Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2418135

Let x be 4 units. Calculating total blue length of arc. It implies; ½(circumference of a circle with radius 2 units + circumference of a circle with radius 1 unit + circumference of a circle with radius 0.5 units). = ½(2*2π+1*2π+0.5*2π) = ½(4π+2π+π) = ½(7π) units. Calculating green length of arc. It's radius is; ½((x/4)+(x/2)+x) And x is 4 units. ½(1+2+4) = ½(7) units. Therefore green length of arc is; ½(2π(½(7)) = ½(7π) units. It implies; Blue length of arc (½(7π)) = Green length of...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2417679

Sir Mike Ambrose is the author of the question. P coordinate is; P(3, 9) Q coordinate is; Q(2, 5), Q(3, 5) It implies; Shaded area exactly in its square units simplest form is; (Area under the curve at x = 2 and x = 3) - (Area trapezoid with parallel sides ⅓(23) units and 9 units, and height 1 unit). = (8+ln(81/16)) - ½((23/3)+9) = (8+ln(81/16))-½(50/3) = (8+ln(81/16))-⅓(25) = (ln(81/16)-⅓) square units. = 1.2885270991 square units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2417124

Sir Mike Ambrose is the author of the question. Calculating the circle's radius, r. The radius of the circle is; Area triangle with base 21 cm and height r cm + Area triangle with base 15 cm and height r cm + Area triangle with base 12√(2) cm and height r cm = Area triangle with base 21 cm and height 12√(2)sin45 cm ½(21r) + ½(15)r + ½(12√(2)r) = ½*21*12√(2)sin45 21r + 15r + 12√(2)r = 21*12√(2)sin45 (36+12√(2))r = 252r r = 252/(36+12√(2)) cm. r = 3(3-√(2)) cm. It implies; The exac...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2416872

3²+4²+2*3*4cosa = 5²+6²-2*5*6cosa 25+24cosa = 61-60cosa 84cosa = 36 cosa = (36/84) cosa = (3/7) a = acos(3/7) a = 64.6230664748° b = 2a b = 129.2461329497° c² = 5²+6²-2*5*6cos64.6230664748 c = 5.9401779675 units. Therefore, R, radius of the circle is; sin64.6230664748 = (0.5*5.9401779675)/R R = (0.5*5.9401779675)/(sin64.6230664748) R = 3.2872861147 units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2416776

Calculating the shaded area. a² = 4²+6²-2*4*6cos30 a = 3.2296719057 units. sin15 = b/6 b = 1.5529142706 units. c = 90-15 c = 75° Or cosc = 1.5529142706/6 c = acos(1.5529142706/6) c = 75° (3.2296719057/sin30) = (4/sind) d = 38.2619661994° e = c-d e = 75-38.2619661994 e = 36.7380338006° tan36.7380338006 = f/1.5529142706 f = 1.1591109915 units. Therefore, area shaded is; Area triangle with height 1.5529142706 units and base 3.2296719057sin36.7380338006 units - Area triangle with height...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2415939

2r² = 2² r = √(2) units. r is the radius of the circle. Area circle is; πr² = π√(2)² = 2π square units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2414073

Sir Mike Ambrose is the author of the question. Let the radius of the ascribed semicircle be 2 units. Therefore; Radius of the inscribed circle is 1 unit. It implies; Area R is; Area sector with radius 2 units and angle 45° - Area triangle with height and base √(2) unit each. = (45*2*2π÷360)-½(√(2))² = ½(π)-1 = ½(π-2) square unit. Area S is; Area triangle with height and base √(2) unit each - Area sector with radius 1 unit and angle 90° + Area triangle with height and base 1 unit respect...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2414015

Length DG is; cos15 = 0.5(12)/(DG) DG = 6/cos15 DG = 6.21165708246 cm.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2413845

x = 12.416666 - (1). 10x = 124.16666 - (2). 100x = 1241.6666 - (3). 1000x = 12416.6666 - (4). Subtracting (3) from (4). 900x = 11175 It implies x (p/q) is; x = 11175/900 x = 2235/180 x = 447/36 x = 149/12

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2413811

a² = 4²+2² a² = 20 a = √(20) a = 2√(5) units. tanb = 2/4 b = atan(½)° b is angle theta. c = 180-2b c = (180-2atan(½))° d = 360-90-c-b d = 360-90-(180-2atan(½))-atan(½) d = (90+atan(½))° e² = √(20)²+2²-2*2√(20)cos(90+atan(½)) e = 5.6568542495 units Calculating alpha. Let it be f. Observing sine rule. (5.6568542495/sin(90+atan(½))) = (√(20)/sinf) f = asin(0.7071067812) f = 45° Therefore, alpha is 45°

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