Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2380510

Calculating area green. tana = 4/8 a = atan(½)° b = 2a b = 2atan(½)° tanc = 8/4 c = atan(2)° d = 2c d = 2atan(2)° It implies, area green is, 2(area sector with radius 4 units and angle 2atan(2)° - area triangle with height 4 units and base 4sin(2atan(2)) units + area sector with radius 8 units and angle 2atan(½)° - area triangle with height 8 units and base 8sin(2atan(½)) units) - 2(area quarter circle with radius 4 units - area triangle with height and base 4 units respectively). 2((2a...

Mathematics Question and Solution

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Calculating yellow area. It is; 2(area quarter circle with radius 4 units - area triangle with base and height 4 units respectively - area quarter circle with radius 3 units + area triangle with base and height 3 units respectively). = 2(¼(4*4)π-½(4*4)-¼(3*3)π+½(3*3)) = 2(4π-8-¼(9π)+½(9)) = 2(¼(7π)-½(7)) = 2(¼(7π-14)) = ½(7π-14) square units.

Mathematics Question and Solution

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Notice. The ascribed plane shape is a regular pentagon with side length 10 units. Let a be the radius of the bigger inscribed circle. Radius of the smaller pink inscribed circle is r. c = ⅕(180(5-2)) c =108° c is the single interior angle of the ascribed regular pentagon. d² = 10²+10²-2*10*10cos108 d = 16.1803398875 units. Calculating a, radius of the bigger inscribed circle. tan(0.5*108) = a/(0.5*10) a = 5tan(54) a = 6.8819096024 units. d² = e²+5² 16.1803398875² = e²+25 e = √(16.1803398...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2380168

Let BD = a Notice! BC = CD = BD = a AC = 15 cm. Half BD = ½(a) cm. It implies; sin60 = b/a ½√(3) = b/a b = ½√(3)a cm. Therefore; ½(a)+b = AC ½(a)+½√(3)a = 15 a+√(3)a = 30 a(1+√(3)) = 30 a = 10.9807621135 cm. ½(a) is; ½(10.9807621135) = 5.4903810568 cm. It implies; Area of the kite is; ½(AC)*(BD) = ½*10.9807621135*15 = 82.3557158513 cm² Therefore, half the area of the kite is; ½(82.3557158513) = 41.1778579256 cm² Calculating radius, r of the inscribed orange circle using half the kite...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2379897

Let AC be 1 unit. a = 180-12-15 a = 153° a is angle ADC. Observing Sine Rule. (1/sin153) = (b/sin12) b = 0.4579648493 units. b is CD. c = 180-12-18-15-33 c = 180-78 c = 102° c is angle ABC (angle x + angle y). d = 18+12 d = 30° d is angle BAC. Observing Sine Rule. (1/sin102) = (e/sin30) e = 0.5111702974 units. e is BC. Observing Cosine Rule. f² = 0.5111702974²+0.4579648493²-2*0.5111702974*0.4579648493cos33 f = 0.2799368207 units. f is BD. Therefore, Calcul...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2379840

Observing similar plane shape side lengths ratio. 3 - 5 a - (4-a) Cross Multiply. 3(4-a) = 5a 12-3a = 5a 8a = 12 a = 3/2 units. a is the base of the right-angled triangle with height 3 units. b = 4-a b = 4-(3/2) b = 5/2 units. b is the base of the right-angled triangle with height 5 units. c² = 3²+(3/2)² c² = 9+(9/4) c² = ¼(45) c = ½√(45) units. d² = 5²+(5/2)² d² = 25+(25/4) d² = ¼(125) d = ½√(125) units. e = c+d e = ½√(45)+½√(125) e = (3/2)√(5)+(5/2)√(5) e =...

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Online Edumath Educators and Learners are Super Smart and Amazingly, Very Clever. Communicate us to mentor/teach/educate your child/children Mathematics online at affordable tuition, helping them become a lover of Mathematics, and also, a Mathematician. Call/WhatsApp: +2349076614992 or +2348152827445 Email: [email protected] [email protected] [email protected] Facebook Page: Online Edumath We are super smart and amazingly, very clever!

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2379145

Area green is; (Area triangle with height 4 units and base 8√(3) units - Area sector with radius 8 units and angle 30°) + (Area sector with radius 8 units and angle 60° - Area triangle with height 8 units and base (8sin60) unit. = (½*4*8√(3)) - (30*8*8π÷360) + (60*8*8π÷360) - (½*8*8sin60) = 16√(3) - ⅓(16π) + ⅓(32π) - 16√(3) = ⅓(32π) - ⅓(16π) = ⅓(16π) square units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2379124

Let x³ be a. Therefore; a²-a-2 = 0 Resolving the above quadratic equation via completing the square approach. (a-(1/2))² = 2+(1/2)² (a-(1/2))² = (9/4) a-(1/2) = ±(3/2) a = ½±(3/2) It implies; a = -1 Or a = 2 And a = x³ Therefore; x³ = -1 x = -1 Or x³ = 2 x = crt(2) x = 1.25992104989

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2377574

a = ¼(7*7)π-½(7*7) a = ¼(49π)-½(49) a = ¼(49π-98) square units. b = 2a b = 2*¼(49π-98) b = ½(49π-98) square units. It implies; Area of red region is; Half area square with side 14 units - b = ½(14*14)-½(49π-98) = ½(196)-½(49π)+½(98) = 98-½(49π)+49 = 147-½(49π) = ½(294-49π) square units. = 70.0309799871 square units exactly in decimal.

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Mathematics Question and Solution

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