An aquarium 2 m long, 1 m wide, and 1 m deep is full of water. Find the work (in J) needed to pump half of the water out of the aquarium. Use the fact that the density of water is 1000 kg/m^3 Work done

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Q: a. Find a basis for U: b. J Using the Gram - Schmidt onthogonalization, turn the basis of U you got…

A: First, we find a basis and then convert that to an orthonormal basis.

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Q: Please show if each function f  is an inverse. If yes, give the inverse function with the process to…

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Q: 2. Let k be an odd number whose last digit is not 5. Show that the last digit of k4

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A: The given set is .If the set form a basis then the set will be linearly independent.

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Q: Show that the divisibility relation on the natural numbers is transitive.

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Q: Consider the following matrix A: 2 2 2 3 8 8 -3 -6 -4 1 0 3 For each of the following vectors,…

A: (.) Given matrix is,             &(.)  A vector  is in image of a matrix  i.e.  if and only if .

Q: Let a₁ = b , a₂ = and b = (a) Write b as a linear combination of a₁ and a2. T(b) = 32 a₁+ a2. (b) If…

A: (a) We have to write b as a linear combination of a1 and a2.(b) We have to find T(b).

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A: Let V be a finite-dimensional vector space, W a vector subspace of V and  a projection onto W.…

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A: Certainly! For the set F = {0,1,♡}, we can define unique operations + and ⋅ to form a field:1.…

Q: Let f: R² → R be defined by f((x, y)) = 7x - 5y. Is f a linear transformation? a. f((x₁, y₁) + (x2,…

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Q: 18. lim (x,y)-(0,0) COS xy

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Q: ) Suppose ƒ : E → R, p is a limit point of E C R, and lim f(x) > 0. Prove that there exist x-p c> 0…

A: To prove this statement, it can use the definition of a limit. The statement is essentially saying…

Q: Consider the relation R on the set Z defined by a Rb if |a| = |b|. Determine if R is reflexive,…

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Q: TRANSCRIBE THE FOLLOWING TEXT IN DIGITAL FORMAT

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Q: If I = may be Evaluate I 20 do 1-2p000 + p² written using show that it 3=eja dz (1-P3)(3-P) of the…

A: Let the given integral is  --------- (1)            For evaluate the above integral consider the…

Q: Which of the following has no solution? 4 O a) x 2²/₁-2 O b) b) +++255-3 ≤-3 O c) x²+25 x³-36x² - 0

A: In this question, we will check the options.

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Q: Let G and H be groups, and let N be a normal subgroup of G. Decide whether each of the following two…

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Q: 2 2. Let C = {x € R² | ¼ x₁² + x₂² < 1} and denote by cl(C) its closure. E (a Is C closed or not? Is…

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Q: 7 v = 32 32 66 P= 2 7 14 2 b = 11 23

A: Given the vectors  .We need to find the linear transformation  that takes a vector of brand amounts…

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Q: Give the Dedekind cuts in ℝ ≥0 corresponding to the following. Your definition should not refer to…

A: Formally, a Dedekind cut (A,B) consists of two sets A and B such that.A and B are non-empty subsets…

Q: DONT USE CHATGPT Solve the differential equation given by the frobenius method 3xy"+y' - y = 0 ans y…

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Q: Find the determinant of 3 -1 0 20 05 01 1 8 -4 0 1 0 -4 2 NO using properties of the determinant.

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Q: Using the results on determining the sign of quadratic forms, find the six stationary points of the…

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Q: (Composition of continuous functions) Let (S₁, d₁), (S2, d2), and (S3, d3) be metric spaces. Let f:…

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Q: Speedometer readings for a vehicle (in motion) at 3-second intervals are given in the table. t (sec)…

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Q: Find bases for the row space, column space and null space of 2 1 3 4 A: = 1 1 2 4 2 4 2 37 68

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Q: please show me how to move from the first equation to the simplified one with steps. I need to learn…

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Q: For the matrix A, find (if possible) a nonsingular matrix P such that P-1AP is diagonal. (If not…

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Q: A trough is 7 feet long and 1 foot high. The vertical cross-section of the trough parallel to an end…

A: The given function is  and the interval is .The current situation can represents as shown below.

Q: Concerning the Fibonacci sequence, use induction to prove that + F2 = F₂Fn+1 F² + F² +F² + -

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Q: so sorry the matrces are meant to be together so  it's [ 1  0 ] and the numbers below of that matrix…

A: Given set of matrices is{M1=[1101], M2=[1−10−2], M3=[−1−1−11], M4=[04−18]}A set of vectors…

Q: 1 2 + xn (a) Prove by induction that în > 0 for all n € N. (b) Prove that (n) is a contractive…

A: (a) We have to prove by induction that xn &gt; 0 for all nЄ N.(b) We have to prove that (xn) is a…

Q: The population of a city is modeled by the equation P(t) = 253,195e0.25t where t is measured in…

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Q: In the following problems, find the general solution as a linear combination of real solutions, find…

A: Note: We will be solving question 5 only as asked.The given system of differential equation is , .

Q: Find a basis B for the domain of T such that the matrix for T relative to B is diagonal. T: R² → R²:…

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Q: 3. Evaluate f 2 arctan (2) dx + ln(x² + y²)dy where C is defined by x = 4 + 2 cos 0 and y = 4 sin 0.

A: Let   and…

Q: ng statement by mathematical induction. For every integer n ≥ 0, 7 - 1 is divisible by 6. Proof (by…

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Q: Determine the dimensions of Nul A. Col A, and Row A for the given matrix. A= 00 00 0 0 5 5 4 6 0 0 1…

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Q: Determine whether the sequence defined by converges, find its limit. a. 1 b. 5 8 c. 0 d. Diverges 5*…

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Q: Find a state space representation for the system described by ₁ +3 (y1 +32) = U₁ ÿ2 +42 + 3y2 = U₂

A: In control theory, the state space representation is a common approach to modeling and analyzing…

Q: 1. Matrix A has dimension m x n and Matrix B has dimension s x t. Design conditions for m, n, s and…

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Q: Find a basis B for the domain of T such that the matrix for T relative to B is diagonal. T: R² → R²:…

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Q: Use the method of Lagrange multipliers to maximize the function subject to the given constraint.…

A: The given function  subject to the constraint .The aim is to find the maximum value of the function.