Let W be the subspace spanned by u, and u₂, and write y as the sum of a vector in W and a vector orthogonal to W. y= -7 3 8 H - 2 , 4₂ = The sum is y = y + z, where y=[ (Simplify your answers.) -3 -1 Is in W and z= is orthogonal to W.

Q: ) Find the formula for bn given by the recurrence bn+1 = 3bn + 2n, bo = 1

A: As per the guidelines I am answering only first question. i.e. (d) bn+1=3bn+2n, b0=1

Q: f(x, y) = x4 + 13x³y³ - 5xy4 + 14

A: Given: fx, y=x4+13x3y3-5xy4+14To Find: To determine ∂f∂x and ∂f∂y.

Q: Find the partial derivatives (f, and fy) of the below function and simplify your answe f(ru) = (ru)2…

A: Topic:- application of derivatives

Q: Find the equation of the tangent line at the point 0, In 3 3 for f(x)=In 3 e²x² 2e +e²x

A: Topic:- application of derivatives

Q: This graph corresponds to which inequality? y ≤ x + 4 y > x + 4 y < x + 4 y ≥ x…

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Q: 2- The circle ² + (y-2a)2 = 4a² is rotated about the line y = -1 where a > 0. A torus is obtained…

A: Given: the circle x2+(y-2a)2=4a2 is rotated about the line y= -1 then torus is obtained from this…

Q: For each positive integer n, define an = n² sin +∞ 1. Determine if the sequence {an} converges or…

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Q: A particle is moving with a position function given by s(t) = 6t² - in metres and time in seconds.…

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Q: 5., You are building TWO identical pens adjacent to each other with a total area of 100 m², as shown…

A: Let's solve 5th question, dimensions for minimize the amount of fencing.

Q: Solve the differential equation

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Q: Question 3 Evaluate O 1. O 1, O In 2 -S₁² ₂ In 2 2 ln 2 O2ln 2 - O2 ln 2-3 3 2 1 2 314 x ln x dx.

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Q: system, or show that it is inconsistent. (If the system has in = z(t), and w = t. If there is no…

A: Given system can be written as  101201-2012-10213-2xyzw=1130 Augmented Matrix…

Q: 76 6 27 6 Σ [5 (2 + (i - 1) =) * - 7 (2 + (x − 1))"] n n as a definite integral, that is provide a,…

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Q: Find the absolute maximum value and the absolute minimum value, if any, of the function.…

A: This question can be solved using the concept of absolute maximum and absolute minimum.

Q: (b) Sketch, on separate graphs, each of the following functions (ii) sech(x). (iii) coth(x).

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Q: Find the indicated value. f(5,2) if f(x,y)=2x²y-5xy³ f (5,2)= 10 (Type an integer or a simplified…

A: Given a function fx,y=2x2y-5xy3 We have find the value of fx5,2 Derivative of a polynomial function…

Q: An 8 by 8 checkerboard has alternating black and white squares. How many distinct squares, with…

A: Given: an square box in which 64 square box (black and white)

Q: For the given function find an equation for the inverse function f-1(x).  f(x)=3x-1

A: To find out the inverse of the function given.

Q: Define the force field F(x, y, z) = . a. Find the divergence and curl of F. b. Let C be the directed…

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Q: What part of this graph is the solution area for a system of inequalities? The blue and red parts…

A: Let's find area of inequalities from given graph.

Q: Find the area bounded by y = x and y = x³. 02 00 01 O 2 01 4

A:

Q: Question 16 Determine which of the following power series is equal to the function f(x) = M8 M8 M8…

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Q: Find the area of the surface given by z = f(x, y) that lies above the region R. f(x, y) 13 + 9x -3y…

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Q: Solve the following system of equations: 2x - 3y = 21 and 5x + 4y = 18 (6,-3) (9,-1) (2,2)…

A: To solve the given system of equations.

Q: An arithmetic sequence begins 7, 13, 19, 25, 31, ... (a) Find the common difference d for this…

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Q: Allouette Shipping Company has a peculiar fee schedule. When determining the price to ship a…

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Q: a. b. C. d. G++++ 3 +++++:+). 3

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Q: Need Help? TEACHER How long will it take for an investment of $3000 to double in value if the…

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Q: Solve the given initial value problem. y'' - 4y' + 3y = 0; The solution is y(t) = y(0) = - 1 2 y'(0)…

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Q: Find the area of the region enclosed by y = 6x² and y = x² + 1. Round your answer to three decima…

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Q: What object is sliced to get conic sections? A pyramid A cone A sphere A cube

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Q: ) In the following exercises, use direct substitution to show that each limit leads to the…

A: The objective of the question is determine the limits of the given function.

Q: For the function f(x) = two periods. Amplitude: A Period: P = -2 sin HARE Number Xx 37 4 Enter the…

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Q: Calculate the definite integral by referring to the figure with the indicated areas. d d a f(x) dx…

A: Solution

Q: car company has $44,000 to spend on robots to put paint on new cars. There are 2 types of robots,…

A:

Q: + y² x² + y² = 64 from x=-1 to x=-3 Find the length of arc of the curve x²

A: Given: x2+y2=64 From the limit  x=-1 to x=-3 To obtain the length  of the arc:

Q: Question 4 (a) Calculate the following: i. the area of the region in the first quadrant bounded by…

A: According to students we will solve second part for you.

Q: (d) y = πx+π³

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Q: f(x)= x² tan(x)

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Q: ) (a) (b) (c) Differentiate y == the function by using rules. 1 2x - 3 y = ln(7x + 5) y = 3x³e5x

A: In this question, we need to differentiate the given functions. Please note that as per bartleby…

Q: Find the integral of f(x) = 1 √1-16x² between 0 and 1.

A: The given integral is 1/sqrt(1-16x2).

Q: Consider the integral (ln(x))6 dx:

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Q: Find the exact average value fave of f(x) [0,5] where f(c) = fave. fave = C= Submit Question = 25-2…

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Q: Evaluate sin³ x cos²x dx.

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Q: dy+y=x²y² X-

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Q: Evaluate lim 0 00 0 1 02 O Infinity 3x²+5 cos x-5 2x

A: Given: limx→03x2+5cosx-52x   As we know the Power rule: ddxxn=nxn-1

Q: Consider the function f(x) = 9 x³ Let F(x) be the antiderivative of f(x) with F(1) = 0. Then F(x) =

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Q: 25. The vector field F(x, y, z) = (2xy + tan x)i + (x²-√y² - 1)j is conservative. a) True b) False

A: To determine whether the following statement is True or False.The vector field F→x, y, z=2xy+tan…

Q: 8. [In(x² + 1) dx

A: Formula for Integration by parts: ∫fg'=fg-∫f'g

Q: Use Part 1 of the Fundamental Theorem of Calculus to find each of the following when f(x) = t³d =…

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