Prove the identity 2 tan 0 tan²0 + 1 = sin(20).

Q: Question 2 (a) It is known that, x² x³ -+-+-+- 2 3 In(1+x) = x - Derive the Maclaurin expansion for…

A: It is known that, To derive the Macluarin expansion for as far as the term shown based on  given…

Q: dx x2 -25)2

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Q: Given f''(x) = 8x- 2 and f'(- 2) = – 2 and f(- 2) = 3. Find f'(x) = and find f(3)

A: Solution:

Q: The slope field above is drawn in the ty-plane. Add these two solutions to the slope field: • Sketch…

A: We are given the following slope field in the ty - plane. The sketch of the approximate solution…

Q: A street light is at the top of a 17 ft tall pole. A woman 6 ft tall walks away from the pole with a…

A: Given that A street light is at the top of a 17ft tall pole.  A woman 6ft tall walks away from the…

Q: You want to determine whether the gas mileage (in miles per gallon) and the speed that an automobile…

A: Introduction: It is required to identify the most appropriate test for the given research question.

Q: Let a 0, then for all partition P of [a, b], U(ƒ, P) – L(ƒ, P) = b − a > €. Therefore, if we

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Q: Evaluate the integral dx (5x + 11)" by making the appropriate substitution: u = dx (5x + 11)

A: To evaluate the given integral.

Q: 4. Determine whether or not the following functions are linearly independent in the vector space P4.…

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Q: The average time to run the 5K fun run is 22 minutes and the standard deviation is 2.3 minutes. 17…

A: Note- As per our policy we can answer only the first 3 sub-parts of a question. If you want…

Q: Which nodes are sources? (Enter list with only one space between nodes.) Which nodes are sinks?…

A: The graph given to us is as follows: We are asked to find the nodes which are the sources of the…

Q: These figures are congruent. What series of transformations moves quadrilateral ABCD onto…

A: Transformation moves quadrilateral ABCD onto A'B'C'D'  will be

Q: The altitude of a triangle is increasing at a rate of 1 centimeters/minute while the area of the…

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Q: This is the idea of a slope field graph: 1. Our goal is to sketch the unknown function y (t). 2. We…

A: Basic propoerties of the curve y(t). The curve y(t) touches the tangent at every point. It never…

Q: Find an equation for the tangent line to f(x) = xe²x at x = -1

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Q: A 20-ft by 30-ft swimming pool is filled with water. The depth is measured at 5-ft intervals,…

A: 0510152025300245678852457898102468101210152345687202222344

Q: 8. Is there any value(s) of the domain of x² + y² = 8 that passes the vertical line test? If so,…

A: Apply Vertical Line Test,

Q: Use a triple integral to find the volume of the given solid. The solid enclosed by the paraboloids y…

A: Consider y=x2+z2 and y=72-x2-z2      ..... (1) Find the point of intersection…

Q: luate the integral. /2 7 cos?(0) de

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Q: A manufacturer estimates that if each shipment of raw materials contains z units, the total cost in…

A: There is a mistake in the part (b) question.  It's not 8000/x. It's 80000/x which is the term in…

Q: Suppose that the amount of time that students spend studying in the library in one sitting is…

A: Note- As per our policy we can answer only the first 3 sub-parts of a question. If you want…

Q: Gravel is being dumped from a conveyor belt at a rate of 30 cubic feet per minute. It forms a pile…

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Q: 1. For page 8 of chapter 9 notes, what is the regression model? O y=30.81+3.540x Oy=a+bx O y…

A: The general simple linear regression equation is as follows. y^=a+bx y is the dependent variable. x…

Q: 2 (i) Show that the result 1+ 5+9 +... + (4n – 3) = n(2n – 1) is true %3D for the casen= 1. (ii)…

A: The given question mainly depends on the the sum of the sequence which is in the form of arithmetic…

Q: "Differentiate both sides of the equation V = Tr*with respect to t AP (using the chain rule on the…

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Q: Using Laplace transform solve the following partial differential equation au =2- U(0,1)=0, U(5,1)=0,…

A: The given partial differential equation is: with To find: The solution of given PDE using Laplace…

Q: III. Find the inverse of the following matrices: (Apply Gauss Elimination) 1.) (0.50 3.60) 3 -1 2.)…

A: To find the inverse of the matrices.

Q: 2) Use Lagrange multipliers to find all extreme values of f (x, y,z)= 2x+2y+z subject to x + y² +z²…

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Q: 1. Find the three cube roots of z =-j and sketch the result in a single Argand plane. (express…

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Q: As a log falls in a waterfall, its velocity is given by v(t) = -32t - 18 in feet per second. The…

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Q: Find the LCM (Least Common Multiple) for the numbers 12 and 16. Show all your work.

A: Find the LCM  Steps :  1 ) list the first several multiples of each number . 2 ) Look for multiples…