Find the centroid of the region. NOTE: Enter the exact answers. Y (x, y) = (,) y = x 19 يع

Q: two questions from practive exam

A: Question 3:- I am attaching the image of the solution.Question 4:- Q(4) Second part is also…

Q: Please answer parts a and b

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Q: Solve the initial-value problem by using integrating factors. y' + y = x, y(0) = 7 y(x) =

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Q: • Evaluate the surface integral s F dS where F= (3x, z,-y) and S is the part of the sphere x² +…

A: Surface Integral over a Parametrized SurfaceWe can evaluate a surface integral over a surface S…

Q: 8

A: We can estimate the Riemann sum using left and right-hand endpoints by calculating the width of each…

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A: First, note that (sin(2θ)) completes one full cycle from  (0) to (2π) as (θ) ranges from (0) to…

Q: Using the attached theorms, Solve dx/dt =4x+y , dy/dt=-2x+2y

A: Step 1: Step 2: Step 3:

Q: Let h(t) = tan t. Find the maximum and minimum values of h on the interval I = [0, π/3]. Then use…

A: The objective of this question is to find the maximum and minimum values of the function h(t) = tan…

Q: Problem 1. (1) The integral 1 So + √√x(1+x)dx is improper in both ways we have discussed in class:…

A: Step 1: Evaluate the first integral Step 2: Evaluate the second integral Step 3: Therefore the…

Q: n Given the following matrix, and the associated cofactor matrix C 1-2 -21 600 A = 0 3 1 C = 4-20…

A: Approach to solving the question:  Detailed explanation:

Q: 12 3. F(s) = = 53 +8 + sin 2t - 1). Suggestion: After finding the three cube roots -2 and 1±√√√3i of…

A: The given Laplace function is: F(s)=s3+812​ F(s)=(s+2)(s2−2s+4)12​ Now using partial fraction…

Q: 2.4

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Q: Evaluate the line integral F dr, where C is given by the vector function r(t). F(x, y, z) = (x + y²)…

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Q: Sketch the region bounded by the graphs of the equations. Find the area of the region. f(y) = y² + 7…

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Q: Let u == (7,5,-5) and = (−1, −2, 2). Compute the following: u v . . = 2 7(ū. v) = (7) · v = ū. (77)…

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Q: Find the value of the summation. 19 Σ sin(πk) = k=0

A: we have to find the value of ∑k=019​sin(πk) We have to substitute k = 0 to 19 in sin(πk) and have to…

Q: Don't use chat gpt , previous answer is wrong

A: Step 1:Step 2:

Q: Find a solution for y in terms of x that satisfies the differential equation and passes through the…

A: Step 1: Step 2: Step 3: Step 4:

Q: 10

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Q: Please do the following questions with full handwritten working out.

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Q: Consider two functions f and g on [2,9] such that √ f(x)dx = 11, √ g(x)dx = 7, √ f(x)dx = 4, and √…

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Q: 4. 5

A: If you have any problem let me know here in comment box for this thankyou for your question.

Q: 1. Find all critical points of this function. f(x, y) = 7x8y+2xy - x² + y ³ Then classify each…

A: Step 1: Step 2: Step 3: Step 4:

Q: Find two positive numbers such that the sum of twice the first number and three times the second…

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Q: Use the Fundamental Theorem of Calculus to find 8 cos() da

A: Steps and explanations are as follows:In case of any doubt, please let me know. Thank you.

Q: Calculate the integral of f(x, y, z) = 6x² + 6y² + z² over the curve c(t) = (cost, sin t, t) for 0 ≤…

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Q: NO zion Given the following information, find the matrix A. 1. (47) ¯ = (25) = Instructions for the…

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Q: The radius of a circular oil slick expands at a rate of 7 m/min. (a) How fast is the area of the oil…

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Q: Question 3

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Q: Application 19. Determine the derivative of the following & simplify (within reason): [ a)…

A: Thanks for your patience!Kindly comment if you need any clarifications.

Q: Question 6

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Q: Given f(x, y) = -4x³- xy + 2y², find the following numerical values: f=(0, 4) = fy(0, 4) =

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Q: Evaluate the definite integral. π/3 ³ sec(t) (tan(t) ° sec(t) (tan(t) + sec(t)) dt = Hint: First…

A: Step 1: Simplify the given integral :∫03π​​sec(t)tan(t)+sec2(t)dtStep 2:Seprate the single integral…

Q: Solutions to question 2 please

A: Step 1: Step 2: Step 3: Step 4:

Q: Find the absolute minimum value of f(x) = 7 x² - 10 x + 10 on the interval [0, ∞). Note: You need to…

A: The given function is: f(x)=7x2−10x+10 The restricted domain of the function is: [0,∞) Let us recall…

Q: Assume there is a certain population of deer in a forest whose growth is described by the logistic…

A: We can find the population of deer in the forest after one breeding season by using the logistic…

Q: Use the substitution u = √(x) to calculate the indefinite integral from image.

A: Given:∫x​+x​3dx​First, we need to simplify the denominator, we have:=∫x​+(x​)2x​1​dx=∫x​+xx​1​dxWe…

Q: 2 x = (y-1)² x = 3 y 1 X = 2√y 2 x

A: Step 1:Step 2: Step 3: Step 4: thanks

Q: tyyping

A: The miller indices for hexagonal lattice:Miller indices for any direction; The miller indices is…

Q: When doing calculus problems, how would I identify that I should do long division of polynomials in…

A: 1. Polynomial division: If you're asked to divide one polynomial by another, long division is…

Q: Evaluate the definite integral. 7-7sin²0 de 3cos20

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Q: Let f(x) = 4x. (a) Sketch the region R under the graph of f on the interval [0,2]. 1 2 3 Find its…

A: (a) To sketch the region R under the graph of f(x) = 4x on the interval [0, 2], we'll draw the line…

Q: Question 6 Evaluate the following Integrals. (a) |√1-de dr 422 (b) 25 √1+x² dx (c) s sin (1/x) -da…

A: Step 1: Step 2: Step 3: Step 4:

Q: Question 5

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Q: 2.1

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Q: ☐ ☐ 1. Approximate the following integrals using the trapezoid rule. (Round answer to three decimal…

A: 1).ans:- method  We can follow below steps to find the solution: i). Calculate the width of each…

Q: Q2

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Q: Use left and right end points and 4 rectangles to find two approximations of the area of the region…

A: Step 1:​The left Riemann…

Q: 7

A: Step 1: Step 2: Step 3: Step 4:

Q: The rate of change of the population of a small town is d/dt (P) = k*P where P is the population, f…

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