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Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3377220

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Sir Mike Ambrose is the author of the question. Calculating Total Area Red. Area Red Total in 1 decimal place square units is; Area Square with side 2√(2) units - Area triangle with height 2√(2) units and base 1.1313708499 units + Area triangle with two side √(13) units and 3.28571428572 units, 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 units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3376180

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Sir Mike Ambrose is the author of the question. Point P coordinate is; P(4, -3) Point R coordinate is; R(0, ⅓(37)) Point Q (maximum turning point) coordinate is; Q((-3√(259)/14), (4√(259)/7)) Therefore; Area green exactly in square unit decimal form is; Area triangle with height 14.2909320391 units and base (15.8464857653sin(atan(23/6)-atan((8√(259)+42)÷(3√(259)+56))) units. = 0.5*14.2909320391*15.8464857653sin(atan(23/6)-atan((8√(259)+42)÷(3√(259)+56)) = 32.7...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3375960

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Sir Mike Ambrose is the author of the question. Calculating Area Aqua. Area Aqua, in square units to 2 d. p. is; Area triangle with two side 5 units and 6 units, and angle acos(0.2)° - Area triangle with two side 5 units and 3.9332754507 units, and angle 14.2804126089° - Area triangle with two side 3.9332754507 units and 4.44921801671 units, and angle (2*14.2804126089)° - Area triangle with two side 7 units and 4.44921801671 units, and angle 14.2804126089° - Area triangle with two side 1.534...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3374843

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Calculating the chord length. Let x be the radius of the half circle. a = (x-4) units. b = (x-9) units. c = (x-7) units. d = a+b d = (x-4)+(x-9) d = (2x-13) units. d is the length of the chord. e = ½(d) units. e = ½(2x-13) units. f = x-4-½(2x-13) f = ½(2x-8-2x+13) f = ½(5) units. It implies; 7² = g²+(½(2x-13))² g² = 7²-¼(4x²-52x+169) g² = ¼(196-4x²+52x-169) g² = ¼(52x+27-4x²) g = ½√(52x+27-4x²) units. Calculating x. (½(5))²+(½√(52x+27-4x²))² = (x-7)²...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3373935

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Calculating FM ÷ ML. Let 2 units be the side length of square. Calculating FM. tana = 2/1 a = atan(2)° a is angle AFB. Let b, be the radius of the small inscribed circle. c = (1-b) units. Therefore; Calculating b. tan(½atan(2)) = b/(1-b) b = 0.6180339887(1-b) 1.6180339887b = 0.6180339887 b = 0.3819660112 units. Again, b is the small inscribed circle radius. It implies; c = 1-0.3819660112 c = 0.6180339888 units. c is FM. Calculating ML. Let d, be the...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3373683

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Calculating area of the square. Let x be the side length of the square. 7² = x²+3²-2*x*3cosy 49 = x²+9-6xcosy 6xcosy = x²-40 cosy = (x²-40)/(6x) --- (1). 5² = x²+3²-2*x*3cos(90-y) 25 = x²+9-6x(cos90cosy+sin90siny) 6xsiny = x²-16 siny = (x²-16)/(6x) --- (2). At (2). (x²-16) is opposite. (6x) is hypotenuse. Calculating Adjacent. Adjacent = √((6x)²-(x²-16)) = √(36x²-(x⁴-32x²+256)) Adjacent = √(68x²-x⁴-256) units  It implies; cosy = √(68x²-x⁴-256)/(6x) --- (3)....

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3372880

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Calculating Area Orange ÷ Area Large Square. Let length AB be 3 units. Therefore; AC = 20 unit. It implies; Area large square is; 20² = 40 square units. Area orange is; Area triangle with two side 17 units and 32.0319709782 units, and angle (180-atan(10/7))° + Area triangle with two side 20 units and 44.0408623507 units, and angle 53.4269678346° - Area square with side 20 units + Area triangle with height 3 units and base 4.2857142857 units. = (0.5*32.0319709782...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3372873

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Calculating Area Square ÷ Area Enclosed S Let the side of the square be 2 units. Therefore; Area square is; 2² = 4 square units. Area S is; Area triangle with two side 0.98921899145 units and 1.02554900641 units, and angle 14.318078177° - Area sector with radius 2 units and angle 28.6361563539° + Area triangle with two side 2 units each, and angle 28.6361563539° = (0.5*0.98921899145*1.02554900641sin14.318078177) - (28.6361563539*2²π÷360) + (0.5*2²sin28.6361563539) =...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3372019

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Calculating Area T ÷ Area (R+S) to 2 d. p.  Let the side of the inscribed square be 2 units. Therefore; Area S is; Area triangle with two side 1.03528 units and 0.53589838486 unit, and angle 45° = 0.5*1.03528*0.53589838486sin45 = 0.1961531464 square units. Area R is; Area triangle with two side (2√(2)-2) units and 0.65961372961 units, and angle 72.367664609° = 0.5*(2√(2)-2)*0.65961372961sin72.367664609 = 0.26038499708 square units. Area T is; Area sector with radius 2√(2) units and...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3372017

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Calculating Area Green Total. Area green total, in square unit decimal form is; Area triangle with height 6sin(atan(3/5)) unit and base 6cos(atan(3/5)) unit + Area triangle with height 4 unit and base 4tan(atan(2/5)) unit. = ½*6sin(atan(3/5))*6cos(atan(3/5)) + ½*4*4tan(atan(2/5)) = 7.94117647059 + 3.2 = 11.1411764706 square unit.
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