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Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3289995

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Calculating angle x. Let the top horizontal length of the ascribed quadrilateral be 1 unit. a = 180-50-60-20 a = 50° b = 180-60-50-10 b = 60° It implies; x = ½(180-20) x = ½(160) x = 80°

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3289255

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Calculating r, radius of the circle. a = (10-r) units. It implies; r² = (10-r)²+5² r² = 100-20r+r²+25 20r = 125 2r = 12.5 r = 6.25 units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3288180

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Calculating blue area (area triangle BDE). a = ½(32+7) a = ½(39) a = 19.5 units. a is the radius of the ascribed half circle. b = 19.5-7 b = 12.5 units. 12.5² = 17²+19.5²-2*17*19.5cosc 663cosc = 17²+19.5²-12.5² c = acos(17²+19.5²-12.5²/(663)) c = 39.3076481161° (12.5/sin39.3076481161) = (19.5/sind) d = 81.2025892909° f² = 17²+(2*19.5)²-2*17*2*19.5cos39.3076481161 f = 28 units. It implies; 7*32 = g*28 g = 8 units. h²+8² = 17² h = 15 units. Therefore, blue...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3287310

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Sir Mike Ambrose is the author of the question. Calculating Area Lilac ÷ Area Large Square. Let the radius of the semi circle be 1 unit. Therefore; Area lilac is; Area triangle with height 0.26794919243 units and base 1 unit = ½(0.26794919243) = 0.13397459622 square units. Area large square is; Area square with side length 1 unit = 1² = 1 square units. Area Lilac ÷ Area Large Square in its simplest decimal form is; 0.13397459622 ÷ 1 = 0.13397459622

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3286161

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Sir Mike Ambrose is the author of the question. Calculating Area Blue ÷ Area Green in its simplest form. Let the single side length of the regular octagon be 2 units. Therefore;  Area green is; Area triangle with height and base √(2) units + Area triangle with height 2√(2) units and base 1 unit - Area triangle with height √(2) units and base ½ units. = ½(√(2))² + ½(2√(2)) - ½(½*√(2)) = 1 + √(2) - ¼√(2) = ¼(4+4√(2)-√(2)) = ¼(4+3√(2)) square units. Area blue is; A...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3285246

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Calculating r, radius of the circle. a = (r-4) units. b = a+r b = (2r-4) units. 8c = 4(2r-4) c = (r-2) units. d = 8+c d = (6+r) units. e² = 2r²+2r²cos120 e² = 3r² e = √(3)r units. It implies; Calculating r, radius of the circle. e² = (6+r)²+11²-22(6+r)cos60 3r² = 36+12r+r²+121-66-11r 2r² = r+91 2r²-r-91 = 0 2r²-14r+13r-91 = 0 2r(r-7)+13(r-7) = 0 (2r+13)(r-7) = 0 It implies; r ≠ -6.5 units. r = 7 units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3284371

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Calculating r, radius of the half circle. Let x be the diameter of the half circle. x² = 16²+a² a = √(x²-256) units. b = a-21 b = (√(x²-256)-21) units. c = (x-7) units. Calculating x. 7(x-7) = 21(√(x²-256)-21) 7x-49 = 21√(x²-256)-441 7x+392 = 21√(x²-256) (7x+392)² = 44x²-112896 49x²+5488x+153664 = 441x²-112896 392x²-5488x-266560 = 0 It implies; x ≠ -20 units. x = 34 units. Again, x is the diameter of the half circle. Therefore r, radius of the half circle...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3283403

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Calculating r, radius of the half circle. a²+9² = 23² a = 8√(7) units. a = 21.1660104885 units. tanb = 8√(7)/8 b = atan(8√(7)/9)° c = (r-5) units. (r-5)² = d²+(½*8√(7))² r²-10r+25 = d²+112 d = √(r²-10r-87) units. e = (9+√(r²-10r-87)) units. Calculating r. (½*8√(7))²+(9+√(r²-10r-87))² = r² 112 +81+18√(r²-10r-87)+r²-10r-87 = r² 106+18√(r²-10r-87)-10r = 0 18√(r²-10r-87) = 10r-106 324(r²-10r-87) = 100r²-2120r+11236 324r²-3240r-28188 = 100r²-2120r+11236...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3282638

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Calculating r, radius of the half circle. a²+14² = (2r)² a = √(4r²-196) units. b = (r-2) units. √(4r²-196)² = 2²+7²-28cosx 4r²-196 = 53+28cosx 28cosx = 4r²-249 cosx = (4r²-249)/28 --- (1). r² = 7²+(r-2)²-14(r-2)cosx 4r-53 = (28-14r)cosx cosx = (4r-53)/(28-14r) --- (2). Calculating r. Equating (1) and (2). (4r²-249)/28 = (4r-53)/(28-14r) 28(4r-53) = (28-14r)(4r²-249) 112r-1484 = 112r²-6972-56r³+3486r 56r³-112r²-3374r+5488 = 0 8r³-16r²-482r+784 =...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3282397

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