A student attempts to find the shortest distance between A and B as shown below. There are two lines where the working does not follow on from the previous line.

Q: Consider the polar curve r= 2 sin(0) + 3 ,0ses27, whose plot is shown below. 2.0 1.5 1.0 0.5…

A: Given that: r=2sinθ+3, 0≤θ≤2π

Q: (iv) Let be an odd prime number and let r be the rational number 1 1 r = 1+ 2 1 + 3 Prove that p…

A:

Q: (i) Use Euclid's algorithm to find a multiplicative inverse of 23 modulo 75, and hence solve the…

A: This is a problem of Number theory, counting, and modular arithmatic.

Q: -1 4 07 A = -5 0 -6 4 5

A:

Q: 2 Let L be the line in R3 that consists of all scalar multiples of the vector -2. Find the…

A: The solution is given as

Q: sin x – e-* = 0, [0,1]

A: Let,f(x) = sin(x) - e-xso, f(0) =-1<0 and f(1) = 0.47 > 0 ⇒there is root between 0 and 1In…

Q: minimize f1(x) = 5x1 – x2, f2(x) = x1 + 4.x2]| subject to -51+ 2x2 3 Xi + 2x2 > 4 X1, X2 > 0…

A:

Q: The slope of the surface z = ry in the r-direction at the point (2,3) is slope of this surface in…

A: The slope of the surface z=f(x, y) at x0, y0 in the x-direction is fxx0, y0. The slope of the…

Q: 24. The following data resulted from a stress-strain experiment where a given strain was applied and…

A: Sol

Q: Williams Custom Sportswear 9000 8000 7000 E 6000 5000 4000 3000 2000 +2000 1000 +2001 January…

A: Red graph (2001) graph is below blue graph(2000) graph just 2 times and after that its always above…

Q: Q4) Find plane area inside the polar function r= 2 and outside the polar function r= sin -e) +1 in…

A:

Q: dxdy

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Q: Final the complement afthe graphs in fig-1-34 figti3t

A: The complement of the following graphs can be found by adding the edges between every two vertices…

Q: Cometer e dar te, )aten the faur dete ta t hen1,).1-1,8(0.1), (-1) he yar,( the r uher trta(2, , aan…

A: Sol

Q: 8. Find the root of cos(x)-xe¬* using the Newton-Raphson method.(Use radians in solving)

A: Newton-Raphson method uses the formula: xn+1=xn-f(xn)f'(xn) to perform the iterations and to…

Q: 4. I, Let L: V W be a linear transformation from the vector space V to the vector space W such that…

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Q: Consider the quadratic function f: R3 →R defined by f(X) = xỉ – x1x2 + x – x2x3 + x3 + 1 A: Express…

A:

Q: Bossing bought two bags, one for P700,000 and the other for P300,000. He sold the first at a gain of…

A: Given that Bossing bought two bags, one for P700,000 and the other for P300,000. He sold the first…

Q: 2. The slope of the surface z = ry in the r-direction at the point (2,3) is slope of this surface in…

A: We have to find the slope of the surface in the x and y direction at (2, 3).

Q: In three dimensions the equation 22 +y? = 1 represents a |. Similarly, the equation y? + 22 = 1…

A: The blanks in the given paragraph are filled as shown below.

Q: Factor these two matrices into A = XAX-1: [1 2] A = X = A = [1 1] A 3 3 X = A = (Note that you must…

A:

Q: Describe the set S ={ x: |(1/2)x-3| > 4 }

A: Given set is S = { x: |(1/2)x-3| > 4 }

Q: Q2: Employ fixed-point iteration to locate the root of S(x) = sin ( vx)-0.5 x Use an initial guess…

A: Ans: x= 0.525

Q: The Fibonacci numbers are defined by Fo = 0, F = 1, Fx = Fx + Fk=1 for k = 1,2, .... Relations such…

A:

Q: A radio transmission tower is 424 feet tall. A guy wire is to be attached 6 feet from the top and is…

A:

Q: A cubical box has one of its edge equal to 4cm. Pass a plane to the cube so that the section form…

A:

Q: 3. Let f(r, y) = Isin ry. Find: (a) fa(1,9) (b) fy(1, y) (c) fyy(I, y) (d) fyz(I, y)

A: To find  Partial derivatives of the given function.

Q: A company has 30,000 employees in three cities as shown in the table below. It wishes to give…

A:

Q: Aayush and Abbey have the following system of differential equations da dt -5 x + 12 y dy = -2 x + 5…

A:

Q: Write at least 5-10 sentences essay/discussion on what you can observe on the values in table and…

A: This graph denotes the position of an object at certain time interval and the distance of the object…

Q: a) Find the matrix A. Hint: A = PDP!, Note: you don't need to know A for the rest of this problem.…

A: Disclaimer: Since you have posted a question with multiple sub-parts, we will solve the first three…

Q: (a) Let m be a positive constant. Calculate the Fourier Transform Ü(§) of e-m|x| U(x) x E R³. |x|…

A: Sol

Q: Let -2 -3 3 4 2 and let W the subspace of R4 spanned by i and v. Find a basis of W+, the orthogonal…

A:

Q: 2. Let X = R² – (0,0) and ~ be defined over X by setting x~y + y = tx for some non-zero t € R. Given…

A: Sol

Q: Let X be the graph of f(x) = r²/3 given below that is, X is the subset of R x R satisfying the given…

A: Sol

Q: The relative error in reading a galvanometer is given by tanx + cotx, where x is the angular…

A:

Q: 3. All vertical parabolas. Ans: y" = 0

A:

Q: find y(t) 2.) y" + 7y' +12y = 16e^2t + t ; y(0)=6, y'(0) = 4

A:

Q: Use disk's (washer's) method to set up the integral finds the volume of the solid obtained by…

A: This is a problem of the volume of rotation.

Q: 3. Integration by parts a.J 18x ( x+ 4)»

A: Given integral is ∫18x(x+4)dx

Q: Prove by contradiction that if a sum of three real numbers is less than 30, th at least one of the…

A: We have to prove by contradiction that if a sum of three real number is less than 30, then at least…

Q: Compute dS where F = (x, Y, z) and S is the surface of the cone z2 = x² + y² for 0 < z < 4 plus its…

A:

Q: sin x – e-* = 0, [0,1]

A: To do the calculations in Excel, first enter the numbers in separate cells. Each number is…

Q: If y is the solution to the initial value problem 9x? y(0) = 1 2y then y(2) =

A:

Q: Let B = as a subset of R. (a) Show B is a basis for R. (b) Find the change of coordinates matrix P.…

A:

Q: Using the following election preference table for candidates: A B, C, D, does any candidate win by a…

A: Please find the answer in next step

Q: Fin o all SoinEl ons 6 x EIO mod

A: For x in {0, 1, 2, . . . . . 43}, value of 6x ranges from 0 to 6x43 = 258. Now 6x = 10 (mod 44)…

Q: hw.2 Evatuate the fotawing cartesian integrats by changing theminte equivalent Pala integrals: dy dx

A:

Q: Consider the ceiling function [æ] = min{z € Z\z > a}. This basically rounds up any real number. For…

A: To show that  limx→2x does not exist.

Q: Let f(x) = 1-1 if 0 < x < 1 if 1<a < 3 %3D for 0<x < 3. At x = 4, the Fourier cosine series for f…

A: