Write each equation in polar coordinates. Express as a function of t. Assume that r > 0. (a) y = -9 T= (b) x² + y² = 8

Q: If r²y - 12y, calculate dy dr using implicit differentiation.

A: According to company rules.. I need to solve first question... Please repost second question

Q: analyze the function f(x) = * +19 if <10 I 2 10 z +14 if # 2 10

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Q: New question: 37 please as well

A: The given function is; y=xx.

Q: Determine the sum of the following series. 71=1 (4)n-1 6n

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Q: 1. Convert the following general form to standard form of parabola. 4x²-24-40y-4-0 b. x²-2x-6y+25=0…

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Q: 8. Consider a'y dA, where R is the region bounded by 0 ≤ x ≤ 2, a ≤ y ≤0+4. (a) Sketch the region of…

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Q: How do you evaluate the following integral: Integral of (-sin2(x)) dx I'm tempted to use the basic…

A: As we know the trigonometric identity: cos2x=1-2sin2x And use the common integral:…

Q: Use the linear approximation of f(x, y) = e²x²+2y at (0, 0)

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Q: Question 6 Which of the following techniques is best to use to evaluate the given integral? A e 3+e…

A: Given, ∫ex3+e2xdx

Q: Let F(x, y, z) = x³i+y³j+z³k. Compute the following: (i) V.F (ii) V X F

A: i) Given:       Fx,y,z=x3i+y3j+z3k then         ∇·F=∂∂xx3+∂∂yy3+∂∂zz3                 =3x2+3y2+3z2…

Q: Suppose that f(x, y, z) = x²yz - xyz³ is a function of three variables. 1. Find the gradient of f(x,…

A: The given function is; f(x,y,z)=x2yz-xyz3.

Q: Find the gradient of the function f(x, y, z) = zy², at the point (0,-1,-1) ▼ƒ(0, −1, −1) =

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Q: In (ecos5x) dx

A: Given query is to find the integral.

Q: The weight of a lake trout as a function of age satisfies the formula where Wis in kg and t is in…

A: The weight of a lake trout as a function of age satisfies the formula Wt=241-e-0.22t3 We have to…

Q: Use the First Derivative Test to find the location of all local extrem below. Enter an exact answer.…

A: Given

Q: 2. Obtain the general solution by the indicated technique: 2.2 y'=x-2ycot 2x linear equation of…

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Q: Find the eigenvalues of the upper triangular matrix [3 4 5 0 6 7 0 0 8]

A: The given matrix, 345067008 We have to find the eigen values of the matrix.

Q: Find the sum of the first 14 terms of the geometric sequence 1 9,  1 3, 1,   . (Round your answer…

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Q: = x³ +. 5. f(x) = 忘 3x = y + 4 = U x + 2y 6=0

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Q: Water is leaking out of an inverted conical tank at a rate of 8000 cubic centimeters per min at the…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: If C(x) is the cost of producing x units of a commodity, then the average cost per unit is c(x) =…

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Q: Question 4 Your answer is CORRECT. Suppose that f is a differentiable function of x and y such that…

A: We have to find if (0,0) and (1,1) are saddle point or extreme points.

Q: 1. Evaluate the following integrals: b. I sin(4x) cos² (3x) dx

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Q: dy (y-1)√y²-2y-3 S.

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Q: Obtain the differential equation of the family of plane curve described and sketch at least 5…

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Q: 2. A 71.6m tower is to be constructed on a hill with a slope of 15.6°. Both cables make a 42.5°…

A: We will use sin Rule to find the length of each cable.

Q: Determine the convergence or divergence of the sequence with the given nth term. If the sequence…

A: Given query is to find series converges or diverges

Q: Use Newton's method to approximate the x-coordinate of the point where the graph of 4x3 - 10x-5…

A: NOTE: Refresh your page if you can't see any equations. . the given function is  and the given line…

Q: Find f′(x) and simplify.   f(x)=6x5 (x 4 − 2)  F'(x)=.......?

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Q: Describe and sketch the following set of points defined by the following conditions. (x + 2)² + y² +…

A: Given : we have a surface     (x+2)2+y2+z-12=9 and with the conditions :   x≥-2, y≥0, z≥1    To find…

Q: • [ε (a) Evaluate S (b) Evaluate 3.re dr. r² sin z dr.

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Q: 7. Determine the standard equation of the parabola in the figure given only its focus and vertex.…

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Q: Part 1. Sint / Part 2. Cost a) 13 b) None () / 0) F) Part 3. tan t (a) डे उ F) 0 b) I C) 9 d) none h…

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Q: An engineer is building experimental, dome-shaped living quarters 33 m high and modeled by the…

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Q: A stone is thrown vertically upward with a velocity of 96 ft/s from the top of the tower 112 feet…

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

Q: dx (6-x²)z 1.ſ. 3

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Q: 1. Consider the graph of the function f below. I -4 -3 42 1 5 4 3 2 -1 -2 -5 Y I 1 y = f(x) I I 3 Т…

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Q: 3. Consider the recurrence relation an = an-1 + 6an-2 with first two terms a = 0 and a₁ = 1. a.…

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Q: Consider two nonnegative numbers x and y where x + y = 15. What is the maximum value of 14xy? Enter…

A: Given query is to find the maximum value of the Indicated expression.

Q: Evaluate f(x) = 3 sin x + 5 cos at x = π/3. 1. f(π/3) = 4 4√3 2. f(π/3) 3. f(π/3) 3√3 4. f(π/3) =…

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Q: raph of the function f(x) = x³ + 2x - 1. So, the point (2,1) lies i (f¹)'(2). (Here f-1 denotes the…

A: Given query is to find indicated function.

Q: Why can we pull the 2 out front and change the bounds of the integral from -2 to 2 to 0 to 2…

A: Substitute y^2=u then integrate with respect to u

Q: In (ecos5x) dx

A: Given query is to find the integral.

Q: Find the slope of the following lines.

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Q: Find the sum of the series -6 -6 -6+- +...+ 2 Answer: -6 2n-1 ✔

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Q: Initially an 800 gallon tank contains 400 gallons of water in which is dissolved 50 lbs of salt.…

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Q: 4. Let (n) be an increasing sequence of real numbers. Assume, furthermore, that (x₂) has a…

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Q: (c)  Compute the Jacobian J (u, v). (d)  Set up but DO NOT evaluate the integral using the work…

A: We need use transformation here

Q: Solve the formula for r. 1 n=f+c+ = r

A: The given formula n=f+c+16r We have to find the formula for r.

Q: For each item, use Desmos to graph the given equations and shade the plane region bounded by the…

A: Area of a region is bounded by curves is given by A=∬dydx