Mathematics Question and Solution

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a = atan(2)° b = 180-2a b = (180-2atan(2))° Where b is angle FBP. Notice; CQ = 5 cm. Calculating FP using sine rule. Let FP be c. (c/sin(180-2atan(2))) = (5/sin(atan(2))) c = 4.472135955 cm. Therefore; PQ is; CF-CQ-FP = √(10²+5²)-5-4.472135955 = (3√(5)-5) cm. = 1.7082039325 cm.

Mathematics Question and Solution

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Let the AB be 4 cm. Therefore, radius of the inscribed semi circle is; radius = 2 cm. Let the radius of the inscribed circle be r. Calculating r. (2+r)² = (4-r)²+(2-r)² 4+4r+r² = 16-8r+r²+4-4r+r² 4+4r+r² = 20-12r+2r² r²-16r+16r = 0 (r-8)²+16-(-8)² = 0 (r-8)² = 64-16 (r-8)² = 48 r = 8±4√(3) It implies; r ≠ (8+4√(3)) cm. r = (8-4√(3)) cm. Therefore; MQ = 2+r MQ = 2+(8-4√(3)) MQ = (10-4√(3)) cm. a = 2-r a = 2-(8-4√(3)) a = (4√(3)-6) cm b = acos(a/MQ) b = acos((4√(3)-6))/(10-4√(3))) b = 72...

Mathematics Question and Solution

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Let the inscribed blue quarter circle radius be r. Calculating r. Considering similar triangles rule. r = 4 8 = r (cross multiply). r² = 32 r = 4√(2) cm. Therefore; Area blue (area quarter circle) in terms of π is; ¼(4√(2))²π = ¼(32π) = 8π cm²

Mathematics Question and Solution

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Calculating the side length of square ABCD. 2x² = 8² x² = 32 x = 4√(2) units. Where x is AB. Let BG = y Semi circle radius r is; r = ½(4√(2)+y) units. Calculating y. sin45 = ½(4√(2)+y)/7 ½(√(2)) = (4√(2)+y)/14 √(2) = (4√(2)+y)/7 y = 7√(2)-4√(2) y = BG = 3√(2) units. Calculating r. r = ½(4√(2)+y) And y = 3√(2) units. r = ½(4√(2)+3√(2)) r = ½(7√(2)) units. a = x-r a = 4√(2)-½(7√(2)) a = ½√(2) units. Calculating BF. (BF)² = r²-a² (BF)² = (½(7√(2)))²-(½√(2))² (BF...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/1842275

a² = 10²+10²-2*10*10cos150 a = 19.31851652578 cm. Where a is AF which is equal AE. (19.31851652578/sin150) = (10/sinb) b = 15° Where b is angle BAF. tan15 = c/10 c = 2.67949192431 cm. It implies; Area Green Region is; Area square with side 10 cm - 2(area triangle with height 2.67949192431 cm and base 10 cm. = 10² - ½*2(10*2.67949192431) = 100-26.7949192431 = 73.2050807569 cm²

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/1841371

Let the small inscribed square side be a. Let b be the side of the big inscribed square. It implies; b = 10-a Therefore; Calculating a. tan(90-75) = a/(10-a) a(1+tan15) = 10tan15 a = (10tan15)/(1+tan15) a = ⅓(15-5√(3)) cm. b = 10-⅓(15-5√(3)) b = ⅓(15+5√(3)) cm. Blue area is; a²+b² = (⅓(15-5√(3)))²+(⅓(15+5√(3)))² = ⅓(200) cm²

Inspirational Math Quotes

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1. “Pure mathematics is, in its way, the poetry of logical ideas.” —Albert Einstein 2. “Without mathematics, there is nothing you can do. Everything around you is mathematics. Everything around you is numbers.” —Shakuntala Devi 3. “Mathematics is the language with which God wrote the universe.” — Galileo 4. “Mathematics is the music of reason.” —James Joseph Sylvester 5. “Mathematics is the most beautiful and most powerful creation of the human spirit.” —Stefan Banach 6. “It is the duty...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/1839124

Let the radius of the inscribed circle be r. The square side is 8 cm. b = 8-r c = 2+r Therefore; (2+r)² = 2²+(8-r)² 4+4r+r² = 4+64-16r+r² 4r = 64-16r 20r = 64 5r = 16 r = (16/5) cm. Area circle is; πr² = 256π/25 cm² = 32.16990877276 cm²

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Our Certified, Experienced, Hardworking, Resilient and Productive Mathematics Educators will be happy to be at your service to educate your learner/learners become a lover of Mathematics, and a better Mathematician at affordable tuition. We make the necessary Mathematics Curriculum/Scheme of work a priority as we mentor learners experience the beauty of Mathematics. Be nice to communicate us; Call/WhatsApp: +2349076614992 +2348152827445 Email: [email protected] educators@online...

Mathematics Question and Solution

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The triangle's height is; 3x^(⅓) Triangle area = Triangle perimeter Therefore; ½(3x^(⅓)*4x^(⅓)) = 12x^(⅓) 6x^(⅔) = 12x^(⅓) x^(⅔) = 2x^(⅓) x^(⅓) = 2 Therefore; x = 8 units.

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Mathematics Question and Solution

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