Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3231291

Calculating x. tana = 30/40 a = atan(¾)° Let y be each of the two equal lengths. b² = y²+x² b = √(y²+x²) units. It implies; y+b = 40 y+√(y²+x²) = 40 y²+x² = (40-y)² x² = 1600-80y --- (1). tan(atan(¾))= y/x 3/4 = y/x y = ¼(3x) --- (2). Calculating x. Substituting (2) in (1). x² = 1600-80(¼(3x)) x² = 1600-60x x²+60x-1600 = 0 x²-20x+80x-1600 = 0 x(x-20)+80(x-20) = 0 (x-20)(x+80) = 0 Therefore; x ≠ -80 x = 20 units. Or c = ½(180-...

Mathematics Story

https://onlineedumath.com/update/mathematics-story/3230998

Banana the Frog-Chasing Pup. Once upon a sunny street, there lived a dog named Banana. He was no ordinary pup; his love for bananas was unmatched. Every morning, he'd eagerly await the fruit truck, watching it turn the corner with his tail wagging. Banana's coat was as golden as the sun, and he lived in a house painted yellow to match. His owner, Lily, would often find him munching on a banana, leaving the peels all around. On the other side of the road lived Lily's friend Sarah, who had a...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3230784

Calculating the ascribed square area. Let x be the square side length. a = 6+7 a = 13 units. b²+x² = 13² b = √(169-x²) units. Calculating x², area of the ascribed square.. √(169-x²) ~ 6 13 ~ x Cross Multiply. x√(169-x²) = 78 x²(169-x²) = 6084 x⁴-169x²+6084 = 0 (x²-½(169))² = -6084+(-½*169)² (x²-½(169))² = ¼(-24336+169²) (x²-½(169))² = ¼(4225) x² = ½√(169)±½√(4225) x² = ½(169)±½(65) x² = ½(169±65) It implies; x² ≠ ½(169-65) ≠ ½(104) ≠ 52...

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.

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

https://onlineedumath.com/update/mathematics-story/3230121

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.

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