Mathematics Question and Solution

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

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

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

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

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

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

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.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3372005

Calculating the inscribed orange triangle area. Notice. a = ½(3) a = 1.5 units. a is the radius of the inscribed circle. tanb = 3/4 b = atan(3/4)° tan(atan(¾)) = c/1.5 ¾ = ⅓(2c) c = 9/8 units. d = (3/2)-(9/8) d = 3/8 units. e = (180-atan(4/3))° e = 126.869897646° (1.5/sin(180-atan(4/3))) = ((3/8)/sinf) f = 11.5369590328° g = 180-2f g = 156.926081934° h² = 2*1.5²-2*1.5²cos156.926081934 h = 2.93938769134 units. j = 180-(180-atan(4/3))-11.5369590328 j =...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3368641

Calculating k. k^(k) = 3^(k)*3⁹ k^(k) = 3^(k)*19683 (k/3)^(k) = 19683 It implies; k = 9 Checking Accuracy. (9/3)⁹ = 3⁹ = 19683

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3367656

Calculating x, the side length of the square ABCD. 3² = x²+4²-2*4xcosy 9 = x²+16-8xcosy 8xcosy = x²+7 cosy = (x²+7)/(8x) --- (1). 5² = x²+4²-2*x*4cos(90-y) 25 = x²+16-8xcos(90-y) 8x(cos90cosy-sin90siny) = x²-9 -8xsiny = x²-9 8xsiny = 9-x² siny = (9-x²)/(8x) --- (2). At (2). (9-x²) is opposite. (8x) is hypotenuse. Calculating adjacent. Let it be a. a²+(9-x²)² = (8x)² a² = 64x²-(81-18x²+x⁴) a² = 64x²-81+18x²-x⁴ a = √(82x²-81-x⁴) units. Again, a is adjacent. It...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3366743

Calculating Shaded Area. a²+10² = 12² a = √(144-100) a = √(44) a = 2√(10) units. b = 10-a b = (10-2√(10)) units. b = 3.67544467966 units. cosc = 10/12 c = acos(⅚)° d = 90-45-c d = (45-acos(⅚))° tan(45-acos(⅚)) = e/10 e = 2.02410864032 units. f = 10-e f = 10-2.02410864032 f = 7.97589135968 units. Therefore, shaded area is; ½*d*f = 0.5*3.67544467966*7.97589135968 = 14.6574737317 square units.

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