Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3292074

Calculating r, radius of a circle. a = (r-2) cm. b = (r-1) cm. It implies; r² = (r-2)²+(r-1)² r² = r²-4r+4+r²-2r+1 r²-6r+5 = 0 r²-r-5r+5 = 0 r(r-1)-5(r-1) = 0 (r-1)(r-5) = 0 It implies; r ≠ 1 cm. r = 5 cm. Again, r is the radius of the circle. The square side length is; 2r-2 = 2*5-2 = 10-2 = 8 cm.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3291289

Calculating Area Red. tana = 12/6 a = atan(2)° b = 90-a b = atan(½)° c = 180-2a c = 2atan(½)° Red area is; Area square with side 12 cm - Are ma quarter circle with radius 12 cm - 2(area triangle with height 6 cm and base 12 cm) + Area sector with radius 12 cm and angle 2atan(½)° - Area sector with radius 6 cm and answer 2atan(½)° = 12²-¼(12²π)-2(½*6*12)+(2atan(½)π*12²/360)-(2atan(½)π*12²/360) = 144-113.097335529-72+66.7652556961-16.691313924 = 8.9766062431 square un...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3290916

Calculating the yellow shaded area. a² = 2²+4² a = √(20) a = 2√(5) cm. tanb = 2/4 b = atan(½)° tanc = 4/2 c = atan(2)° It was; d = 180-b-c d = 90° Shaded yellow area is; ¼(2√(5))²π-½(2√(5))² = ¼(20π)-½(20) = 5π-10 = 5(π-2) cm²

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3290493

Calculating x. a² = 24²+x² a = √(x²+576) units. a is the diameter of the ascribed circle. b = ½(a) b = ½√(x²+576) units. b is the radius of the circle. c = (x-11) units. d = ½√(x²+576)-7+½√(x²+576) d = (√(x²+576)-7) units. Calculating x. 7*(√(x²+576)-7) = 11*(x-11) 7√(x²+576)-49 = 11x-121 7√(x²+576) = 11x-72 49(x²+576) = 121x²-1584x+5184 49x²+28224 = 121x²-1584x+5184 72x²-1584x-23040 = 0 9x²-198x-2880 = 0 x²-22x-320 = 0 (x-11)² = 320+(11)² (x-...

Mathematics Question and Solution

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

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

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

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

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

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

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.

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