Find the arc length L of the graph of r(t). r() = r° i + 1 j+Vor k, 3

Q: 2 - (2x 3y)dx - (2y + 3x)dy 0

A: 2)-(2x-3y) dx-(2y+3x) dy=0dydx=(2x-3y)-(2y+3x)dydx=3y-2x2y+3xdydx=3yx-22yx+3y=vxdydx=v+xdvdx

Q: 5. A ladder of length 4v3 metres is resting on a wall. The wall makes a 60-degree angle with the…

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Q: Solve the given differential equation by separation of variables. dy ху + бу — х— 6 dx ху — 5у + х —…

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Q: ||r(t) × r"(t)|| ||r(t)||* Use the formula k(t) to find «(t). 13 9t: r(t) = e"i+ etj

A: r(t)=e9t i +e-t jr'(t)=9e9t i -e-t j||r'(t)||=81 e18t+e-2tr''(t)=81e9t i +e-t…

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Q: 20) Solve the higher order initial-value problem y"=x+1/x;y(2) =1 and y '(2) = 0 1 7 7 1 15 + -- X-…

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Q: A cylindrical tank of radius 20 ft and height 6 ft is two-thirds filled with water. Find the work…

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Q: Please do it right

A: We have to solve

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Q: Evaluate (2x - y) dx + (x + 3y) dy. C: arc on y = x12 from (0, 0) to (4, 8) 528/5

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Q: Sketch the region whose area is represented by the iterated integral. dyds un

A: Option C is correct.As lower limit in inner integration is tanx2 which you can see in the graph.if…

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Q: Let f a) Simplity the expression tlath), f() XRt 50C43. Using f loc)

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Q: -z“, where T is The temperature at a point (x, y, z) is given by T(x,y, z) = 200e measured in…

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Q: Answer only option b.

A: Given, C is the consumption of fuel in litres per kilometer. s is the car's speed in kilometer per…

Q: olve the following differential equations of

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Q: t- 36 Let g(t) = VE -6 a. Make two tables, one showing the values of g for t= 35.9, 35.99, and…

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Q: The motion of a point on the circumference of a rolling wheel of radius 3 feet is described by the…

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Q: Evaluate the vector-valued function at each given value of t. (If an answer does not exist, enter…

A:

Q: Evaluate the line integral along the path C given by x = 4t, y = 8t, where 0 s t < 1. dy

A: Given: I=∫Cx+3y2dy And x=4t, y=8t  and 0≤t≤1   As we know that; The Power rule: ∫xndx=xn+1n+1+C

Q: Use Green's Theorem to evaluate the line integral (y - x) dx + (2x – y) dy for the given path. C:…

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Q: QUESTION 3 Three machines turn out all the products in a factory, with the first machine producing…

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Q: Evaluate the definite integral. NOTE: Enter the exact answer. 8j i2 + 3

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Q: Evaluate the triple iterated integral. xyz dx dy dz Jo

A: To evaluate the triple integral.

Q: Use the figure to give approximate values for the following (if they exist). Enter your answer as a…

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Q: QUESTION 4 At an awards ceremony, 6 women and 4 men are each to receive an award and are to be…

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Q: QUESTION 12 Solve the following system of equations and fill in the values below: x + 2y - 2z = -15…

A: Here we have to solve the following system of equations. x+2y-2z=-152x+y-5z=-21x-4y+z=18

Q: Verify Green's Theorem by evaluating both integrals y? dx + x2 dy dA ду for the given path. C:…

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Q: Find the curvature of r(t) = 5(cos t) i + 12(sin t) j + tk at t = m/2. Ok = 8/13 Ok = 5/13 O k =…

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Q: Use the Integral Test to determine whether the infinite series E is convergent. (Use symbolic…

A: We have to find if the series converges.

Q: 5 4 3 1 -1 T/2 3T/2 -2 -3 - -4 -5 The graph of the function f(x) = csc x is given above for the…

A: The graph of the function fx=csc x is given for the interval x∈0, 2π. We have to find one-sided…

Q: Find the domain of r(t) and the value of r(to). NOTE: Round your answer to two decimal places when…

A: This question can be solved using the concept of domain.

Q: The graph of f shown below has vertical asymptotes at X= - 2 and x = 4. Find the following limits.…

A: Solution is given below

Q: 2. S 2z+8 dz (z+7)a

A: A detailed solution is given below

Q: of tue reigon boundrd by the graph of tue algebraic fundin. 2) Find tue asea f(x) = x+12x +36 2 =…

A: Given

Q: Find the intervals on which f is increasing and the intervals on which it is decreasing. f(x) = - 10…

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Q: Matching Type. Match the functions in Column A with their corresponding antiderivatives in Column B.…

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Q: (D² + 4)y=12; y(0) = 0 , y'(0) = 2 %3D

A: (D2+4)y=12

Q: What is the annual nominal rate compounded daily for a bond that has an annual yield of 5.2%? The…

A: Use formula of annual percentage yield

Q: Determine whether the series is absolutely convergent, conditionally convergent, or divergent. n5 +…

A: Use alternating series test for checking the convergence of series .

Q: 2 For the function f(x) = 2x² – 4x, evaluate and simplify. - f(x + h) – f(x) h. II

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Q: Activity 1.5.3. A company manufactures rope, and the total cost of producing r feet of rope is C(r)…

A: Given problem :- A company manufactures rope, and the total cost of producing r feet of rope is C(r)…

Q: es conve n=1

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Q: d d. Calculate ri(t) - r2(t)] and ri(t) x r2(t)] first by differentiating dt the product directly…

A: r1(t)=9t i +9t2 j+6t3 kdr1dt=9 i +18t j +18t2 kr2(t)=t4 kdr2dt=4t3 kr1(t)·dr2dt=(9t, 9t2, 6t3)·(0,…

Q: 2Tan 'x -x 9. lim, 2x – Sin^x

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Q: Describe the domain and range of the function. (x, y) = 9x2 - y Domain: y): x is any real number, y…

A: We need to find domain and range.

Q: hW (3 Xy'a4Y) dx + (3 X*y'+2x) dy = o I) sin X dy - Sin 2X -y Cos X dx

A: Given

Q: 5. A ladder of length 4v3 metres is resting on a wall. The wall makes a 60-degree angle with the…

A:

Q: A company determines that its demand function is given by p(g) = - 0.4q + 2211 and that its cost…

A: Given