Mathematics Question and Solution

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

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

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

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

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

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.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2200038

a = atan(⅓)° ⅓ = b/3 b = 1 unit. It implies; Area Red is; Area triangle with height 1 unit and base 3 units + ½(2(area quarter circle with radius 3 units - area triangle with height and base 3 units respectively))) = ½(1*3) + ½(2(¼(π*3²) - ½(3*3))) = ½(3) + ¼(9)π - ½(9) = ¼(9π) - ½(6) = ¼(9π-12) square units. = ¾(3π-4) square units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2199763

Let the regular pentagon side length be 1 unit. a =⅕(180(5-2)) a = ⅕(180*3) a = 108° a is an angle of the regular pentagon. Calculate x. b = 108-90 b = 18° x = ½(180-18) x = ½(162) x = 81° c = 108-60 c = 48° d = 180-18-48 d = 114° (e/sin48) = (1/sin114) e = 0.8134732862 units. f = 1-e f = 1-0.8134732862 f = 0.1865267138 units. (0.8134732862/sin48) = (g/sin18) g = 0.3382612127 units. sin30 = 0.25/h h = 0.5 units. j = 0.5-g j = 0.5-0.3382612127 j =...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2197378

Let DE be 1 unit. AC = 4 units. Area ABC is; 8sin60 = 4√(3) square units. a² = 1+2²-4cos45 a = 1.47362575821 units. (1.47362575821/sin45) = (1/sinb) b = 28.6750500631° c = 60-b c = 31.3249499369° d = 360--60-150 d = 150° e = 240-d e = 90° f² = 1²+1² f = √(2) units. g = 180-15-45-60 g = 60° h² = 4²+1.47362575821²-8*1.47362575821cos31.3249499369 h = 2.84622917461 units. (2.84622917461/sin31.3249499369) = (1.47362575821/sini) i = 15.61499741821° j = 60-i j = 44.38500258179° k = 120-j...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2197369

Area Aqua, in square units to 2 d. p. is; Area triangle with two side 5 unit and 6 unit, and angle acos(0.2)° - Area triangle with two side 5 unit and 3.9332754507 unit, and angle 14.2804126089° - Area triangle with two side 3.9332754507 unit and 4.44921801671 unit, and angle (2*14.2804126089)° - Area triangle with two side 7 unit and 4.44921801671 unit, and angle 14.2804126089° - Area triangle with two side 1.53404004392 unit and 1.98043718084 unit, and angle (0.5acos(0.2))° = (0.5*5*6sin(a...

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