Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2648447

Let a be the radius of the circle. It implies; a² = 16²+b²-2*16bcos45 a² = 256+b²-16√(2)b --- (1). a² = 8²+b²-2*8bcos135 a² = 64+b²+8√(2)b --- (2). Equating (1) and (2) to get b. 256+b²-16√(2)b = 64+b²+8√(2)b 192 = 24√(2)b 8 = √(2)b b = 4√(2) units. b = 5.6568542495 units. Calculating a, radius of the circle. Recall. a² = 256+b²-16√(2)b at (1). And b = 4√(2) units. a² = 256+(4√(2))²-16√(2)*4√(2) a² = 256+32-128 a² = 288-128 a² = 160 a = √(160) a = 4√(10) u...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2648428

a² = (8√(3))²+(3√(3))²-2*8√(3)*3√(3)cos60 a = 7√(3) units. a = 12.124355653 units. a is AC. (7√(3)/sin60) = (8√(3)/sinb) b = 81.7867892983° c = 180-b c = 98.2132107017° c is angle ACB. d = 2c d = 196.4264214035° e = 360-d e = 163.5735785965° e is angle AOB where O is the centre of the circle. f = ½(e) f = 81.7867892983° sin81.7867892983 = (0.5*8√(3))/g g = 7 units. g is the radius of the circle. Therefore, diameter of the circle is; Let it be h. h = 2g...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2648412

x = 30° Please, move the above question left/right one time to review the solution. Thank you.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2648402

Let the single side length of the three side regular hexagon be 1 unit. Therefore; The width of the rectangle is; 2 units. The length/height of the rectangle is; 4 units. It implies; Area rectangle is; 4*2 = 8 square units. Calculating Area Purple. It is; Area rectangle with length 2 units and width 1.56698729811 units - Area triangle with height 1.56698729811 units and base (¼) units - Area triangle with height ¼(7) units and base 0.27919817891 units. = (...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2646699

Let the radius of the circle be a. b = (a-1) cm. c = (a-2) cm. It implies, observing Pythagoras rule to get a, radius of the circle. a² = b²+c² a² = (a-1)²+(a-2)² a² = a²-2a+1+a²-4a+4 0 = a²-6a²+5 Resolving the above quadratic equation via factorization approach to get a. It implies; a²-a-5a+5 = 0 a(a-1)-5(a-1) = 0 (a-1)(a-5) = 0 Therefore; a ≠ 1 cm. a = 5 cm. Recall. c = (a-2) And a = 5 cm. c = 5-2 c = 3 cm. Therefore; a² = c²+d² Where d is ha...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2646670

Let the three equal lengths of the quadrilateral be 1 unit each. Therefore; a² = 1²+1²-2cos100 a = 1.5320888862 units. a is BD. b = 60-½(180-100) b = 60-40 b = 20° b is angle ABD. c² = 1²+1.5320888862²-2*1.5320888862cos20 c = 0.6840402866 units. c is AD. Therefore, the required angle, angle BAD (?) is; Let it be e. (0.6840402866/sin20) = (1.5320888862/sind) d = 50° It implies; e = 180-d e = 130° Again, e is the required angle, angle BAD.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2646650

Calculating Area of the Circle. Let a be the radius of the circle. Calculating a. a² = 8²+6²-2*8*6(-cosb) a² = 100+96cosb --- (1). a² = 8²+16²-2*8*16cosb a² = 320-256cosb --- (2). Equating (1) and (2) to get b. 100+96cosb = 320-256cosb 352cosb = 220 b = acos(220/352) b = 51.3178125465° Recall. a² = 320-256cosb at (2). And b = 51.3178125465° It implies; a² = 320-256cos51.3178125465 a = 12.6491106407 units. Or Recall again. a² = 100+96cosb at (1) And...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2646614

Shaded Area is; Area sector with radius 1 unit and angle 2atan(½)° - Area triangle with two lengths 1 unit each and angle 2atan(½)°, the angle they form + Area sector with radius ½ units and angle 2atan(2)° - Area triangle with two lengths ½ units each and angle 2atan(2)°, the angle they form. = (2atan(½)π/360)-(½sin(2atan(½)))+(2atan(2)*0.25π/360)-(½*0.25sin(2atan(½))) = 0.063647609+0.17678717945 = 0.24043478845 square units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2646597

Area triangle ABC is; ½(3*(36/5)) = (54/5) square units. Calculating Area Yellow. The point coordinates are; ((54/23), (36/23)) (3, 2) ((3/2), (18/5)) Therefore Area Yellow is; = (39/46) square units. Therefore; Area Yellow ÷ Area Triangle ABC is; (39/46)÷(54/5) = 65/828

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2646585

Area Triangle Blue (S2) is; ½(12) = 6 square units. Area Triangle Yellow (S1) is; ½(1.4)sin(atan(4/3)) = (14/25) square units. Therefore; S1/S2 = (14/25)/6 = 7/75

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