1) Determine the solution of the differential equation dy x +y = r² + r da

Q: Solve for 8: cos²0 (1 + 2cose) = 0 on the interval 0 sesn. = 06-1플 100-10. ㅠ 3 품 품 3 3 00-27, 0.ㅠ…

A: To solve the trigonometric equation cos2θ1+2cosθ=0 ; 0≤θ≤π.   As the general solution of the…

Q: Compute the flux of the vector field F = xỉ + y) + zk through the surface S, which is a closed…

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Q: Use logarithmic differentiation to find dy/dx. (x + 1)(x-2) (x - 1)(x + 2) dx || y = X > 2

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Q: Write a polynomial with degree 4 that has a zero at x = -1- i√2, and a zero at x = -6 with a…

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Q: Find the derivative of the function. y' = y = 3 tan-¹(x - √₁+ 1 x² +

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Q: Consider the given function and the given interval. 14x f(x) = (1+x²) 2¹ [0, 2] (a) Find the average…

A: According to question,Given Function,fx = 14x1+x22

Q: 1 5) Let A= 1 -1 0 0 -1 2 3 -6 a) Find A-¹. b) Find det(A), that is, the determinant of A.

A: (a)  A-1=1Aadj(A)where  A=determinant if Agiven  A=1-1010-1-623

Q: What is dy given that y = ln (4- x? 1 x-4 dx 4 O I da I 4 dx 4-x

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Q: Determine the x-coordinate(s) of any relative extrema and inflection points of the function y=x³ In…

A: Solution: y=x3lnx4 This can be written as y=x3(ln(x)-ln(4)) Then: for having any relative extrema…

Q: he function y = omain tercepts ymmetry 2x+3 x+2 do the following.

A: we will find the required.

Q: Question 8 Consider the indefinite integral U= du = x5 (x6 + 4)6 This can be transformed into a…

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Q: Let F(s) = L-¹{F(s)} = ? 1 f(t) = e-8 tsin(√7t) √7 f(t)=e8tsin(√7t) O O f(t) = e 1 s²+16 s+71 -8 t…

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Q: Assume f and g are functions such that f(x) dx O 5G(x) - 2x + C OG (5x-2) + C O 5G(5x-2) + C OG(a) +…

A: Please see the below picture for detailed solution.

Q: Determine if the vector u is in the column space of matrix A and whether it is in the null space of…

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Q: (4) y = Tan' (*); d =? A) 4 4+x² B) 15) ys A) 2 SecX 11 2√4-X² Sec (X); dy = ? +Y 2 secx. ranx D)…

A: 16) The given equation is; Sinx - Cosy - 2= 0

Q: 14. Given g(x) = f(t². + 6t16) dt, find intervals on increasing / decreasing and concave up/ concave…

A: The given integral function is: g(x)=∫-22x t2+6t-16 dt

Q: Determine which graph corresponds to the area enclosed by the curves y= O O Find the area of the…

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Q: Consider F and C below. F(x, y, z) = yz i + xz j + (xy + 10z) k C is the line segment from (2, 0,…

A: Solve the following

Q: If y is inversely proportional to x, and y = 9 when x = 6, write a formula for y in terms of x. Use…

A: Given y is inversly proportional to x let k = proportionality constant

Q: A rock is thrown into a still pond. The circular ripples move outward from the point of impact of…

A: To find the rate at which the area is changing

Q: 2 Find the area between the graph of y = 5 – 5x³ and x-axis and − 1 ≤ x ≤ 8 using properties of…

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Q: 44 If 2x=y¹/5 +y=1/5, then express y as an explicit d²y dy = 25 y. dx dx² function of x and prove…

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Q: 1 COS X sin² x O - cscricot - O sec x O tan x dx = cotx +C - tam x - C + C secx + C O csc x - cotx +…

A: First we need to simplify the given trigonometric ratio and then integrate it accordingly.

Q: Given the graph below, solve the following inequality: k(t) < 0 +10 +RVEY 9 8 7 6 5 4 3 2 1…

A: To solve the given inequality

Q: Explain and demonstrate how to find the eigenvalues of the matrix 0 2 2 3]. -3

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Q: Given the following equation of a circle in general form, find the equation in standard form by…

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Q: dentify the circle that has center (4, -2) and radius 4. Select the correct answer below: (x-4)² +…

A: Given query is to find the equation of the circle.

Q: A glass sphere given by the equation (-1)+(y-2)²+(-3)² = 36 is floating above the plane 2x+y-2x =…

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Q: x = The position of an object at time t is given by the parametric equations y = 5t² + 1 Find the…

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Q: This problem is concerned with the squeeze theorem. Suppose that is a bounded function and satisfies…

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Q: Let f(x) = x for x < 0 and f(x) = sin(x) for x ≥ 0. Match the following. Here DNE means does not…

A: The function is  f(x)=x for x &lt; 0 and f(x)=sin(x) for x≥0

Q: Differentiate the function. g'(t) = g(t) = ln(8 + tº)

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Q: er the equation of the parabola graphed below, using the vertex form y = a (x-h)²+k. y = (-1,0)…

A: To solve the following problem using graph

Q: Find dy/dx by implicit differentiation. 7x²y + 4y²x = -1 dy/dx =

A: Given query is to find derivative.

Q: 15

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Q: Find the area of region enclosed by=t-t², y=t-t³, 0≤t≤1 using Green's Theorem.

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Q: 31. dy If x³ - 2xy + 2y³ = 4 then, in terms of x and y, dx

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Q: 28-30) Given f(x) = 2x + 3 and g(x) = 3x + 5 28. If P(x) = f g then P' (2) = 29. If D(x) = then…

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Q: Determine the values of constants a, b, c, and d so that f(x) = ax³ + bx² + Determine the values of…

A: Given,            fx=ax3+bx2+cx+d has a local maximum at the point 0,0 and a local minimum…

Q: a. Find the first four nonzero terms of the Maclaurin series for the given function. b. Write the…

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Q: A large rectangular movie screen in an IMAX theater has an area of 9,064 square feet. Find the…

A: To find the length and width.

Q: he effectiveness of a certain medical injection is modeled by 0.03t(70−t), where t is time in…

A: Let effectiveness denoted by E E = 0.03t( 70 - t ) E = 2.1t - 0.03t2

Q: Which of the following represents a geometric sequence with a common ratio r = 5?  1 2, 10, 15, 75,…

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Q: ven the following equation of a circle in general form, find the equation in standard form by…

A: Given query is to find the standard form of circle.

Q: f(x) = x4−32x−12  Determine where the function is concave up and concave down. Enter your answers…

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Q: 1. Find f'where f(0) 2 Find all = 1+sec(0) 1-sec(0)

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: 7. Find the area of the portion of the plane that is inside the triangle with vertices (0,0,4), (8,…

A: See this solution in below.

Q: Given f(x) = 13x³ + 18x² - 4x + 22

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Q: Find the length of the cardioid r = 3+3 cos 0. The length of the cardioid is (Simplify your answer.)

A: formula for  length of cardioid is  L=∫abr2+(drdθ)2dθgiven  r=3+3cosθdcosθdθ=-sinθ

Q: You are given a feasible region. Find the maximum and minimum (if they exist) for the given…

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