why is the topologist's comb connected but not path-connected?

Q: All solutions approach the curve y = 2-t² ast → ∞.

A: This is the question of the differential equation.

Q: Solve the area bounded by y³+y²+10 = (x+1)², the lines y=−2 and y=2 *

A: The given problem is to find the area bounded by given region and between the given lines y=-2 and…

Q: Solve y(4) - 25y" = 0

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Q: e al HIIL equ U VILII the discrete topology T, then (X,T) is compact. * O True O False

A: Given that X be an infinite set equipped with the discrete topology T.

Q: 3. Given f(x) = x + 1 and g(x)=x² - 2x - 3 a) Graph f(x) and g(x) on the same axis. V b) Use the…

A: For a function: y=f(x), the dependent variable is y and the independent variable is x. The value of…

Q: 1. Find the following sums, applying Gauss procedure. a. 1+2+3+...+ 397 +398 + 399 + 400 b.…

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

Q: 1. A ladder 8 m long is leaning against a wall. If the bottom of the ladder is pulled horizontally…

A: We will draw figure and use differentiation  to find rate of change . Note . Only one question…

Q: max Z = 3x₁ + 2x₂ -X₁ + X₂ ≤4 3x₁ + 2x₂ ≤ 125 X₁ X₂ ≤3 X₁, X₂ ≥ 0

A: The given problem is to solve the linear programming problem over the within given constraints.  We…

Q: State the order of the given ordinary differential equation. (1-x)y" - 9xy' + 2y = cos x Determine…

A: Order of the differential Equation :  The highest order of the differential Equation is called the…

Q: dy ² dx d²y dx² ev

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Q: the given graph and

A: We have a connected graph G. Graph G has 6 vertices in it. We need to find the vertex-connectivity…

Q: . Consider the vectors W₁ = W2 1 0 and the subspace W = span{W₁, W2, W3} CR¹. (a) Find an orthogonal…

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Q: 1. Show that a frination fiłamb ]->1R is differentiable at xolamb) is and only if its lower and…

A: Solution:f:[a,b]→ℝ is differentiable at x0(a,b)Let us take upper derivative at x0+then…

Q: 11. Determine the solution of Utt = u (x,0) = 0, u (0, t) = h, where h, k, and A are constants. c²ur…

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Q: 13 5. In the process of calculating the inverse Laplace transform of the function F(s) = -27- arctan…

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Q: Topic: Theory of Interest a. Express i6 as a function of d2  b. Solve for d4given that i4 = 0.048.…

A: a) Given: The variables are i6 and d2 To find the function d2 expressed in terms of i

Q: x²yy' = (y² - 1)3/2

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Q: 2. Show that the function. 2 in 12 F(x) == x2 (x=0) is not of bounded variation on [1,1]. (x40)

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Q: PLEASE EXPLAIN THE DIAGRAM AND EQUATIONS

A: The sum of the series: a+ar+ar2+⋯+arn-1 can be defined as:  a+ar+ar2+⋯+arn-1=arn-1r-1, where a is…

Q: 2. Prove that a positive integer n is even if and only if nis even.

A: We prove that a positive integer n is even if and only if n2 is even.

Q: ar = Consider the linear system = AY with A = dt 26 20 and Y₂ (t) = (22(1)) - (+1(0)) Find the…

A: Introduction: In linear algebra, eigenvalues are related to eigenvectors. In the analysis of linear…

Q: 1. Consider L{y(t)} = Y(s). By solving the equation ty"(t) + 2ty(t)=0 con y(0) = 0 you have to: A)…

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Q: (a) Draw a direction field for the given differential equation. (b) Based on an inspection of the…

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Q: (c) What conclusion can be drawn about coefficients in the system of homogeneous differential…

A: Given: X'=Ptx To find: Solution

Q: The function f is defined as follows. X if x #0 f(x) = 2 if x = 0 (a) Find the domain of the…

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Q: The function f is defined as follows. X if x #0 f(x) = 2 if x = 0 (a) Find the domain of the…

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Q: 3. Given (3, 10,-8) and v = (-1,6,4), b) find a unit vector in the same direction as v-u

A: The given problem is to find the unit vector in the same direction of the vector v-u. Given vectors…

Q: Lic 15 F(s) s² +9 Your answer should be a function of t. L-¹{F(s)} = 3 = 8¹

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Q: If A = i-2j-2k, B = 6i +3j + 2k, find A.B if 0 = 70 7.182 4.897 O 12.5 O 5.12 O

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Q: y=-3log10 (x-1) +2 Parent Function y = log10x (x, y) VA Domain Range State the transformations…

A: Use the following rules, to obtain the transformation of the parent function y=fx. Replace x by…

Q: Solve the given differential equation. All solutions should be found. dy 3x² - 6y - y³ dx 6x + 3xy²…

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Q: Ex.9 The work of the force F(x, y) = (x², xy²) along the boundary of the square [0, 1] x [0, 1]…

A: This is the question of vector calculus.

Q: 41. y' + (1/t)y= 3 cos 2t, t> 0

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Q: Solve the differential equation y" + y = 0 y(0) = 1, y'(0) = -1

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Q: In a laboratory setting, the heart rate of a patient was carefully monitored. Below is the graph of…

A: Solution:At t=0, heart rate is 110, Maximum is 160 and minimum is 60.This sinusoidal function will…

Q: Solve y" - 2y + 17y=0

A: If the roots of the characteristics equation are complex numbers a±bi, then the general solution of…

Q: Given vectors and with || = 8 and || = 13 and an angle of 50° between them. b) Find the angle of ū -…

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Q: [10-2] 1 1 6. Find the inverse of the matrix A = 2 2 3. if it exists. 14 2 5

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Q: Three coin are tossed and the number of head appears a- Find the sample space b- Find P(1), P (2), P…

A: here we can use basic formula of probablity

Q: 3 2 (4-x²) dy dx = 7 true False Q6

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Q: 7. Given three point A(1, 1, 3), B(-14, 4, 21) and C(-4, 2, 9), a) use a vector method to show that…

A: We have to solve given Questions.

Q: 3Q. If z₁ = (cos50 – i sin 50), z₂ = (cos70 + i sin €) and z3 = (cos40 – i sin 40) then find 4 polar…

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Q: x(n) = { 2,4,5,7,0,1}

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Q: let W be vector that space and suppose USV SW are subspaces of W. Show that W N/u W ~ V/₁ defined…

A: Let W be a vector space over F   and suppose that U⊆V⊆W are subspaces of W. To show: WUVU≈ WV

Q: Suppose y and on an open interval I that contains the origin. Express the following as a n=0…

A: Here given the differential equation asy=∑n=1∞anxn 3+x2y''+xy'+4y=0 ........(1) the solution of the…

Q: Consider the following table. X f(x) X f(x) 0.0 6.5 2.0 7.9 0.4 6.1 2.4 8.5 0.8 6.4 2.8 8.6 1.2 6.6…

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Q: Determine whether each statement is Existential Quantifier (EQ) Universal Quantifier (UQ) or Unique…

A: Given: Statement condition To find: Solution

Q: 3. Suppose that {f(t)} = F(s) with F a differentiable function and that L{f'(t)} Exists. Then…

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Q: For the function f(x) = 6x-5, construct and simplify the difference quotient The difference quotient…

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Q: log3814 4log100-2 b) -log0.0135 d) 2log4128-5

A: According to our guidelines we can answer only one question and rest can be reposted.