Mathematics Question and Solution

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Radius of the semi circle is 5 units. Calculating r, radius of the inscribed circle. (5-r)² = 3²+r² 25-10r+r² = 9+r² 10r = 16 r = ⅕(8) units. a = 3-r a = ⅕(7) units. b² = 5²-a² b = ⅕(24) units. c = atan((8/5)/8) c = atan(⅕)° d = 2c d = 2atan(⅕)° tan(2tan(⅕)) = e/(5+(7/5)) e = ⅓(8) units. f = atan(12/5)° g = b-f g = (32/15) units. h² = 50-50cos(180-4atan(⅕)) h = (120/13) units. sin(2atan(⅕)) = (8/3)/i i = (104/15) units. j = h-i j = (448/195) units. k = atan(24/7)° l = (180-atan(24/7))° m = (18...

John, Josh and The Wild Animals

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Short Story written by: Luis Muñoz (Spain). There was a country house in a beautiful valley. It was very big, beautiful, built with good taste, and full of details. The owner was a well off landowner called John. He was a person who had a good heart, loved animals, and he liked going hunting. He used to capture different living birds and put them into cages. He liked seeing the animals close-up, to take care of them and to protect them. Before capturing them, these wild animals lived in the va...

Mathematics Question and Solution

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Let the two equal lengths be 1 unit. (a) Calculating Theta exactly. Let theta be x. Calculating x. x = ½(90-54) x = ½(36) x = 18° sin18 = a/1 a = 0.30901699437 unit. b = 90-18 b = 72° sin72 = c/1 c = 0.9510565163 unit. tan36 = 0.9510565163/d d = 1.30901699437 units. Area Blue is; 0.5(1.30901699437*0.9510565163) = 0.62247457122 square units. e = 270-54-96 e = 120° f = 360-120-72 f = 168° g² = 2-2cos168 g = 1.98904379074 units. h = ½(180-168) h = 6° (1.98904379074/sin54) = (i/sin24) i = 1 units....

Anna's Story

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Short Story written by: Chris Morales. There was a girl called Anna, who was studying in Esmarth Vil, a primary school in the United States. She was the most hardworking girl at her school, her marks were higher than the others. She was the best, but nobody wanted to be her friend. They didn't want to play with her and teased her. One day, the teacher set an exam and a boy called Robert signed his exam using Ana´s name. So, when the teacher returned all the exams, everybody was shocked. Ann...

Mathematics Question and Solution

https://onlineedumath.websites.co.in/update/mathematics-question-and-solution/1771369

Let x^(7) be p. Therefore; p²-843p+1 = 0 p = ½(843±377√(5)) p = ½(843-377√(5)) Or p = ½(843+377√(5)) And p = x^(7) It implies; x = (½(843-377√(5)))^(1/7) Or x = (½(843+377√(5)))^(1/7) x = 0.38196601125 Or x = 2.61803398875 Therefore; x^(5) + (1/x^(5)) is; For x = 0.38196601125 x^(5) + (1/x^(5)) = 123 For x = 2.61803398875 x^(5) + (1/x^(5)) = 123 Answer is 123

Four principles of deeply effective math teaching

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$four-principles-of-deeply-effective-math-teaching_1682229626iGZVCQ.jpeg$

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...

Mathematics Question and Solution

https://onlineedumath.websites.co.in/update/mathematics-question-and-solution/1770457

The side length of the congruent Hexagons is 2 unit. Area hexagon is; (6*2²)/(4tan30) = 6√(3)) square units. a² = 8-8cos30 a = √(8-4√(3)) unit. Area ABC is; ½(√(8-4√(3)))²sin60 = (2√(3)-3) square units. (d) Area Hexagon ÷ Area ABC exactly is; (6√(3)) ÷ (2√(3)-3) = 6(2+√(3)) (c) Calculating Area Green to 2 decimal places. b = a + √(2²+2²) b = √(8-4√(3))+2√(2) b = (√(2)+√(6)) units. b = 3.86370330516 units. c² = 8-8cos120 c = 2√(3) units. Area Green is; 2((0.5x2*2sin120) + (0.5*2√(3)*(√(2)+√(6)...

Mathematics Question and Solution

https://onlineedumath.websites.co.in/update/mathematics-question-and-solution/1769801

Let the biggest regular pentagon side length be 2 units. sin72 = a/2 a = 1.90211303259 units. tan72 = (1.90211303259/b) b = 0.61803398875 unit. c = 2b c = 1.2360679775 units. Where c is the side length of the regular red and blue pentagon. Calculating area of the regular red and blue pentagon. (5*1.2360679775²)/(4tan36) = 2.6286555606 square units. d² = 8-8cos108 d = 3.2360679775 units. e = ½(3.2360679775-c) e = 1 unit. f² = 8-8cos36 f = 1.2360679775 units. g² = 2-2cos36 g = 0.61803398875 unit...

Mathematics Question and Solution

https://onlineedumath.websites.co.in/update/mathematics-question-and-solution/1769331

a = atan(⅓)° ⅓ = b/3 b = 1 unit. It implies; Area Red is; Area triangle with height 1 unit and base 3 units + ½(2(area quarter circle with radius 3 units - area triangle with height and base 3 units respectively))) = ½(1*3) + ½(2(¼(π*3²) - ½(3*3))) = ½(3) + ¼(9)π - ½(9) = ¼(9π) - ½(6) = ¼(9π-12) square units. = ¾(3π-4) square units.

Mathematics Question and Solution

https://onlineedumath.websites.co.in/update/mathematics-question-and-solution/1768960

Let DE be 1 unit. AC = 4 units. Area ABC is; 8sin60 = 4√(3) square units. a² = 1+2²-4cos45 a = 1.47362575821 units. (1.47362575821/sin45) = (1/sinb) b = 28.6750500631° c = 60-b c = 31.3249499369° d = 360--60-150 d = 150° e = 240-d e = 90° f² = 1²+1² f = √(2) units. g = 180-15-45-60 g = 60° h² = 4²+1.47362575821²-8*1.47362575821cos31.3249499369 h = 2.84622917461 units. (2.84622917461/sin31.3249499369) = (1.47362575821/sini) i = 15.61499741821° j = 60-i j = 44.38500258179° k = 120...

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Mathematics Question and Solution

John, Josh and The Wild Animals

Mathematics Question and Solution

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Mathematics Question and Solution

Four principles of deeply effective math teaching

Mathematics Question and Solution

Mathematics Question and Solution

Mathematics Question and Solution

Mathematics Question and Solution

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