answers above is NOT correct. e ite the given third order linear equation as an…

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Q: Each character in a password is either a digit [0-9] or lowercase letter [a - z]. How many valid…

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Q: Evaluate f(V x F) dS where S is the surface x² + y² +3z² = 1, z ≤0 and F = (y, -x, zx³y²). Let the…

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Q: Let f(x) = |x|+|x−2], x € R. Find points where f is not differentiable.

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Q: Q6: ) Suppose (X, 7) is aftopological space, and p a point not in X. Let Q = {UU {p}, UET, and X-U…

A: Let's go through the two parts of the question:a) To show that T=Q∪T is a topology on Y=X∪{p}, need…

Q: A sheet of water of uniform thickness (h= 0.03 m) flows from the device shown in the figure below.…

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Q: 7. Consider the boundary value problem x" + x = 0, x(0) = 0, x(π) = 0. Then A=4 is an eigenvalue for…

A: Eigenvalue of the differential equation

Q: Calcula la distancia entre los puntos A y B. A 7,2 m nà als of bles E 50° 73° D B 71° 5,25 m 48° C

A: Consider the triangle Using the first formula we getor, or, Therefore, the length of AD is

Q: 1. Let S be the portion of the graph z=4 - 2x² - 3y² that lies over the region in the xy-plane…

A: \We have to set up the double integration

Q: Consider the following region R and the vector field F. a. Compute the​ two-dimensional curl of the…

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Q: I can't follow any of the writing.  Some of it is dim, and some doesn't make sense: In the problem,…

A: One must not assume f(c)= 0.But If one assumes that , then the claim "" is true.

Q: Consider the following initial value problem. 0 1 ≤1 12 1 ≤ 1 < 6 0 6 ≤ 1< 00 y' + 3y = y(0) = 10…

A: The Laplace transform of a function f(t) is defined as L{f(t)}=∫0∞f(t)e−stdt .Formulas: (1)…

Q: 2. Let T: P₂ (R) → P₂(R) be defined by T(p)(x) = p(0) + p(1)(x+x²). (a) Prove that T is…

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Q: 2. The behavior of the system is a saddle. y' -x + y, = -x - Y =

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Q: The system of first order differential equations y₁ = 5y₁ + 1y2 32 y₂ = −4y₁ + 1y2 where y₁ (0)= 4,…

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Q: Consider the vector field F (x, y, z) = (3z + 4y)i + (z+4x)j + (y + 3x)k. a) Find a function f such…

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Q: 0 i 0 Let A = 1 10 as a matrix over C, where i = √√-1. Li 0 i Find p₁(x), m₁(x) and determine if A…

A: Eigenvalue: A number  is said to be an eigenvalue of a matrix A if there is a non-zero vector xsuch…

Q: Use the divergence theorem to evaluate the surface integral JF CFN dS where F = 10xy²zi +10yrx²zj +…

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Q: 2. Is R bounded with respect to this metric? 3. Compare the open balls B(0,2), B(0,4), and B(1, 4).…

A: Sequential compactness.

Q: A spherical snowball is melting in such a way that its radius is decreasing at a rate of 0.4 cm/min.…

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Q: Prove the conjecture bn= 2(bn-1)+1, n>=3 using strong induction. Recurrence is given bn=3bn-1-2bn-2…

A: We shall solve these question by use of induction

Q: 3. Suppose that A, B C R2. (a) If A and B are homeomorphic, are A and B homeomorphic? (b) If A and B…

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Q: Set up but do not evaluate the integral (s) that would give the area between the graphs of f(x) =…

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Q: Let f(0, z) = z² and S be the cone parametrized by r(0,z) = (z cos 0, z sin 0, z) with |z| ≤ 1.…

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Q: Exercise 7. Let A = 1 2 3 0 1 2. Find the eigenvalues and eigenspaces of A. 3 7 11 Does R³ have a…

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Q: Let Sn = n Σ k-1 √k Estimate how many terms are required before sn ≥ 100.

A: We shall be using basic inequalities to solve this problem.

Q: 3. Let S be the sphere of radius R. (a) Argue by symmetry that [[₁,²³² ds = [[ ²³ ds = [[, 2²¹ ds.…

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Q: A mass weighing 20 pounds stretches a spring 6 inches. The mass is initially released from rest from…

A: The objective of the question is to find the position of the mass at different times, the velocity…

Q: The system of first order differential equations y₁ = −4y₁ + 5y2 +1 y2 = 5y₁ - 4y2 +1 where y₁ (0) =…

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Q: For each of the following vector fields F, decide whether it is conservative or not by computing the…

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Q: We know that the harmonic series has a growth rate comparable to In n. Let an = 1/2 and defin a new…

A: Now, let’s consider the sequence (tn) defined by tn=sn−lnn=1+1/2+…−1/n−ln(n), where s_n is the nth…

Q: can this be done on paper?

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Q: For the function F(x) = -6+ (a) graph the rational function using transformations. (b) use the final…

A: Vertical shifting: To graph of y=f(x) -c, shift the graph of y=f(x) down by c units.

Q: Consider the function f(x) = arctan(3x). Show that the graphy = f(x) and its tangent line y = g(x)…

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Q: The limit is equal to 0 ∞ -3 O 3 lim x→0 St³+27 dt X

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Q: Calculate the integral of f(x, y) = 7x over the region D bounded above by y = x(2 - x) and below by…

A: We will find out the required value.

Q: nt or A= Pert to solve. Use the compound interest formulas A = P1+. n 41) Find the accumulated value…

A: The given investment amount  at  compunded for  years.The aim is to find the accumulated amount if…

Q: 3. Let TV → V be an operator on a finite-dimensional space V. (a) Prove that T is not invertible if…

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Q: The graph of f(t) is given below. 765 4 7₁ 6 5 y 3₁ 2 1 t o 10 Find the Laplace transform F(s) =…

A: The given graph has 4 stages.       First stage:      for         Second stage:  The…