Show that in any collection of 7 or more natural numbers there are ALWAYS TWO numbers whose sum or difference is divisible by 11.

Q: Determine the values of r for which the given differential equation has solutions of the form y =…

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Q: The functions f₁(x)=x³+4, f2(x)=x³-2, and f3(x)=x³+5, are LINEARLY INDEPENDENT.

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Q: Find the volume of the solid generated by revolving the region bounded by 2y = e-x², the x-axis and…

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Q: 2. Given the definition of the main window of the periodic function g(t)=t-t². -1<t<2. g(t+3) = g(t)…

A: Red colour graph is the main window and the right window is denoted by blue curve

Q: Consider the function f(x) = cos x − 3x + 1. Since ƒ (0)ƒ () < 0, f(x) has a root in [0,]. If we use…

A: Given, function f(x)=cosx - 3x+1 f(0)f(π2)&lt;0hence, f(x) has root in [0,π2] We have to calculate…

Q: 3. Determine if the assigned improper integral is convergent or divergent. Leve+I de 1

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Q: 7. Determine the roots of y4 + y"" −y" -y+1=0 a. 1,-1,1 b. 1-1,-1 c. 1,-1,2 d. 1,-1, -2

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Q: Solve the initial value problem. 4 -4 4 y' = 3 -3 - 10 2 15 y, y(0) 1 = 16 14 6

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Q: Let V = R³. a) Give a definition of addition '+' on that makes (V,+) unable to satisfy property…

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Q: Set-up the iterated double integral in polar coordinates that gives the volume 1++ and under the…

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Q: Find the general Solution of the following PDES ди -5X -3x 17 9 = 2 ди +u, ucx;o) = ду + 2 е ax…

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Q: The equation y = C₁e(-x) + C₂e(-2) is the general solution of:

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Q: A mass weighing 5 lb stretches a spring 9 in. If the mass is pushed upward, contracting the spring a…

A: Given information is weight  w = 5 lb And, mass m =wg =532  lb s2/ ft k= Fs 14 = 514 =20  lb/ft As,…

Q: For every nonempty set A, there exists a relation R which is both an equivalence relation and a…

A: A relation R is said to be equivalence relation if R is Reflexive ,Symmetric and Transitive . R is…

Q: I. Solve the following Linear Systems of Equations by Gaussian Elimination: 1.) 6x + 2y4z = 15 -3x -…

A: Given system is 6x+2y-4z=15-3x-4y+2z=-64x-6y+3z=8 We can write it in matrix form…

Q: The von Bertalanffy growth model states that the rate of increase in the length L(t) of a shark of…

A: according to question, rate of increase in length of a shark of age t in years is proportional to…

Q: Determine the location of the centroid of the solid formed by revolving about the y- axis, the area…

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Q: 02u 0t2 = аг 02u ?x2

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Q: Determine the general solution of the following differential equation: (D²-4D+4)y=(6e2x)/(x4) O A. y…

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Q: Consider the differential equations dx dt 4x+y+z dy dt = 2x + 5y + 4z dz = -x-y dr Show that if it…

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Q: II. Minor and Cofactor 1. Find the cofactor of 6 in matrix D 9 8 4 2 7 -9 3 4 D = -3 2 3 9 3 2 6 8 ㅋ

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Q: 10 [ Σ 15m3 n=m =

A: Given summation is ∑m=11015m3 we can write it as 15∑m=110m3         (1)

Q: Multiple choice. Choose the correct answer without giving a reason 1. The following are the…

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Q: 5. If Evaluate the following. (a) F' (9) (b) F (0), by interpreting F (0) as an area 1) = ₂√25 - 1²…

A: We solve this using differentiation under integral sign. The detailed solution is given in the next…

Q: Use the pick-a-point method to show that if A and B are subsets of some universal set U, then A ∪ (B…

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Q: Evaluate ¬⇒(PV¬q) if p and r are True and q is False. Select one: O True O False Tim

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Q: Determine the general solution of y" + y = tanx using variation of parameters

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Q: Q1/ Find the determinant of the matrix [2 4 11 38 5 16 2 41

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Q: 3. 6, 10, 16, 24,... Find the explicit formula for an, where n ≥ 1. 4. 1 4 7 10' 15' 20' ... Find…

A: Part (3):-  Given sequence is 6, 10, 16, 24, .....

Q: e of ne nded by

A: We have to find the volume of solid generated by revolving the region bounded by 2y = e-(x^2) , the…

Q: Question: Verify Green's theorem in the plane for (x³ − x²y)dx + xy²dy, where C is the - C boundary…

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Q: 32u at2 J2u a2 дх2

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Q: cos(2³) COS 2 sin 2 2 (A) z = 0) is a simple pole (B) z = 0 is a removable singularity (C) Resf(0) =…

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Q: 4. Evaluate the double integral: L Loddy. dx dy. y¹/3 x7 +1 (Hint: Change the order of integration…

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Q: {"₁ = [-²] * 1. Consider the basis B = -3 2 be the coordinate map for the basis B. (a) Find the…

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Q: Consider the function f(x) = cos x - 3x + 1. Since f (0)ƒ () <0. f(x) has a root [] If we use secant…

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Q: Let A = {1, 2, 3, 5, 6, 10, 15, 30} and define R on A by xRy if and only if x divides y. a. Find…

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Q: II. Problem Solving/Proving. Show all complete solutions. 1. Show that V=M22. the set of all 2 x 2…

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Q: 5. If Evaluate the following. (a) F' (9) (b) F (0), by interpreting F (0) as an area F(x) = √ √ 25 -…

A: Given: Fx=∫x525-t2dt

Q: Prove that if a function f is one-to-one, then f[A ∩ B] = f[A] ∩ f[B].

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Q: (c) If F(t) is an antiderivative of f(t), explain why the function F(t) is always increasing. (d)…

A: Let us start solving the problem step by step... D) given f(0)=0 Total rainfall=150 mm Which means…

Q: 5. The graphs of f(x) and g(x) are shown. What is g((4))? f(x)

A: Solution :    From given graph   f(4) =-2  ,  g(-2) =-4

Q: Find the area of the region bounded by x = and the y-axis using the horizontal strip. 2y²+1

A: Given curves are x=42y2+1 and y-axis.

Q: ди ди x====u+Yay ?х

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Q: 4 Find the area of the region bounded by x = 2y² +1 and the y-axis using the horizontal strip.

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Q: Q1\ A\ Define and give an examples with its solutions for the following terms: (1) Strongly…

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Q: Evaluate the integral: Soft² et du d

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Q: Define a relation T on R by xT y if and only if (sin^2) x + (cos^2) y = 1. (a) Prove that T is an…

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Q: 7. Classify the matrix as upper triangular, lower triangular, or diagonal, and decide by inspection…

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Q: Consider a continuous function f(x)=2ex−1−2x. The graph of f is decreasing on which interval/s?

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