北美数学代考

COMP0011 – Mathematics & Statistics Alternative Assessment – 2019/20 cohort

北美数学代考 This Assessment has a Mathematics part and a Statistics part. Thetwo parts will be equally weighted in determining your ···

This Assessment has a Mathematics part and a Statistics part. Thetwo parts will be equally weighted in determining your overall mark.
Please upload your answers to the Maths part (section A) and theStats part (section B) in separate pdfs.
Forboth parts, clear handwritten answers are preferred, but type written answers are permitted if you have a SoRA.
This task (parts A and B together) is expected to take one working day to complete.

Section A – Mathematics

Themathematics section has two
Part I has short exam paper like questions that a well-prepared student,consulting their notes, should expect to score 80-90% of the available marks.
PartII has a longer, more challenging question, that a well-prepared student should expect to make some progress with, but may struggle to complete perfectly.
PartI has 54 marks and Part II has 46 marks, for a total of 100
For both parts working should be included and will be considered when marking.

Part I 北美数学代考

1.a)Using polar coordinates, a scalar-valued function of the plane can be written coordinates. r ² cosq . Express the same function using Cartesian

[1 mark]

b）Wheredo the diagonals of the convex quadrilateral with vertices at (0, 0), (2, 0), (0,1), (1, 2) intersect? [2 marks]

2.a)Give an equation for the line that intersects perpendicularly on the x-axis.

b）Forwhat x is ( x + 1)-1 ( x – 7)2 ³ 0 ?y = 2x + 3

3.a)What is the 4^th order Taylor series for tan x ?

b）What is the arc length of one turn of the helix

4.a)What are the roots of x⁴ – 2x³ – x² + 2x = 0 ?

b）H0 , H1, H2 ,are a family of polynomials in x satisfying

8.a) If hard drive capacity doubles every five years, and the rate of reading data from a disc doubles every three years, then how long from now will it be 1024 times quicker to read an entire disc?

b）For an equilateral triangle, what is the ratio of the areas of its circum-circle(passes through vertices) and inscribed-circle (tangent to sides)?

12.a)Give a function whose 2^nd order Taylor series at x = 1 is 10 – 7 ( x -1) + 4 ( x -1)2 + o (( x -1)3 ) .

13a)If polynomial p has degree n, what is the degree of p² ?

b)Definespan, linear independence, basis and dimensionality in the context of vector spaces.

14a) Where and what is the critical point of z = 3x² – xy – 2 y² + x + 2 y ?

b) (x,y, z ) = (sin t, cos t, t + 1) describes a helical space curve parameterized by t . What is the length of the curve for each unit increase in t ?

18a)What are the complex-valued roots of x³ + x² + x + 1 = 0 ?

b）Give real-valued A,B that satisfy (cosq + i sinq )n = for all A + iB q Î .

Part II 北美数学代考

Imagine an infinite sequence of computations; each, after the first, taking the previous computation’s output as input.
Assumethat with current hardware, if the input was ready now, each and every computation would take t years to perform.
Assume that computing speed increases geometrically, doubling every 2 years, and this continues indefinitely; and assume that the fastest hardware, currently available, is used for each computation.
Assume that each computation can be started, without delay, after the previous even if there is a change of hardware.

What is the largest value of t such that each and every computation in the sequence will be completed soonest if there is no delay before starting the computations, and no delays between them?[40 marks]

[ DIFFICULT ] Assuming the value of t above, will the infinite sequence of computations finish in finite time?[6 marks]

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