Prove that any closed interval [s, t] can be written as the intersection of a collectable collection of an open set.

Q: The flat surface shown is submerged vertically in water. Find the fluid force against the surface. T...

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Q: 3. Find the Laplace transform of the following IVPS. 4 y"(t) + 3 y' (t) – y(t) = t² e=t, y(0) = 0, y...

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Q: A small country with a population of 7,000,000 consists of four states, A, B, C, and D. There are 14...

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Q: 4) Let f : C – C be a homomorphism of rings with f(x) = x for all x E R. Show that f is either the i...

A: If a function f is ring homomorphism from a ring R to another ring R'. Then We knew from the definit...

Q: If two cards are drawn without replacement from an ordinary deck, find the probability of a queen an...

A: Brief answer is given below.

Q: 6: Determine the most general bilinear transformation which transforms the circle| z | = lonto| w = ...

A: To find a bilinear transformation which transforms the unit circle z=1 onto w=1. (a). We know that a...

Q: 14 (Type an integer or decimal rounded to the nearest hundredth as needed.) b) Determine each resort...

A: The complete solution is in below  

Q: Find the average x-coordinate of a point on the half-torus with the following parametrization (drawn...

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Q: Pls do part b pls

A: Part (b)

Q: graph the following hyperbola

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Q: Use Naïve Gauss Elimination with Partial Pivoting to determine the solution of the system of linear ...

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Q: Solve the following word problems. 1. Rohit gave a party and ordered pizzas. 6 of one pizza was left...

A: # we are entitled to solve one question at a time. Please resubmit the other question if you wish to...

Q: Show that 1) The columns of a (row-reduced) echelon matrix that contain the non-zero pivots are line...

A: Linear Dependence: Let A = v1, v2,…, vr be a collection of vectors from ℝn . If r>2 and at least ...

Q: Exercise 1: Let f(r) = |sin(2r)|. %3D 1. Find the cosine series C() of ƒ on (0, 7). 2. Find the sine...

A: We are given the function f(x)=sin(2x). For (1), Here, we need to find the cosine series C(x) of f o...

Q: 1. The monthly sales (in thousands) of burgers (B1) and bites (B2) in three fast-food restaurants (R...

A: a) The sales in the months of January and February in the matrix form are represented as:Matrix repr...

Q: Prove the following propositions fo all positive integers n. 10' + 10² + 103 +… … + 10" = (10" – 1) ...

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Q: Describe the notion of completeness of R in layman's term by using the idea of least upper bound pro...

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Q: sin t cos y = dy find dx Example 6. If x = cos 2t <. Vcos 2t

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Q: Solve the following S-L problem y"(x) + Ay(x) = 0, y'(0) = 0, ul L) -0

A: This is a Sturm Liouville problem.

Q: Show the following: (a) The vector (7) spans R'. (b) The vectors (1,2), (–2, 1) span R?. (c) The vec...

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Q: Use Naïve Gauss Elimination with Partial Pivoting to determine the solution of the system of linear ...

A: We have,  4y+5z=77x+5y+6z=-55x+3y+4z=-5 This is of the form Ax = b The corresponding matrix A is 045...

Q: Date: ame: rections: Find the area of each rectangle as quickly as vou can. Don't forget your unit! ...

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Q: Express the following function in the form f(z)=u(x,y)+iv(x,y) 1. cos(z^2)

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Q: 6. We defined the relation ~ between sets by A ~ B means that there there is a 1-1 correspondence ƒ ...

A: The complete  solution is in given below  

Q: 6 for the Use sigma notation to write the Taylor series about x = function. 1 x+5 k =

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Q: Prove by induction that if p is any real number satisfying p > –1, then (1+p)" >1+np for all n E N.

A: To prove  (1 + p)n ⩾ 1 + np    ∀ n∈NFor  n = 1, ( 1+p) = 1+p So it is true for n = 1let it be true f...

Q: b) Is f one-to-one? Answer yes or no and explain. Do not just quote the definition, but give a reaso...

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Q: 6t R(t) = „A - (a) 6 (b) R(1) (c) R(-1)

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Q: 3

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Q: 2.) y"-3y'+4y = sint ; y(0) = 0, y' (0) = 1 The answer should be: (1/6)cos t + (1/6)sin t - (1/6)e...

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Q: 1. Calculate by the Power Series Method the value of y as general solution (term-by-term from n = 0 ...

A: Second order differential equations,with Power series method

Q: Find the maturity value and the amount of simple interest earned. $5118 at 4.46% for 6 months

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Q: Let a, b e Z and n E Z*. Prove that if a = b(mod n), then gcd(a, n) = gcd(b, n).

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Q: Let S {3k : k E Z} be the set of integer multiples of 3. Let R be a relation defined on Q by x Ry if...

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Q: X1 6. X1 Let T : R? R- be defined by T X2 7 For which of the following bases B is [T']B a diagonal m...

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Q: Let D be the solid in space lying beneath the ry-plane and between the sphere r2 + y? + z² = 3 and t...

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Q: Find the domain of the function

A: 1. Given, the function                        H(x)=2x+3x3-4x                   

Q: EXERCISE 1 dy -dx = 0

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Q: Hotel A Total Number of rooms 213 182 655 1050 a) Determine each hotel's modified quota using the di...

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Q: 4x f(x) = %3D 9+r*

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Q: f(x) = cos(r)(1+ cos(x)) - sin(r)(1+ sin(x)) f(x) = sin(x) + (1+x) cos(x) f(x) = (1+ sin(r)) + (1+ x...

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Q: 2. Multiple Choice: If log x + log y = - 2, which of the following is correct? А. х+у3-2 В. ху %3D— ...

A: Brief answer is given below.

Q: To find the inverse transforms, first express the given function of s into partial fractions which w...

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Q: Let F, denote the nth Fibonacci number (F1 = F2 = 1, Fn+2 Fn+1 + Fn for n > 1). Use %3D induction to...

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Q: Exercise 4: Use separation of variables to find a family of solutions to the following PDE u:(x, t) ...

A: To find- Use separation of variables to find a family of solutions to the following PDE utx, t - c2u...

Q: a) Find the image set f (S) for S = {-2, 5}.

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Q: S | = cosh (v4 t) s²-2- False True

A: L{ sinat} = as2 + a2,   L{ sin2t} = 4s2 + 42a is falseL{ eat f(t)} = F(s-a) where F is Laplace trans...

Q: 8. In order to have P50,000 in 5 years, how much should you invest if the compound interest is 5%?

A: Given : Amount=50,000 Time=5 years Rate of interest=5% Formula to calculate the Principal amount P=A...

Q: The part of the sphere x^2+y^2+z^2=4z that lies inside the paraboloid z=x^2+y^2

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Q: Define the set A as A={-2<z<-1} or {|z|<1} or z=1 or z=2. Sketch A and find the set of all interior ...

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