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Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2214642

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Notice; Red circle and black circle are congruent, they have equal radius, 1 cm. Calculating Area Shaded. a = 60-45 a = 15° It implies; Area Shaded is; Area sector with radius 1 cm and angle 60° - Area triangle with base 1 cm and height sin60° + Area sector with radius 1 cm and angle 15° = (60π/360) - ½(sin60) + (15π/360) = (π/6)-¼(√(3))+(π/24) = (4π-6√(3)+π)/24 = (5π-6√(3))/24 cm² = 0.2214857676 cm²

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2209645

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Let AB be x. Therefore BC = 2x. Calculating x. Yellow area + Area triangle with height 2x and base ½(3x)sin60 = Area trapezoid with two parallel side ½(3x) and 2x, and height ½(3√(3)x). Therefore; 30√(3)+¾*√(3)x² = (21√(3)x²)/8 30+¾x² = (21x²/8)  240+6x² = 21x² 15x² = 240 Therefore; x = 4 unit. Calculating Area Orange, exactly in square cm decimal form. It will be; Area trapezoid with two parallel side 4 unit and 6 unit, and height 6√(3) unit - Area triangle with height 6 unit and base 2...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2209118

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Area blue exactly in cm² decimal is; Area trapezoid with two parallel sides 12 unit and (12-16tan15) unit, and height 16 unit - Area triangle with height (12-16tan15) unit and base 4 unit - Area triangle with height and base 12 unit each - Area triangle with height 8√(2) unit and base (8-8tan15)sin45 unit. = ½*16(12+12-16tan15) - ½*4(12-16tan15) - ½(12²) - ½*8√(2)*(8-8tan15)sin45 = 157.702503369 - 15.4256258422 - 72 - 23.4256258422 = 46.8512516846 cm²

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2207657

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Notice; cos2x = 1-2(sinx)² --- (1). Substituting (1) in the given equation. ½(3-6(sinx)²+3)+4sinx+1 = 0 3-6(sinx)²+3+8sinx+2 = 0 6(sinx)²-8sinx-8 = 0 Calculating sinx. Let sinx be p. 6p²-8p-8 = 0 6p²-12p+4p-8 = 0 6p(p-2)+4(p-2) = 0 Therefore; p ≠ 2 p = -⅔ And p = sinx sinx = -⅔ Therefore; cosx = ⅓(√(5))  It implies; The exact value of Tanx is; tanx = sinx/cosx tanx = (-⅔)/(⅓(√(5)) tanx = (-2/√(5)) tanx = l-2/√(5)l tanx =  (2/√(5))

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2205999

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sinxcos60+sin60cosx-(cosxcos45+sinxsin45) = 0 0.5sinx+½(√(3)cosx)-½(√(2)cosx)-½(√(2)sinx) = 0 0.5sinx-½(√(2)sinx) = ½(√(2)cosx)-½(√(3)cosx) sinx(1-√(2)) = cosx(√(2)-√(3)) sinx = ((√(2)-√(3))cosx)/(1-√(2)) sinx = ((√(2)+2-√(3)-√(6))cosx)/-1 sinx = -(√(2)+2-√(3)-√(6))cosx sinx = (√(3)+√(6)-√(2)-2)cosx (sinx/cosx) = (√(3)+√(6)-√(2)-2) tanx = (√(3)+√(6)-√(2)-2) x = atan(√(3)+√(6)-√(2)-2)) x = 37.5° It implies; sinx = (√(3)+√(6)-√(2)-2)cos(37.5) sinx = (√(3...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2205354

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Sir Mike Ambrose is the author of the question. Let the side length of the regular pentagon be 2 unit. Therefore the angle theta is; asin(2sin42÷1.65418183057) = 54° Area green is; Area triangle with height (1/cos54) unit and base 2.45859333557sin12 unit - Area triangle with height 2cos54 unit and base 2cos54*tan12 unit = (0.5*2.45859333557sin12*(1/cos54)) - (0.5*2cos54*2cos54*tan12) = 0.43482742672 - 0.14687297185 = 0.28795445487 space unit. Area yellow is; Area triangle...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2203991

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Calculating yA. Notice; xA = 4 And y = (16+e^(0.5x))/4 y = ¼(16+e²) Where y is yA. Therefore; Shaded Area as a single fraction is; Area Rectangle with width 4 units and length ¼(16+e²) units - Area under the curve at x = 0 and x = 4 = (4*¼(16+e²))-((16+0.5e²)-½) = (16+e²)-16-½(e²)+½ = e²-½(e²)+½ = ½(2e²-e²+1) = ½(e²+1) square units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2203282

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Sir Mike Ambrose is the author of the question. Let the two equal lengths be 1 unit. (a) Calculating Theta exactly. Let theta be x. Calculating x. x = ½(90-54) x = ½(36) x = 18° sin18 = a/1 a = 0.30901699437 unit. b = 90-18 b = 72° sin72 = c/1 c = 0.9510565163 unit. tan36 = 0.9510565163/d d = 1.30901699437 units. Area Blue is; 0.5(1.30901699437*0.9510565163) = 0.62247457122 square units. e = 270-54-96 e = 120° f = 360-120-72 f = 168° g² = 2-2cos168 g = 1.98904379074 units. h = ½(180-...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2203078

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Let the single side length of the regular dodecagon be be 1 unit. Therefore; Area purple is; Area triangle with height √(3) unit and base 1 unit. = ½*√(3)*1 = ½√(3) square unit. Area ABCD (square) is; Area square with side (1+√(3)) unit. = (1+√(3))² = 1+2√(3)+3 = 2(2+√(3)) square unit. It implies; Area Purple ÷ Area ABCD (square) in its simplest form is; ½√(3) ÷ 2(2+√(3)) = √(3) ÷ (8+4√(3)) = ¼(2√(3)-3)

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2202081

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Area Red Total in 1 d. p. Square unit is; Area Square with side 2√(2) unit - Area triangle with height 2√(2) unit and base 1.1313708499 unit + Area triangle with two side √(13) unit and 3.28571428572 unit, and angle atan(3/2)° = (2√(2))² - 0.5*2√(2)*1.1313708499 + 0.5*√(13)*3.28571428572sin(atan(3/2)) = 8 - 1.6 + 4.92857142858 = 11.3285714286 ≈ 11.3 square unit.
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