Determine the area of the parallelogram with vertices (7,-4, -7), (10, −5, -4), (13, -3, 2), and (16,-4, 5). Use the square root symbol '' where needed to give an exact value for your answer.

Q: c. How many subsets of A contain only even numbers? d. How many subsets of A contain an even number…

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Q: Use the method of reduction of order to find a second solution of the differential equation 1²y" +…

A: I have given the answer in the next step. Hope you understand that

Q: Consider the following initial-value problem. St, lo, 0≤t<1 t≥1 Write the function f(t) in terms of…

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Q: Prove | cosz |2 = cos²x+ sinh²y.

A: To Prove: cos z2=cos2x+sinh2y

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A: Introduction: Only when there is a 0 degree angle between two vectors can it be said that they are…

Q: Identification. Refer to the documentary The Math Mystery: Mathe- matics in Nature and Universe. [.…

A: Given below detailed answer

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Q: Q4: (1) y = 3logst (2) y = t sin¹(t) + √1-t² 4 (3) y = (sech t) (1 - In(sech t)) (4) y = (t² + 2t)…

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Q: Apply the Gram-Schmidt orthonormalization process to transform the given basis for R into an…

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Q: Consider the ordinary differential equation y" (x) = 4y(x) + 4, y(0) = y'(0) = 1, (d) which is…

A: Given differential equation is y''x = 4 yx + 4,  y0=y'0 =1 -------(d) Also, given that zx = y'x +2…

Q: Find the directional drevative of f(x, y, z)=xsinyz at the point (1,3,0) in the direction of v = i +…

A: we have to find the directional derivative of f(x,y,z)=xsin(yz) at the point (1,3,0) in the…

Q: Can you please hand write or make the work more clear?

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Q: 4. Proving by Example. Let U := { x | 0 < x < 10}, A = { 1 € U|x is odd), and B:= {xe U|x is even}.…

A: This is a problem of set theory.

Q: B) Using two iterations of the Bisection Method, find the real root of the equation x²-x=6x with…

A: In Bisection Method, we find a root of f(x)=0, in an interval [a, b] as follows: (i) First we find…

Q: y" + xy' = 0, x0=0

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Q: 27 7. Find a power series for the function f(x) = 3²-52-2 and its interval of convergence. 8. Given…

A: Consider the given function, fx=2x3x2-5x-2 Now for power series,…

Q: Compute the orthogonal projection of onto 7. Use the square root symbol 'V' where needed to give an…

A: Given u→ = -996,  v→ = 1-1-1

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Q: Given the points x = -2; x₁ = 0 and x₂ = 1 and let f be a function such that f(x) = 0, f(x₁) = 1 and…

A: Given x0=-2 x1=0 x2=1 fx0=0 fx1=1 fx2=-1

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Q: 42. Given that la converges, does In (n) 1-1 (n²+5) ² $-10 converge or diverge? A. Dive B. Cannoe…

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Q: 1 Using intervals, describe the concavity of f(x) = x + = x Determine absolute max over interval…

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Q: 2 f: TR² x R² → R f (x, y) = 1 (2ax₁ y₁ + bx₁ y₂ + bx₂y₁ +2Cx₂4₂) 2 Examine whether the function is…

A: Given :   fx , y =122ax1y1 + bx1y2 + bx2y1+2cx2y2 To check : whether  f(x ,y) is 2 - linear  and…

Q: Use row operations to change the matrix to reduced form. 10-5 012 00 3 10-5 0 1 2 00 3 0 - 12 0 -12…

A: This question is related to matrix reduction using row operation.

Q: If f(t)= e^iwt at the interval (-π, π) determine fourier series of the f(t) ?

A: Given that the function ft=eiwt ,-π≤t≤π

Q: Consider the following initial-value problem. y' - y = 2 cos(6t), y(0) = 0 Find L{f(t)} for f(t) = 2…

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Q: Question 4. Find the general solution of x" - 2x² + x = t when t> 0

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Q: 12 ೧೯ - [435.:4645 มะ 55 26 317 5 28 25

A: To find- Solve 351285 43528 168125

Q: Jesse tossed a paint brush off her roof. The height of the brush (in meters above the ground) ttt…

A: Given That : the Function h(t)=-5t2+5t+10  To Find : Rewrite the function in different form

Q: Let S be the triangular region in Rº with vertices at (2,0,0), (0,6,0), and (0, 0,3) with upward…

A: Hint: It is given that S be a rectangular region with vertices (2,0,0), (0,6,0) and (0,0,3).

Q: 5) Consider the vector function r = (9- 2t, 4+2t, √2t²) a. Find the length of the path on 0 ≤ t ≤1.…

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Q: Answer the following questions related to the Rank Theorem and the Rank and Nullity Theorem: a)…

A: This question related to linear algebra

Q: Find the largest t-interval such that a unique solution of the following initial value problem is…

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Q: Finding coefficients 5 function (1 - 6x) of convergence R. in a power series expansion of a rational…

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Q: The total cost and revenue (in dollars) for the production and sale of x units are given,…

A: The total cost (C(x)) and the revenue (R(x)) in dollars for the production and sale of x units are:…

Q: Show that R[x]/ is a field.

A: In this question, we have to show that ℝxx2+1 is a field.

Q: Use Definition 7.1.1. Definition 7.1.1 Laplace Transform 0≤t 0) Dat dt

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Q: Use Definition 7.1.1. DEFINITION 7.1.1 Laplace Transform Let f be a function defined for t20. Then…

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Q: For each of the following sets of vectors, determine whether it is linearly independent or linearly…

A: We know that , a set of vectors is said to be linearly independent if no vectors can be expressed as…

Q: 13. Which of the graphs is a subgraph of the graph in Fig 9.19? (i) I A (iii) (iv) (v)

A: Please find the answer in next step

Q: 2. At what point does g(x) == have a removable discontinuity? A. x=8 B. x= -8 C. Nowhere D. x = 1 E.…

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Q: 1. Find the radius of convergence and interval of convergence for the following power series. [Don't…

A: Let us consider the series ∑n=1∞an(x-a)n Determine the limit L=limn→∞an+1an(x-a) The series is…

Q: Use Theorem 7.1.1 to find L{f(t)}. (Write your answer as a function of s.) f(t) = (4t - 1)3 L{f(t)}:…

A: The Laplace transform of the function f(t) is represented as F(s) or L[f(t)], it is defined as…

Q: Let series c,, be positive for all values of n and; fa+1 A. B. C. D. 025 B unlim aum 4 for n 21.…

A: Given recurrence relation cncn+1=4 for n≥1 and cn is positive for all n.…

Q: Determine whether the equation is exact. Otherwise find the integrating factor that will make it…

A: We have to determine whether the equation is exact. Otherwise find the integrating factor that will…

Q: Let A and be any sets. Mark the statement that is true OAUB CA OA - B C В В СВ O AC = { } = OANB C в

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Q: Let S be the negatively oriented surface defined by R(u, v) = (u², v², uv), ere (u, v) € [0, 1] ×…

A: This is a problem of vector calculus.

Q: Prove or disprove: The function f : [0, 1] → R defined by x sin (¹) if 0 < x≤1, {₁ 0 if x = 0, f(x)…

A: Theorem: If f : K→R is continuous and K⊂R is compact, then f is uniformly continuous on K. Given:…

Q: 2) Let two vector functions be defined by r₁(t) = (2t, t², t²) r₂(t) = (sint, sin(3t),5t) a. Find…

A: a. Consider the given vector functions, r1(t)=2t,t2,t4r2(t)=sint,sin3t,5t if two vector function…

Q: Show your work. Simplify your results. -{()}--0). and b=0 2 Let L = Span (a) (b) (c) Find the matrix…

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