Q5: A circular torus (i.e. a ring-doughnut shape) in which the overall diameter of the whole shape is ? = 2? and the diameter of the ring is ? = 2? has the total surface area ? = ?(?, ?) = 4?2?? and the volume ? = ?(?, ?) = 2?2??2. By manipulating these formulae into appropriate alternative forms, and then evaluating these with the given values (&? = 3.142), determine;a) ? (to 2 dec.pl.) when ? = 52.082m2 & ? = 0.319m,b) ? (in Sci.Not. to 3 sig.dig.) when ? = 1.26 × 108m3 & ? = 6.19 × 104m. l 48 LTE07:3623% OA 1-xythos.content.blackboardcdn.com C2 of 2Q1: Simplify the following expressions;a) 2(х + 1) — 3(2 — х)b) x(2у - 3) - Зу(1-х)c) 3x(x – 2) – 2(x – 1)(x +3)Q2: Simplify the following expressions, and determine any value(s) of the variable(s) for which theexpressions are not defined;2x-31a)3+2xx+12x+1c)x+13y-2y+1Q3: Factorise the following quadratics by means of the quadratic algorithm, and hence find their roots;a) x2 - 9x + 20b) x? - 14x + 24c) 2x? + 5x – 3Q4: Solve the following equations giving your answer in an exact form, and if this is not a rational numberalso to 3 dec.pl. accuracy;a) 2(x + 1) – 3(2 - x) = 0b) Зx(х — 2) - 2(х - 1)(х + 3) 303+2x 4xc)= 32x+1x+1Q5: A circular torus (i.e. a ring-doughnut shape) in which the overall diameter of the whole shape is D = 2Rand the diameter of the ring is d = 2r has the total surface area A = A(R,r) = 4n²Rr and the volumeV = V(R,r) = 2n²Rr². By manipulating these formulae into appropriate alternative forms, and thenevaluating these with the given values (& = 3.142), determine;a) R (to 2 dec.pl.) when A = 52.082m² & r = 0.319m,b) d (in Sci.Not. to 3 sig.dig.) when V = 1.26 x 10 m³ & D = 6.19 x 10*m.After marking, your marks and any comments will immediately be available to you in 'My Grades',and after all marking is complete a summary for the whole group of the results on this assignmentand the current overall totals will be published.

c) 2x+1 Q5: A circular torus (i.e. a ring-doughnut shape) in which the overall diameter of the whole shape is D = 2R and the diameter of the ring is d = 2r has the total surface area A = A(R,r) = 4n²Rr and the volume V = V(R,r) = 2n²Rr². By manipulating these formulae into appropriate alternative forms, and then evaluating these with the given values (&n = 3.142), determine; a) R (to 2 dec.pl.) when A = 52.082m? &r = 0.319m, b) d (in Sci.Not. to 3 sig.dig.) when V = 1.26 x 10"m & D = 6.19 x 10°m.

c) 2x+1 Q5: A circular torus (i.e. a ring-doughnut shape) in which the overall diameter of the whole shape is D = 2R and the diameter of the ring is d = 2r has the total surface area A = A(R,r) = 4n²Rr and the volume V = V(R,r) = 2n²Rr². By manipulating these formulae into appropriate alternative forms, and then evaluating these with the given values (&n = 3.142), determine; a) R (to 2 dec.pl.) when A = 52.082m? &r = 0.319m, b) d (in Sci.Not. to 3 sig.dig.) when V = 1.26 x 10"m & D = 6.19 x 10°m.

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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