Suppose that f and g are both continuous functions. Also f, g € [a, b] and that f= fg. Prove that 3c [a, b] such that f(c) = g(c).

Q: A trough is full of liquid of weight density 9,000 N/m³. The ends of the trough are equilateral…

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Q: Find the center of curvature of xy = 4 at (2, 2).

A: Solution

Q: Show that the compactness in satability theorem is neccessary.

A: The Stability Theorem fails when X is not compact

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Q: The glee Club is planning to conduct a charity concert at the theatre hall. The theatre hall is…

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Q: Let p and q be the propositions: p: The election is decided q: The votes have been counted Express…

A: P: the election is decided q: The votes have been counted p↔q represents if and only if

Q: The Cantilever truss in figure below is hinged at D and E. Find the force in each member. 1000 lb B.…

A: Solution :-

Q: Example 9.1. Form the difference equation corresponding to the family of curves Y = ax + hr²

A: Please find step by step answer below:

Q: Example 12.14. Find an optimal solution to the following L.P.P. be computing all basic solutions and…

A: The problem belongs to the concept of L.L.P.

Q: The real part of csch (2-j3) is O -0.5118 O none of the other choices O -3.5906 O 9.8844 O 1.0357 O…

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Q: IfF is a field of charact f(x) = x²*

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Q: Calculate the area of the smaller region (to the left of the parabola) bounded by (x + 5)² = 2y, the…

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Q: 1. Let 1, y € R" be given. (a) If ||z|| = ||y|| = 1 and z-y = 1, show that z = y. (b) If ||z|| ≤ 1…

A: \documentclass{article}\usepackage{amsmath,amssymb}\begin{document} (a) Norm x=Norm y=1\\ Let angle…

Q: A ball is thrown from an initial height of 5 feet with an initial upward velocity of 35 ft/s. The…

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Q: 3. Write the following triple integral !!! = x+y dA R in iterated form where S is the region bounded…

A: Let us consider a triple integral ∫S∫∫f(x,y,z)dxdydz To solve the triple integral  Integrate with…

Q: Find the divergence of = ea + sin(xy) a + cos² (xz) a X O yey+x cos(xy) - 2x cos(xz) sin(xz) ọ xe…

A: U→=exyax+sin(xy)ay+cos2(xz)az

Q: Example 10.16. Using Runge-Kutta method of fourth order, solve y(0) = 1 at x = 0.2, 0.4. y² + x²…

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Q: Given that A and B is a group. Find out if : A→B is a homomorphism. If it is a homomorphism, also…

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Q: Example 10.9. Given ay dx 2..1. y-x y + x with initial condition y = 1 at x = 0; find y for x =

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Q: Solve for the laplace transform. Show your solution.

A: The Laplace transform of the function f(t) is represented as F(s) or L[f(t)], it is defined as…

Q: Consider the following ODE y' = y+t/y+1 Which kind of ODE is ?

A: Given ODE is y'=y+ty+1. Simplify y'=y+ty+1. ⇒dydt=y+ty+1⇒y+1dydt=y+t⇒y+1dydt−y=t..........1 Since,…

Q: In Problems 17-20, expand f(z) = annular domain 0 <z - 2 <3 N (z + 1)(z-2) in a Laurent series valid…

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Q: Solve for x. All final answers must be in Znwhere n is the modulus.   x+ 2 mod 9 ≡ 0

A: We have given that ,  x + 2 mod 9 ≡ 0 We need to find the value of x under modulus 9. We know that…

Q: dy Example 10.24. If dx mula by calculating y(1), y(2) and y(3) using Euler's modified formula. = 2e…

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Q: Calculate the area of the smaller region (to the left of the parabola) bounded by (x + 5)^2 = 2y,…

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Q: : At a resection point P, the following horizontal angles were observed to three control points L, M…

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Q: 2. Let A € M, (R) be given. (a) If AA = 0, prove that A = 0₁. Does this hold if A € M₂, (C)? (b)…

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Q: A trough is full of liquid of weight density 9,000 N/m³. The ends of the trough are equilateral…

A: We have to Find the hydrostatic force on one end of the trough.

Q: c) Set up the objective function. d) Suppose that in the optimal solution for this problem, a…

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Q: C: 2: Find the first 4 terms of the Maclaurin series for : In(1+x)

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Q: Example 10.25. Solve the initial value problem dy/dx=x-y², y(0) = 1 to find y(0.4) by Adam's method.…

A: We will use runge-kutta 4th order method to solve given problem.

Q: the first swing is 40 inches. How far does the bob travel in coming to rest? ELABORATE Exercise…

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Q: a polynomial of deg. F. then there exists of F in which f(x) h

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Q: Calculate the area of the smaller region (to the left of the parabola) bounded by (x+5)²=2y, the…

A: Find the slope of the tangent to the curve x2+y2=25 at (3,4). 2x+2ydydx3,4=0dydx3,4=-xydydx3,4=-34

Q: H.W p.564/ use Trapezoidal method and Simpsons' rule to evaluate. dx 1) So √1+x² n = 4 se as Ars

A: # as per the guidelines we are entitled to solve one question at a time, please resubmit the other…

Q: Calculate the area of the smaller region (to the left of the parabola) bounded by (x + 5)2 = 2y, the…

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Q: Express all answers as decimals rounded to 3 decimal places, if needed. Express percentages decimals…

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Q: 5. An object attached to a spring oscillates around a position and is represented by the function y…

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Q: s these functions O(x) ? f(x) = 10 f(x)= 5 logx f(x)= x2+x+1

A: The big O notation is very significant in analyzing a function. It represents the efficiency of a…

Q: A family has two cars. The first car has a fuel efficiency of 25 miles per gallon of gas and the…

A: Given that there are two cars. First car has fuel efficiency of 25 miles per gallon of gas. Second…

Q: answer letter b Note: y(pi/2)=y'(pi/2)=y''(pi/2)=0

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Q: Find a non-zero vector 7 perpendicular to the vector u 12 [3]. -6

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Q: B: 2: Find the first 4 terms of the Taylor series for : f(x)=sin лx near a=0.5

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Q: A trough is full of liquid of weight density 9,000 N/m3. The ends of the trough are equilateral…

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Q: The rose r = 3 cos (50) is shown below: 3 -3 Find the area of the region bounded by one loop of the…

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Q: Solve the following system of nonlinear equations 2x₁x₂2=0 x₁² - 4x₂ -4 = 0 Using the fixed-point…

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Q: the volume of the solid in the first octant bounded by using z = 1+x² + y² and z = 4 using…

A: The volume is the amount of space occupied by the closed surface. It is measured in terms of the…

Q: 5. Solve the DE dy d²y xdx² dx - 4x = 0, 1<x<2 with y(1) = y(2) = 0. a) Using weak form and Galerkin…

A: Let us start solving the problem step by step    For the given DE we will start solving by the…

Q: Example 10.26. Using Picard's method, find approximate values of y and z corre- sponding to x = 0.1,…

A: please comment if you need any clarification. If you find my answer useful please put thumbs up.…

Q: B:1: Solve 1. L{t²cosat} 2. L-

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