Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/1851676

Let the height of the triangle be a. Let angle alpha be b. tanb = 3/a ----- (1) tan2b = 8/a ----- (2) And tan2b = 2tanb/(1-tan²b) Therefore; 2tanb/(1-tan²b) = 8/a ----- (3) Substituting (1) in (3). (2*(3/a))/(1-(3/a)²) = 8/a (6/a)/(1-(9/a²)) = 8/a (6/a)/((a²-9)/a²) = 8/a (6a/(a²-9)) = 8/a 6a² = 8a²-72 2a² = 72 a² = 36 a = 6 units. Notice, a is the height of the triangle. Therefore x is; √(6²+8²) = √(100) = 10 units.

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/1811565

Let the side of the regular pentagon be 1 unit. Notice; The regular pentagon side is equal the regular heptagon side. a = ⅐(180*5) a = ⅐(900)°, the single interior angle of the regular heptagon. b = 2a b = ⅐(450)° tan(⅐(450)) = c/0.5 c = 1.03826069829 units. cos(⅐(450)) = 0.5/d d = 1.15238243548 units. Where d is the radius of the ascribed circle. e = 180-⅐(900) e = ⅐(360)° tan18 = 0.5/f f = 1.53884176859 units. g² = 1.15238243548²-0.5² g = 1.03826069828 units. h = f-g h = 0.5005810...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/1810441

Let the side of the regular pentagon be 1 unit. a² = 2-2cos108 a = 1.61803398875 units. sin30 = b/0.5 b = 0.25 unit. c = 2b c = 0.5 unit. Where c is the inscribed square side. Area Square is; (0.5)² = 0.25 square units. Inscribed circle radius d is; d = ½(b) d = 0.125 unit. e = 0.5-0.125 e = 0.375 unit. f = 2atan(0.125/0.375) f = 36.86989764584° tan36.86989764584 = g/0.5 g = 0.375 unit. Shaded Area is; 0.5*0.375*0.5-π*0.125*0.125 = 0.04466261479 square units. (a) Area Shaded ÷...

Mathematics Question and Solution

https://onlineedumath.com.free/update/mathematics-question-and-solution/1797707

Calculating r, radius of the circle. (r/tan40)+(r/tan30) = 10 r = 3.42020143326 cm. (a/sin60) = (10/sin40) a = 13.47296355334 cm. tan40 = 3.42020143326/b b = 4.07603734548 (4.07603734548/sin50) = (c/sin80) c = 5.24005260459 cm. d = 13.47296355334-4.07603734548 d = 9.39692620786 cm. e² = 9.39692620786²+5.24005260459²-2*9.39692620786*5.24005260459cos130 e = 13.38142726359 cm. (13.38142726359/sin130) = (5.24005260459/sinf) f = 17.45618925878° g = 100-17.45618925878 g = 82.54381074122°...

Mathematics Question and Solution

https://onlineedumath.com.free/update/mathematics-question-and-solution/1796969

Notice; AB = 25 units. cos30 = 8√(3)/a a = 16 units. tan30 = b/(8√(3)) b = 8 units. Let the side of the regular hexagon be c. c = ¼(AC) Calculating AC. ((AC)/sin46) = (25/sin74) AC = 18.70821971213 units. c = ¼(18.70821971213) c = 4.67705492803 units. Calculating r, radius of the circle. (r/sin16) = (25/sin148) r = 13.00374294827 units. Calculating Shaded Area. cos30 = d/4.67705492803 d = 4.05044838257 units. e = 2d e = 8.10089676514 units. tan16 = f/(0.5*25) f = 3.58431732199 uni...

Mathematics Question and Solution

https://onlineedumath.com.free/update/mathematics-question-and-solution/1778432

Area purple is; Area square with side 10 cm - 3(area circle with radius 2.5 cm) - 8(area quarter circle with radius 1.5 cm - area triangle with height and base 1.5 cm respectfully) = (10*10) - 3(π*2.5²) - 8(¼(2.5²)π - ½(2.5²) = 100 - 18.75π - 8(1.5625π - 3.125) = 100 - 18.75π - 12.5π + 25 = 125 - 31.25π = (125-¼(125π)) = ¼(500-125π) square units.

Mathematics Question and Solution

https://onlineedumath.com.free/update/mathematics-question-and-solution/1777221

Let the radius of the large circle be 1 unit. Diameter of the large circle = 2 units. sin60 = 2/a a = ⅓(4√(3)) units. Where a is the side length of triangle ABC. b² = 2-2cos b = √(3) units. c = a-b c = ⅓(√(3)) units. (d/sin50) = (4√(3)/(3sin100)) d = 1.79639514045 units. e² = (⅓(2√(3)))²+1² e = ⅓√(21) units. 1² = (⅓√(21))²+f²-2*⅓√(21)f cos(atan(3/(2√(3))-10) f² - 2.62161244054f + 1.33333333333 = 0 f = 1.93113 units. g² = 1.93119²+(⅓(4√(3)))²-2*1.93119(⅓(4√(3)))cos10 g = 0.5...

Four principles of deeply effective math teaching

https://onlineedumath.com.free/update/four-principles-of-deeply-effective-math-teaching/1771333

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Principle 1: Let It Make Sense Let us strive to teach for understanding of mathematical concepts and procedures, the "why" something works, and not only the "how". This understanding, as I'm sure you realize, doesn't always come immediately. It may take even several years to grasp a concept. For example, place value is something children understand partially at first, and then that deepens over a few years. This is why many math curricula use spiraling: they come back to a concept the next yea...

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Mathematics Question and Solution

Mathematics Question and Solution

Mathematics Question and Solution

Mathematics Question and Solution

Mathematics Question and Solution

Mathematics Question and Solution

Mathematics Question and Solution

Mathematics Question and Solution

Four principles of deeply effective math teaching

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