Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2823616

Calculating the area of the red rectangle. Let a be the radius of the half circle. b = ½(a) units. Calculating a. a² = (½(a))²+1² a² = ¼(a²)+1 (3/4)a² = 1 a² = 4/3 a = √(4/3) a = ⅓(2√(3)) units. a = 1.1547005384 units. Again, a is the radius of the half circle and also the width of the red rectangle. Notice! b = ½(a) b = ½(1.1547005384) b = 0.5773502692 units. c = a+b c = 1.7320508076 units. c = √(3) units. c is the length of the red rectangle. Therefore, a...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2822228

Calculating red area. a = (1+x) units. a is the diameter of the circle. b = ½(a) b = ½(1+x) units. b is the radius of the circle. c = ½(1-x) units. Calculating x. (½(1+x))² = (½(1-x))²+(½(1-x))² ¼(1+2x+x²) = ¼(1-2x+x²)+¼(1-2x+x²) 1+2x+x² = 1-2x+x²+1-2x+x² 1+2x+x² = 2-4x+2x² x²-6x+1 = 0 (x-3)² = -1+(-3)² (x-3)² = 8 x = 3±√(8) It implies; x ≠ 3+√(8) units. x = 3-√(8) units. x = 0.1715728753 units. Recall. b = ½(1+x) units. And x = 0.1715728753 units. b = ½(...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2822218

Calculating x, the side length of the ascribed square. tana = 14/7 a = atan(2)° b = 90+a b = (90+atan(2))° c² = 14²+7² c² = 196+49 c = √(245) units. c = 7√(5) units. d² = √(245)²+9²-2*9*7√(5)cos(90+atan(2)) d = 24.0416305603 units. d is the diagonal of the square. Therefore, x is; d² = 2x² 24.0416305603² = 2x² x² = 289 x = √(289) x = 17 units. Again, x is the side length of the ascribed square.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2820591

a = 8+2 a = 10 units. a is OA, the radius of the half circle. b = 2a b = 20 units. b is AB, the diameter of the half circle. c = 2+a c = 12 units. c is BC. Notice. BC = BD = 12 units. d²+12² = 20² d² = 400-144 d = √(256) d = 16 units. d is AD. tane = 16/12 e = atan(4/3)° e is angle ABD. f = ½(e) f = ½(atan(4/3))° f is angle ABF Therefore, the required length, BF is; Let it be g. cos(½(atan(4/3))) = g/20 g = 20cos(½(atan(4/3))) g = 17.88854382 uni...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2820581

Calculating x. Let a be the radius of the ascribed quarter circle. b = 4+4 b = 8 units. Notice. BD = 4 units. OB = x+BD OB = (x+4) units. OB is the radius of the ascribed quarter circle. It implies; (x+4)² = x²+8² x²+8x+16 = x²+64 8x = 48 x = 6 units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2818760

Calculating Green Area. a = 2*4 a = 8 units. a is the radius of the ascribed quarter circle. b²+4² = 8² b² = 64-16 b = √(48) b = 4√(3) units. tanc = 4√(3)/4 c = atan(√(3))° c = 60° Therefore, green area is; Area sector with radius 8 units and angle 60° - Area triangle with height 4√(3) units and base 4 units - Area quarter circle with radius 4 units. = (60π*8*8/360)-(½*4√(3)*4)-(¼*4*4π) = ⅓(32π)-8√(3)-4π = ⅓(32π-12π-24√(3)) = ⅓(20π-24√(3)) square units. = 7.087544...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2818754

Inscribed semi circle radius is 4 cm. Inscribed quarter circle radius is 8 cm. tana = 4/8 a = atan(½)° b = 2a b = 2atan(½)° c = 180-b c = 2atan(2)° Blue Area is; Area sector with radius 4 cm and angle 2atan(2)° - Area triangle with height 4 cm and base 4sin(2atan(2)) cm + Area sector with radius 8 cm and angle 2atan(½)° - Area triangle with height 8 cm and base 8sin(2atan(½)) cm - 2(area area quarter circle with radius 4 cm) + 2(area triangle with height and base 4 cm res...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2817281

2^(x+1)+2^(x-1) = 320 Let 2^(x) be p. It implies; 2p+½(p) = 320 ½(5p) = 320 5p = 640 p = 128 And p = 2^(x) Calculating x. 2^(x) = 128 2^(x) = 2⁷ x = 7

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2817269

Let b be 1 unit. a = 50° b = 40° a and b are the two interior complementary angles or acute angles of the small right-angled triangle with hypotenuse b. sin50 = c/b c = sin50 c = 0.7660444431 units. d = 90+40 d = 130° e = 180-b-d e = 180-170 e = 10° It implies; Calculating r. (0.7660444431/sin10) = (f/sin130) where f is (b+r). f = 3.3793852416 units. Again, f is (b+r). Therefore; b+r = 3.3793852416 And b = 1 unit. 1+r = 3.3793852416 r = 3.3793852416-1...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2815684

Calculating angle x. Let 1 be the base of the ascribed isosceles triangle. a = 180-39-2(27) a = 141-54 a = 87° (1/sin87) = (b/sin(2*27)) b = 0.8101272456 units. c = 180-27-15-39 c = 180-81 c = 99° (1/sin99) = (d/sin27) d = 0.4596495484 units. e² = 0.4596495484²+0.8101272456²-2*0.4596495484*0.8101272456cos15 e = 0.3849822481 units. It implies, the required angle x is; (0.3849822481/sin15) = (0.4596495484/sinx) x = 18°

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