Find the center of mass of a thin plate of constant density & covering the given 2 The region bounded by the parabola y = 2x - x² and the line y = - 2x The center of mass is. (Type an ordered pair.)

Q: 21. A balloon is rising vertically above a level, straight road at a constant rate of 0.3 m/s. Just…

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Q: The polynomial C(t) = -0.006t4 +0.140t³ -0.53t² +1.79t measures the concentration of a dye in the…

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Q: 17-22. Position from velocity Consider an object moving along a line with the given velocity v and…

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Q: To find an antiderivative of f(x) = arctan(3x) you used integration by parts, and obtained…

A: The integration by part formula is:                             ..(1)

Q: Let F(x) = * sin(7t²) dt. " Find the MacLaurin polynomial of degree 7 for F(x). Use this polynomial…

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Q: Find a parametrization of the line in which the planes x+2y+4z=-4 and 2x+3y+6z= -7 intersect. Find…

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Q: Vectors A and B form a 30° angle. A = 3 and || = 5. What is A - B? a) 36 b) 2.83 c) 6 d) 10.02

A: The angle between the vectors  isThe magnitude of the vectors are and To determine: The value of…

Q: 5 (x-2) n²+1 n=1 Find the radius of Convergence R₁ of the series. Find the interval of convergence,…

A: The given series is summation of(x-2)n/(n2+1), n from 1 to infinity.

Q: Suzanne must choose between two job offers. The first job offers $56,000 for the first year. Each…

A: Given that Suzanne must choose between two job offers. The first job offers $56,000 for the first…

Q: Find the following for the vectors v=6i +j and u = 9i + √3j. a. v u, vl. lul b. the cosine of the…

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Q: 8. A spring has six coils in the form of the helix x = 3 cost, y = 3 sint, z = 31/(4x), 0≤I≤ 12m,…

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Q: Consider the following function on the given domain. P(x) = (x + 1) + 3.x ≥ −1 Step 2 of 2: Find the…

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Q: a. Find the area of the triangle determined by the points P, Q, and R. b. Find a unit vector…

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Q: 1. Given the following graph and A(x)=f(t) dt, f , find: -2 -1 4 -3- --2- 1- 0 -1 --2- -3 1 2 3 5 6…

A: Given: To Find: To find .

Q: Find all of the zeros of the function f(x) = (x²+2x − 12) (x³ +x² - 12x). If there is more than one…

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Q: ey-x2 Let f(x, y, z) Find gradƒ(1, 1, −1) and G(x, y, z) = fyy — fxz. X

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Q: 29. a(t) = -32; v(0) = 70; s(0) = 10 30. a(t) = -32; v(0) = 50; s(0) = 0 31. a(t) = -9.8; v(0)=20;…

A: 29) a(t)=-32, v(0)=70, s(0)=1031) a(t)=-9.8, v(0)=20, s(0)=0

Q: Considering the definition of f(x) below, find lim f(x). x-*6 Select the correct answer below: O -56…

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Q: Problem #4: Consider SS (V x F) ndS S where F = 14ex²+y² i + 1le=³j + ln(z+2)x-cosy k and S is the…

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Q: Consider moving a particle along a path given by r(t) = (e³¹, e¹, e³¹) with 0 ≤ t ≤ 1 subject to a…

A: Given that a particle moving along a path  with  subjected to force

Q: Question Beginning 156 miles directly east of the city of Uniontown, a truck travels due south. If…

A: The objective of this question is to find the rate of change of the distance between Uniontown and…

Q: Calculate af ax af af ax af Əy (1, -1) af af af af ax' ay ax (1, -1) ay (1,-1) f(x, y) = 7,000 - 65x…

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Q: For Question 5, region W is bounded by f(x) = 4+√9-x², g(x) = cos 7 104 9 8 7 6 5 4 3 2 1 + + + -3…

A: Region W is bounded by f(x)=4+9−x2,g(x)=cos⁡(π6x),x=0, and x=3 Area =∫03[f(x)−g(x)]dx

Q: Sketch the curve with the polar equation r = 2 + 2 cos(0). What is the name for the shape of the…

A: Given that the polar equation

Q: A hall 180 feet in length is to be designed as a whispering gallery. If the foci are located 40 feet…

A: Find your answer below :Length of hall= 180 ftLet the center be orginla= 180 fta=90b=height of…

Q: b(x) = √√√x Answer O 21 2√2|x| t(x) = 2x

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Q: A company manufactures and sells x television sets per month. The monthly cost and price-demand…

A: The objective of this question is to find the maximum revenue, maximum profit, the production level…

Q: Determine the integral by making the appropriate substitution. 1 2 x In 3x dx ⠀⠀

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Q: A landscape architect would like to design a rectangular flower garden with an area of 160 square…

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Q: Problem #8: Use Divergence theorem to find the outward flux of = (3x², e¹², cos³ (1² + x)) of the…

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Q: Calculate 7 af Әх af af af af 7 Әх ду Әх af ах af ду (1, -1) (1, -1) f(x, y) = x4y3 - х = = = , and…

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Q: (BC Topic) Which of the following integrals gives the arc length of the graph of f(x) = cos2x + 5…

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Q: The grid on the right shows the graphs of several functions f(x) whose slope at 8x each x is Find…

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Q: 10) Find the indicated limit 2x x+1 lim( x-x

A: (10) limx→∞(2xx2+1)

Q: Find the volume of the region bounded by the planes 4x + 2y + 3z = 5, y = x, x = 0, z = 0.

A: 4x+2y+3z=5,y=x,x=0,z=0.0≤z≤(5−4x−2y)3z=0⇒y=5−4x2x≤y≤5−4x25−4x2=x5−4x=2xx=56

Q: Find the work done by a force of 18 lbs acting in the direction N35°E (this means start by pointing…

A: The objective of this question is to calculate the work done by a force acting at an angle to the…

Q: Let S be the solid that lies between the paraboloid z = x² + y² and the sphere x² + y² +z² = 2. (a)…

A: Given that  S is the solid that lies between the paraboloid and the sphere The graph of solid

Q: Using n=2 equal-width subintervals, approximate the area of the region bounded by the graph of, f(x)…

A: By using left endpoint and using  equal-width subintervals, to approximate the area of the region…

Q: Determine which test can be used to show that the series (a) Geometric Series Test (b) p-Series Test…

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Q: A gardener has 920 feet of fencing to fence in a rectangular garden. One side of the garden is…

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Q: Sex. (x+y)ds where C is the straight-line segment x = 3t, y = (3-3t), z = 0 from C (0,3,0) to…

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Q: Find F as a function of x and evaluate it at x = 5, x = 7, and x = 9. F(x) = F(5)= F(7) = F(9) =…

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Q: _g(x) = 4x3 (1 – x4)²

A: The given function .The aim is to find the series representation of the given function.

Q: Use a Riemann sum to approximate the area under the graph of f(x)=x on the interval 3≤x≤5 using n =…

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Q: 11. y = x² from (0, 0) to (1, 1)

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Q: 8. Rewrite CLI x+2 dydadz in the order dzdxdy.

A: We need to change the order of integral.

Q: Use implicit differentiation to find dy/dx. 11. xy = cot (xy)

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Q: Find the unit tangent vector T and the principal unit normal vector N for the following…

A: The unit tangent vector:The principal unit normal vector:

Q: 3. g(x) x² +5

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Q: 27. Find a positive number for which the sum of it and its reciprocal is the smallest (least)…

A: Question No. (27): To find a positive number for which the sum of it and its reciprocal is the…