Use Lagrange Multipliers to solve the following: Maximize f(x, y, z) = 4x + 2y + z subject to r² +y + 2² = 1.

Q: 75° 4 A = (b) 0.4 rad 15

A: Given, theta= 75° Radius(r)= 4 units We know that, Area of sector= (theta/360°)×(pi×r²) Substituting…

Q: Determine the values of y such that D(9,3,-2), E(3,4,7) and F(21,y,-20) are collinear

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Q: For j(z) = (3x2 - 7) (-2x* + 7x), find j' (x) by applying the product rule. Provide your answer…

A: j(x)=(3x2-7)(-2x3+7x) The product rule is: (fg)'=f'g+fg' From above:  f(x)=3x2-7g(x)=-2x3+7x Now,…

Q: Given: cosg=-1, sin x =- 13 ,A is in the third quadrant, and x is in the fourth quadrant; evaluate…

A: This question is based on Trigonometric equation.

Q: -3 1 4 What is the transpose of the matrix 5 2-1

A: Transpose of a matrix can be found by interchanging the rows into columns or columns into rows.

Q: the function below f(x, y) = 2x² – 3y – 4

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Q: 23 Given the ordered pair P, determine the requested sin, cos, or tan of angle . P(5,5) tan0 =…

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Q: long will it take an investment to double in value if the interest rate is 4% compounded…

A: Given query is to find the timme in which investment gets double.

Q: the folium (meaning "leaf"). Descartes's scientific colleague Gilles de Roberval called it the…

A: Find your answer below

Q: Find a set of parametric equations for the rectangular equation that satisfies the given condition.…

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Q: lim x? O1 -25 25 -1 ||

A: The detailed solution is given below Thank you

Q: Compute the given integral. fain' sin" x cos xdx +C

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Q: (b) / (4 – t)Vt dt

A: Given integral is definite integral, because here limits are given. In this integral upper limit is…

Q: 3. V4- (x – 3)²dx.

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Q: The rectangular coordinates of a point are given. Plot the point. (-4/z, -4/2) y y 5 5 X -5 -5 -5 -5…

A: Here we will find the correct option and two sets ,

Q: Find the characteristic polynomial of the matrix, using either a cofactor expansion or the special…

A: topic- matrix operations

Q: dy x2 + y = xe*. dx Find the integrating factor to the first order linear equation, В. In x С. х D.…

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Q: Given the following vector field and oriented curve C, evaluate F•T ds. F= (-6y,6x) on the…

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Q: Find div F and curl F of F(x, y,z) = (x z³) i + (3x²y1² )j + (3z?y) k

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Q: 7 7 = 3, f(x)dx = 8, and g(x)dx = 5. Evaluate the following integrals. Sowar=s. 2 2 2 Sawak = -5 7…

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Q: Given the function G(x) = 3x2 + 2x -1, find the value G(a + 2). 3a 2 + 14a + 15 3a 2 + 2a + 15 5a +…

A: Given: Gx=3x2+2x-1.We need to find the value of Ga+2.

Q: e or sin 1 2 and tan 2 cos .2

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Q: 1. rate at two-hour time intervals are shown in the table. Find lower and upper estimates for the…

A: Given:      The lower and upper estimates for the total amount that leaked may be computed as the…

Q: What is the absolute maximum value of the function f(x) = x - 3x2 on the interval [-2, 4] ? а. 16 O…

A: This question is based on application of derivative.

Q: Evaluate the integrals in the following questions using integration by parts For 0 cos T0 de

A: By Parts Rule: ∫u(x)v(x) dx=u(x)∫v(x)dx-∫du(x)dx∫v(x)dx

Q: Evaluate the integral given. sec(2a)tan(2a)dx +C %3D

A: ∫ sec(x)tan(x) dx =sec(x)+C

Q: csc? 20 cot 20 de

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Q: 1 3 20. Find the associated P-vector. A. C. D. E. None B. ON

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Q: Question 16 Evaluate the definite integral - 6 2x2 + 5 d.x 3 194/6 86V3 5 > Next Question

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Q: 2 and v2 = -2 3 be -2 Work Problem 2": - - - ;): Let v1 = two vectors in R². (a) '- ; Determine…

A: Given that,v1=2-2 and v2=3-2

Q: 1- v extends from (0,0) to (-3,2). Vector W extends from (0,0) to (-3,5). a- Find the magnitude of V…

A: This is a problem related to vector. Based on the general formula and concepts we will answer the…

Q: Express cos (a) in terms of cos(2a). Express sin (a) in terms of cos(2a). cos² (a) COS sin (a)

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Q: Use the figure to find the exact values of sin(2u), cos(2u), and tan(2u). sin(2u) cos(2u) tan(2u) II…

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Q: Find the most general antiderivative of the function. (Check your answer by differentiation. Use C…

A: Given query is to find the antiderivative if the expression.

Q: Evaluate the integral of tan 2x dx tan 2x- tan 2x +x +c tan 2x - tan 2x + x + c C. tan 2x --tan 2x…

A: As per guidelines, I can answer only one question. Since you have asked for multiple, so I did first…

Q: Q2: A- The differential equation y"+2y'+y 0 has a characteristic equation with double roots, one of…

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Q: sin 4.r if r>0 3. Suppose f(r) = {0 if r = 0. Find f'(0) using the definition of derivatives. if r<0…

A: This question is related to derivative, we will solve it using given information.

Q: Find the minimum and maximum values of the function y = 1613 + 24t² on [1,2] by comparing values at…

A: Explained below

Q: Express the vector 7i - 6j + 6k as a product of its length and direction. 7i - 6j + 6k =[Oi+…

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Q: Compute the given integral. fGz (6z - 5) (32- 5z + 2)"da | +C > Next Question

A: topic- indefinite integral

Q: - Solve the differential equation y-2y'+y e" In x

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Q: Simplify the expression to the form a" where m is an integer. Find the value of m. Answer:

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Q: -31+2ア-K and ミー-^ -4 +3k in component form. 9ミ-2? +-yk delermine -マ-5+42

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Q: For the points P1 (4,2,3) and P2(5,1,2), find the direction of P,P2 and the midpoint of line segment…

A: Given that coordinate of point P1 is (4,2,3) The coordinate of point P2 (5,1,2) We have to found the…

Q: Give the range of the function f(x) = -x 2. all reals y ≤ 0 y ≥ 0

A: The given function is: f(x)=-x2

Q: Express the following sum using sigma notation. a. 7+8+9+ 10 + 11 5 a. 7 + 8 +9+ 10 + 11 = E| k=1

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Q: Express the vector P, P2 in the form v = v,i+ v2j+ V3k if P, is the point (- 8, - 1,8) and P2 is the…

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Q: The following series is convergent: 3n 2n? – 1 Σ 4 + 5n2 n=1 Select one: True O False

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Q: Evaluate the following: 1. f (5a - 82 + 6z² - 4x + 7) da

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Q: Prove or disprove the following statement by induction 1-3-5. ... ·(2n-1) a.) 2n whenever n is a…

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