Find the center of mass of a thin wire lying along the curve r(t) = 2ti + 4tj+ (x,y,z) = ( (Type exact answers, using radicals as needed.) (3) ₁² k, 0≤t≤2 if the density is 8 = 4√√/20+t.

Q: Without eliminating the parameter t, find a Cartesian equation for the line tangent to the curve C,…

A: Let's find.

Q: 2. Write down the name of the conic given by the polar curve r = 6/ (3 - 2 cose). Determine the…

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Q: Using the Optimization in Derivatives, solve the following problem: A 150-room hotel in Reno will…

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Q: Given the two vectors: å = 2ỉ -j+k, b = i + 2k and d = 3ỉ + 5j in 3D. a) Determine the dot product…

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Q: Find the function f(x), such that f(x)= In(3x) J ƒ(1)=1.

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Q: Consider the polar equation defined by r = 5 cos(2 sin 6), where 0<0< 27. Determine the missing…

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Q: n=5   Use taylor series to approxim. from the interval of: 0-1.5   e^(x^2)dx   Round to 4…

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Q: y² − 5y = x³ - e² +c where c is the of integration. Setting x= we have . Thus, we have y — 5y — ( —…

A: This is a problem related to integration. Based on the general formula we will answer the question.

Q: A cardboard box manufacturer wishes to make open boxes from rectangular pieces of cardboard with…

A: As per bartleby guidelines we only give first three question answers.

Q: Current Attempt in Progress Evaluate the definite integral. e i + e='j+t k )dt

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Q: Solve the linear differential equation dy y 2x2 dx

A: This ODE can be solved as follows:

Q: Find dy/dx: solution in handwritten 1. y = 5* (** + dx VE х4 3 -x²,

A: Using leibnitz rule for integral.

Q: Identify and sketch by hand the graph of the quadric surface 25r2 – 25y? – 9z2 – 150r + 200 = 0. You…

A: An equation is given                              25x2-25y2-9z2-150x+200=0We have to identigy and…

Q: Solve the system. Give your answer as (a, y, z) 3z - y + z = 7 -2x + 2y + 3z = – 18 3z-6y + 6z = 0…

A: Use the method of elimination and find the value of x, y and z.

Q: f(#n) for For the function f(x) 3x +1, write Newton's formula as , 1 - F(En) f'(an). solving f(x) 0.…

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Q: 22// use the tests indicated in front of each of the series ollowing to determine if the series…

A: 1. Summation of (k+1)/(k2-1) from k=2 to infinity.  2. Summation of 1/(5k+1) from k=1 to infinity.

Q: Find each limit, if it exists. xA + 4 (a) lim x- 00 x4 - 3 (b) lim *+ 4 x- 00 x - 3 (c) x4 + 4 lim

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Q: Evaluate the integral by making the given substitution. (Use C for the constant of integration.) dt…

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Q: determine which statement is true

A: Follow the procedure given below.

Q: Gasoline is pouring into a vertical cylindrical tank of radius 5 feet. When the depth of the…

A: Volume of cylinder(V)=πr2hSubstitute r=5V=π52hV=25πhDifferentiate w.r.t 't'

Q: Find all solutions in [0, 2π): 2 sin (x) - sin (2x) = 0: 4.8 00, π R/+ 4

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Q: A company determines that its demand function is given by p(q) = -0.4q+ 1754 and that its cost…

A: p(q)=-0.4q+1754C(q)=62.97q+3515R(q)=1128000R(q)= q. p(q)R(q)=q (-0.4q+1754 )R(q)=-0.4q2+1754q

Q: ICLO-3 Use the graph to ist() de.x) dx and S(x) dx in order, from smallest to largest 05 0 0.5 52 25…

A: Here, the curve is above the x-axis for [0,1] and the curve is below the x-axis for [1,2] &amp;…

Q: 7x + 4 if x 1 |

A: Here, the given function is: f(x)=7x+4, if x&lt;-2x2+1, if -2≤x&lt;12-3x if x=11-x+x if x&gt;1 where…

Q: -1

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Q: Let the graph below represent an object's velocity as moves away from a sensor. At what time, in…

A: This integration can also be found from area under the curve .

Q: Differentiate the following, and simplify: a) y = x'e* b) f(x) = 2" + 7** evi c) g(1) = 1+ev

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Q: Is the function a power function. If it is, write it in the form f(x) = kxP, and state the values of…

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Q: 3. An airplane with an airspeed of 80 meters per second is due east, gaining altitude, and has a…

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Q: 2 Find the transformed equation of the hyperbola xy = 4 when rotated 45. (x')² - (y')² = 8…

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Q: 2. Describe in word all transformations involved. y = -3sin(180° – 4x) + 5

A: Given problem:- Describe in word all transformations involved.   y = - 3sin(180°-4x ) + 5

Q: 4.0 mR/h = A. 0.004 R/h B. 0.04 R/h C. 400 R/h D. 4000 R/h

A: Problem statement is not given so considering unit conversion by given options.

Q: n 2 (4k – 2) = k=1

A: Recall:  1+2+3+...+n=n(n+1)2

Q: The average cost for a company to produce x units of a product is given by the function A(x) = The…

A: A(x) represent the average cost.A'(x) will represent change in the average…

Q: (4n². En=1 2 - 2n + 6, - limit comparison test -1 (8,² + n – 8) 7

A: The given series,      ∑n=1∞4n2-2n+68n7+n-8

Q: Find an equation of the line tangent to the curve r = sin 30 at the point where 0 =

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Q: -3x+1) -3х 2-3* dx

A: According to our company policy we are supposed to answer only first question and rest can be…

Q: 5. Evaluate sin y - dy dx y

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Q: State the inputs and outputs for arcsin (also stated as sin¹). Explain why the angles for this…

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Q: Consider the parametric curve defined by x = t – 7, y = t* + 13t. What is %3D - the slope of the…

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Q: п(х — for -1)" n(x – 4)" 2n n3D0 8.

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Q: per ale hey sepalating 4. A line passes thru (5, 11) and cuts a right triangle with the coordinate…

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Q: Find the Area bounded by: x = -y2 and x =y-2 %3D

A: This question can be solved using the concept of area bounded by two curves.

Q: Evaluate y' of the given functions: 1 Find y"'for y (x+4)3

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Q: 22. Differentiate. y = asinh x

A: Given,  y=xsinh x

Q: 5. By the Fundamental Theorem of Calculus (Newton-Leibnitz Theorem) √² + x² d VX evaluate

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Q: 4n – 9 5n + 4 S - Given that sequence {an} = { (а) Show that the sequence is monotonically…

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Q: Find the length and width of a rectangle that has the given perimeter and a maximum area. Perimeter:…

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Q: Find the center of 8x 2 + 6y 2 - 32x + 24y + 8 = 0. (2, 2) (-2, 2) (2, -2)

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Q: 1+cosx Show that if f(x) = In| then f'(x) = -cscx. %3D 1-cosx

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