Is there a tank of the same size and same basic shape that would require less work to empty? Explain/justify your answer.

Q: Assume all matrices are invertible. Note that c cannot exist by itself in a matrix equation. Solve…

A: Given, all matrix are invertible.XA = cX + IAlso c can't exist by itself in a matrix equation.

Q: Find the limit x lim (1.3) (0,0) 2¹+ y² + y8

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Q: 4. Let (X, d) be a metric space and d' be a metric on X that is equivalent to d. Let and be the…

A: Let us prove above result

Q: Find a basis for the orthogonal complement of the subspace of R4 spanned by the following vectors.…

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Q: a E R; when a = too, we leave the proof to the reader. Let Sn suplan, an+1,...}; so Sna. By the…

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Q: Q. Y prove that a) X (o) H Lim X(Z) Z→∞ b.) x (∞0) = Lim (Z-1) X (Z) Z-1

A: a) To prove that x(0) = lim(z -> ∞) x(z), you can use the definition of the limit:lim(z -> ∞)…

Q: 8. X₁ X2 X3 + x4 = 0 x2 + x3 = 0 -

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Q: How close is the approximation sin x = x when |x| sinx? How close is the approximation? OA. Error…

A: Let, Graph:From the above graph, we can clearly see what is going on with these graphs.We have given…

Q: Don has nine pairs of shoes, seven pairs of pants, and three shirts. If all items are compatible,…

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Q: y" + y = secx tan x

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Q: ſőt, dt + f(2 − t), dt

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Q: 15. 10 Σ 2+1 – 2 i=0 What is the value the sums of terms of a geometric progression

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Q: #3. Evaluate the triple integral to a number answer: fg (22) dV where E is the solid defined by E =…

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Q: Select an Answer Select an Answer Select an Answer -6 18 -3 -12 30 11.5 = {( 4 )· (~ 6 3)} -6 Select…

A: For a given set S we have to find whether they are linearly independent or not.

Q: Find a basis for the orthogonal complement of the subspace of R4 spanned by the following vectors.…

A: The given vectors .The aim is to find the basis for the orthogonal complement of the subspace of…

Q: 11. a) U₁₁ A₁ Let A₁ = {i,i+1,i+2,...} for i=1,2,3,.... Find b) Ai

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Q: Consider the group G={1,−1,i,−i} under multiplication, where i^2=−1. Determine the inverse of each…

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Q: Your Cd pays a return of 5.95 & Apr Compounded daily.  a) Find the Periodic Interest. b) Find the…

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Q: 1st≤2: r= r = (2-1) (1,1,1)+ (1-1)(2,3,4)= (2-1 + 21− 2)i + (2−1+31 −3)j+ (2−1+ 41 − =ti+(2t-1)j +…

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Q: 2. Solve for m, 2 2m² = 3 - 5m

A: (.) Given,

Q: dy Solve the given differential equation by using an appropriate substitution. The DE is of the form…

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Q: Let x € R and x > −1. Prove that (1 + x)” ≥ 1 + nx for every positive integer n

A: To prove that (1 + x)^n ≥ 1 + nx for every positive integer n when x > -1, you can use…

Q: =rential equation is one of the form dy dx or 1, the Bernoulli equation is linear. For other values…

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Q: Problem #1: Let A = 9 0 1 2 -11 -2 0 0 -3 (a) Find the characteristic polynomial of A. (b) Find the…

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Q: Consider the pattern. use it to solve for 123456789 x 7200 123456789 x 9 = 1111111101 123456789 x…

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Q: S Exercise 6.1.13: Find the inverse Laplace transform of (s²+s+2)(s+4)*

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Q: Let V be the vector space of symmetric 2 x 2 matrices and W be the subspace W-spand W = span{ a.…

A: We need to find two elements X and Y.

Q: 8. d²y dy Solve the Cauchy-Euler equation x²- +8x +6y=0. dx² dx

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Q: The table shows the cost, C'(g), and revenue, R(q), in terms of quantity, q. Estimate the marginal…

A: The given table shows the cost, C(q), and revenue, R(q), in terms of quantity, q. Estimate the…

Q: Mark the following either true or false. Justification is required. A matrix is invertible if and…

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Q: Determine the value of k so that 3x - 1 is a factor of 3x³ + 8x² + kx-2. a) k = 3 b) k = 1 c) k=-1…

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Q: Prove that 1^2 - 2^2 + 3^2 +...+(-1)^(n+1)n^2 = (-1)^(n+1)n(n+1)/2 for all n∊N.

A: We will prove the given result by principle of mathematical induction.

Q: Problem #8: Let R have the Euclidean inner product. Find a unit vector with a positive first…

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Q: Mark the following either true or false. Justification is required. For square matrix A, the (i,…

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Q: Assume all matrices are invertible. Solve for X: A(XB – D) = B

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Q: and if f(x) = sin" (x²) Lim 0 find 2m + n f(x) f'(x) (1 − cos x)m - = 2√√√3

A: Given that                                                            Formula:…

Q: a. Find f'(-2) and f"(-2) b. At which value(s) of x does f(x) have a relative extremum on [2,6]?…

A: f' (-2) = 1f'' (-2) = -(1/2)

Q: Find the power X In t series of the function F(x) = S = √² [² / dt] t-1 0 -dt dy about co 1 =

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Q: Show that translations are commutative. That is, if matrix T(d) represents a translation by d₂…

A: To show that translations are commutative, we'll use the matrix representation of translation. Let…

Q: Suppose that a matrix A has characteristic polynomial p(^) = 24 − 3a³ + 82² – 24. Consider the…

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Q: A tank is filled with a fluid with density 54 The cross-section of the end of the tank is given by…

A: The slice is shown below:The volume of slice is,

Q: Use traces to sketch the surface: x² = 36y² + z²

A: Given surface :Use the traces to sketch the given surface

Q: Give the rank and the nullity of the matrix. - [3 3] rank(A) nullity(A) A = = = 10-1 3 3

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Q: Let Max Z = 1 S.t 21 + 2x2 X2 + X2 x1 X1, X2 ≤ 2 ≤2 < 3 1/ Write the dual (D) of (P). 2/ Use the…

A: Max s.t

Q: 1. Use Gauss elimination method to solve the linear system -1 1 x1 F436-0 1 -1 x2 = -1 X3 32

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Q: 3. Solve the system of congruences Show the steps used. 3x = 2 7x3 8x 7 mod 7 mod 11 mod 19.

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Q: Use the graphs to evaluate the expressions below. (Photo) f(g(5)) = g(f(1)) = f(f(3)) = g(g(2))…

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Q: In Exercises 15-20, W is a subspace of R4 consisting of vectors of the form X = X1 15. x₁ - 2x2 + x3…

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Q: of the A. Write te vertex Form of following quadartic Function +2+8x-20 y = 2²² +4 + + 2 1-y= 2.

A: For given 2 quadratic equation we have to find the vertex form of the equation .

Q: find the general solution by finding the homogeneous solution and a particular solution. please help…

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