A trip in a vehicle covers 80k and takes one hour. Explain why it is guaranteed that the vehicle was travelling at exactly 80km/hour at a leas one instant during the trip.

Q: Example 12.32. Four jobs are to be done on four different machin es) of producing ith job on the jth…

A: Number of rows = 4 Number of columns = 4 Therefore the problem is balanced find the minimum element…

Q: Particle motion At time t, the position of a body moving along the s-axis is s = t³ - 6t² +9t m. (a)…

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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: 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: A spherical tank of diameter 4 m is half-full of water (weight density = 9800 N/m³). Setup the…

A: Solution:-

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

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Q: from Example 10.18. Using Runge-Kutta method of fourth order, solve for y at x = 1.2, 1.4 dy 2xy +…

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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: Obtain the differential equation associated with the given non-derivative equation in x and y. Show…

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Q: QUESTION 6 Sanna and Obadia argued about the definition of .00 e-x Ldx Sanna split the integral as…

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Q: C:1: Solve the following I.V.P. using Laplace transformation: y" - 2y - 5y = 5t-100 such that: y…

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Q: Use Simpson's Rule to evaluate the following. n = 10 3 1 dx 1+x² -3

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

A: Group homomorphism is nothing but a function defined between two groups. The function must be closed…

Q: Example 10.22. Using Runge-Kutta method of order 4, find y for x = 0.1, 0.2, 0.3 given that dy/dx =…

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Q: Use the separation of variables to find, if possible, product solutions (for λ = 0,2 = -a² and 2 =…

A: As per the question we are given a partial differential equation and we have to find its solution…

Q: A spherical tank of diameter 4 m is half-full of water (weight density = 9800 N/m³). Setup the…

A: Consider the information given in the problem and draw the diagram as per given information,…

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: Find the intercepts and the symmetry for the polar equation r = 1+ sine.

A: Note: since you have posted multiple questions. As per our guidelines we are supposed to solve only…

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

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Q: A spherical tank of diameter 4 m is half-full of water (weight density = 9800 N/m³). Setup the…

A: The tank of diameter 4m is half of water Water density ρ=9800 N/m3 Radius R=D2=42=2m ∵  work =F×…

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: verse of a Matrix I. Use the determinant test for no singularity to determine hether items 1-5 of…

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Q: The task is to identify the solution of the given system linear Ordinary Differential Equations. Use…

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Q: Let V be the vector space of all square sub-matrix over R. Examine whether or not W = (A: A E V, A²…

A: Let V be the vector space of all square sub-matrix over ℝ. Let , W = A / A∈V , A2 = A We need to…

Q: If K is a finite extension of a field F, then the group G (KF) of F K is finite and o[G (KF)] ≤…

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Q: Find the area of the region bounded by y = x^2 + 2x -6 and y = 3x. Determine the area of region…

A: Note: As per the guidelines we are supposed to answer only 3 subparts question. For the remaining…

Q: Find the values of x for which the gradient of the tangent to the graph of y=f(x) is equal to the…

A: We have to find the values of x for which the gradient of the tangent to the graph of y=f(x) is…

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

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Q: Example 10.4. Find by Taylor's series method, the values of y at x = 0.1 and x = 0.2 to five places…

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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: az"¹)]sin(a @)-¹ + a² az-1)2]sin(a w)₂-¹ + a² az-1)³]sin(a @)²-¹ + a² -(az-1)³]sin

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Q: 2°) Write the volume integral of the solid bounded by 2 = √√√ x² + y²² and Z=√√2-x²-y²², in a)…

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Q: Q₂/ solve the differential equation. ху 3 xể ý yếu 4 eo

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Q: constants. ple 9.2. From y₁ = A2" + B(− 3)", derive a difference equation by eliminating the

A: Given, yn=A2n+B(-3)n   1 Replacing n with (n+1) and (n+2) in the above relation…

Q: 7. Let A and B be sets, and let f: A → B and g: B → A be functions. Suppose that: • go f(a) = a for…

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Q: Craig, Daniel and Edward shared an amount of money. Craig took 1/3 of the total amount of money.…

A: Let x be some number  1n of the number means 1n x Twice of the number is 2x

Q: Example 10.20. Using Milne's method find y(4.4) given 5xy + y²-2=0 given y(4) = 1, y(4.1) = 1.0049,…

A: Solution : Given, 5xy'+y2-2=0 ⇒y'=2-y25x Table of x and y x 4 4.1 4.2 4.3 y 1 1.0049 1.0097…

Q: 3. Find the volume of the solid formed by revolving the region formed by the curve y = secx about…

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Q: 2°) Write the volume integral of the solid bounded by 2 = √ x² + y²² and 2= √√2-x²-y²¹, in a)…

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Q: Find the Inverse Laplace Transform of 10. F (s) 2s+3 s²+4s+13

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Q: 4. Being careful to allow for parts of the curve being both above and below the x-axis, determine…

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Q: 2. Determining whether odd or even function, state the period. a.) b.) .

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Q: Example 10.23. Given dx = 1.979, evaluate y(1.4) by Adams-Bashforth method. = x²(1 + y) and y(1) =…

A: Problem is solved using Adams-Bashforth Method.

Q: Example 11.1. Classify the following equations : au a²u d²u du (i) +4 0x2 +4 Əxdy 2 ông Ôx ди +2- =…

A: Given the second order partial derivatives; ∂2u∂x2+4∂2u∂x∂y+4∂2u∂y2-∂u∂x+2∂u∂y=0…

Q: The task is to answer the question below: Let A be the positively oriented surface parametrized by…

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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: Given two functions, what can be said of the continuity of their sum? Their product? Their quotient?…

A: Let f and g are continuous function on I ( subset of real number)  ,then i) f + g is also continous…

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: A complex number has a modulus of 3 and an argument of -π/3. Another complex number has a modulus of…

A: We have given a two complex numbers , z1 and z2 We have given modulus and arguments of both the…