Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3230775

Calculating Area Yellow. a = (3+x) units. a is the width of the ascribed rectangle. b = 2(7) b = 14 units. b is the length of the ascribed rectangle. c = ½(a) c = ½(3+x) units. tany = 7/(3+x) --- (1). tany = (0.5(3+x)/7) --- (2). Calculating x. It implies; Equating (1) and (2). ½(3+x)/7 = 7/(3+x) Cross Multiply. 49 = ½(9+6x+x²) 98 = 9+6x+x² x²+6x-89 = 0 (x+3)² = 89+(+3)² (x+3)² = 98 x = -3±√(98) It implies; x ≠ -3-7√(2) x = (7√(2)-3) unit...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3230770

Calculating Length x. Let Alpha be y. Again. Let AB = a. b = 2+6 b = 8 units. tany = a/8 --- (1). tany = 2/a --- (2). Equating (1) and (2). (a/8) = (2/a) Cross Multiply. a² = 16 a = 4 units. Again, a is AB. It implies; x² = 4²+2² x² = 16+4 x = √(20) x = 2√(5) units. x is the required length.

Great Mathematician Leonhard Euler

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Leonhard Euler (1707- 1783) The most prolific mathematician of all time, publishing close to 900 books. When he went blind in his late 50s his productivity in many areas increased. His famous formula eiπ + 1 = 0, where e is the mathematical constant sometimes known as Euler's number and i is the square root of minus one, is widely considered the most beautiful in mathematics. He later took an interest in Latin squares – grids where each row and column contains each member of a set of numbe...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3230261

Calculating Area Blue. Let x be CE = CD = DE. y = 6+4 y = 10 cm. y is AC. Observing Similar Plane Shape Rule. 10 ~ x x ~ 4 Cross Multiply. x² = 40 x = √(40) x = 2√(10) cm. Again, x is the side length of the inscribed blue regular triangle. Area Blue Inscribed Regular Triangle is; ½*2√(10)*2√(10)sin60 = 20sin60 = 10√(3) cm² = 17.3205080757cm²

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3230254

Calculating Area Yellow. Let a be the radius of the ascribed quarter circle. (2a)² = b²+24² b = √(4a²-576) units. c = b-7 c = (√(4a²-576)-7) units. It implies; Calculating a. (√(4a²-576)-7) ~ 2a a ~ √(4a²-576) Cross Multiply. 2a² = 4a²-576-7√(4a²-576) 7√(4a²-576) = 2a²-576 49(4a²-576) = (2a²-576)² 196a²-28224 = 4a⁴-2304a²+331776 4a⁴-2500a²+360000 = 0 a⁴-625a²+90000 = 0 (a²-½(625))² = -90000+(-0.5(625))² (a²-½(625))² = ¼(30625) a² = ½(625)±½√(30625)...

Mathematics Story

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Benny's Button Bonanza. Benny lived in a bouncy house. Not really, but it felt like it! His dad was a bouncy house blower-upper, which is a very bouncy job indeed. One day, Benny’s dad said, “Let’s bounce to the town, Benny! We need buttons!” Benny scratched his head. “Buttons? Why do we need buttons, Dad?” “Why, to button up our bouncy house, of course! It needs three more buttons to be extra bouncy!” Dad chuckled. “Come on, let’s go!” So they hopped in their car, which wasn’t nearly as b...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3229849

Calculate x²+y². Notice. 1 unit is the radius of the circle. a = (y-x) units. 2b² = a² 2b² = (y-x)² 2b² = y²-2xy+x² b² = ½(y²-2xy+x²) b = √(½(y²-2xy+x²)) units. c = 1-b c = (1-√(½(y²-2xy+x²))) units. d = 1+b d = (1+√(½(y²-2xy+x²))) units. Calculating x²+y². It implies; x*y = c*d xy = (1-√(½(y²-2xy+x²)))(1+√(½(y²-2xy+x²))) xy = 1-½(y²-2xy+x²) 2xy = 2-(y²-2xy+x²) 2xy = 2-y²+2xy-x² 0 = 2-y²-x² Therefore; x²+y² = 2 units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3229447

Calculating Length x. cosa = 40/50 a = acos(⅘)° b = 2a b = 2acos(⅘)° Therefore, the required length x is; cosb = x/50 cos(2acos(⅘)) = x/50 x = 50cos(2acos(⅘)) x = 50*(7/25) x = 2*7 x = 14 units. Or c = 180-2(2acos(4/5)) c = 32.5204094166° Therefore; x² = 25²+25²-2*25*25cos32.5204094166 x = 14 units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3229436

Calculate Area Green. Green Area is; Area square with length 4 units - Area quarter circle with radius 2 units - Area square with length 2 units - 3(Area square with length 1 unit) - Area square with length 3 units + Area quarter circle with radius 3 units - Area square with length 2 units + Area quarter circle with radius 2 units - Area quarter circle with radius 1 unit. = 16 - ¼(4π) - 4 - 3 - 9 + ¼(9π) - 4 + ¼(4π) - ¼(π) = 16 - 20 + ¼(9π - π) = ¼(8π) - 4 = 2π - 4 = 2(π-...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3229073

Calculating angle x. Let the radius of the inscribed half circle be 1 unit. Therefore, 2 units is the radius of the ascribed quarter circle. a = (2-y) units. b² = 1²+y² b = √(1+y²) units. b is BD. c = 2(OB) Where OB = 2 units, the radius of the ascribed quarter circle, and also the diameter of the inscribed half circle. c = 2*2 c = 4 units. c is double the radius of the ascribed quarter circle. Calculate y. It implies; 4 ~ √(1+y²) √(1+y²) ~ y Cross Multiply....

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Mathematics Question and Solution

Mathematics Question and Solution

Great Mathematician Leonhard Euler

Mathematics Question and Solution

Mathematics Question and Solution

Mathematics Story

Mathematics Question and Solution

Mathematics Question and Solution

Mathematics Question and Solution

Mathematics Question and Solution

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