Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3112450

Sir Mike Ambrose is the author of the question. Calculating Yellow Area. It is; Area triangle with height 4sin(atan(⅔)) units and base 8√(13)/9 units - Area triangle with height 1 unit and base ⅔ units - Area triangle with height ¼ units and base ⅔ units. = ½*4sin(atan(⅔))*(8√(13)/9) - ½*1*⅔ - ½*¼*⅔ = (32/9)-⅓-(1/12) = (113/36) square units. Area Orange is; Area triangle with height ⅓(10sin(atan(¾))) units and base (5√(13)/9) units. = ½*⅓(10sin(atan(3/2)))*(5√(13)/9)...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3109784

Sir Mike Ambrose is the author of the question. Equation of the curve is; y = ⅔(8x-x²) Calculating Area E. (Area under the curve at x = (3/2) and x = 4) - Area trapezium with parallel sides (13/2) units and (10⅔) units, and height (5/3) units. =(835/36) - ½*(5/2)*((13/2)+(32/3)) = (835/36) - (515/24) = (125/72) square units. Calculating Area F. ½(Area under the curve at x = 0 and x = 8) - Area triangle with height (32/3) units and base 4 units - Area triangle with hei...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3085580

Notice; Single interior angle of a regular polygon with 6 sides (regular hexagon) is 120°. The formula to get it is; (180°(n-2))/n. Where n is the side number of the regular polygon. It implies; Blue area will be; Area regular hexagon with single interior angle and single side length 120° and 6cm respectively - 6(area sector of interior angle and radius 120° and 3cm respectively. = ¼((36x6)/tan(180/6)) - 6((120x9π)/360) = (54/tan30) - 18π = 54√(3) - 18π = 18(3...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3081841

Let x be a side length of the largest possible inscribed square of the scalene triangle with sides 13 cm, 14 cm and 15 cm respectively. It implies; x = 14÷((1/tan(53.13))+1+(1/tan(67.38))) x = 14÷(2.16667222427) x = 6.46152188743 cm. Therefore, area largest possible inscribed square A is; A = x² A = 6.46152188743² A = 41.7512651017 cm²

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3072681

x² = (r+1)² - (r-1)² Therefore x = 2√(r) unit. y² = (r+1)² - (2√(r))² Therefore y = √(r²-2r+1) y = √(r-1)² y = (r-1) unit z = (r+1) - y z = (r+1) - (r-1) Therefore z = 2 units a = r+r Therefore a = 2r units A sincere study and analysis of the composite circles deduced a right-angled triangle with two adjacent sides, 2 units and 2√(r) units respectively, and hypotenuse 2r units. Therefore; Calculating r, the radius of the three congruent circles. (2r)² = 2² + (2√(r)...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3030094

Sir Mike Ambrose is the author of the question. P coordinate is; P(3, 9) Q coordinate is; Q(2, 5), Q(3, 5) It implies; Shaded area exactly in its square units simplest form is; (Area under the curve at x = 2 and x = 3) - (Area trapezoid with parallel sides ⅓(23) units and 9 units, and height 1 unit). = (8+ln(81/16)) - ½((23/3)+9) = (8+ln(81/16))-½(50/3) = (8+ln(81/16))-⅓(25) = (ln(81/16)-⅓) square units. = 1.2885270991 square units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3017238

Sir Mike Ambrose is the author of the question Let the side of the regular Pentagon be 2 units. Therefore; Area orange is; Area triangle with height 1.7013016167 units and base 1.8345763534sin(18) units = ½*1.7013016167*1.8345763534sin(18) = 0.48224693327 square units. Area blue is; Area trapezoid with parallel sides 0.21654236465 units and 1 unit, and height 1.9021130326 units. ½*1.9021130326(0.21654236465+1) = 1.15700054326 square units. It implies; Area Orang...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3011353

Sir Mike Ambrose is the author of the question. Area Green exactly is; Area trapezoid with parallel sides 3 cm and (6-2√(3)) cm, and height (6-3√(3)) cm. = ½(6-3√(3))(3+(6-2√(3))) = ½(6-3√(3))(9-2√(3)) = ½(72-39√(3)) cm² = 3(24-13√(3))/2 cm²

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2993552

Sir Mike Ambrose is the author of the question. Radius of the semicircle is 2 units. Therefore; Shaded area exactly in decimal square units is; Area trapezoid with parallel sides 2 units and (6-3√(3)) units, and height 3 units - Area sector with radius 2 units and angle (120-atan(3-√(3)))°. = ½*3(2+(6-3√(3))) - ((120-atan(3-√(3)))*2*2π÷360) = ½(24-9√(3)) - 2.38279212814 = 4.20577136594 - 2.38279212814 = 1.8229792378 square units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2985798

Sir Mike Ambrose is the author of the question. Area green exactly in decimal is; Square side is (16/√(17)) units. Area trapezoid with parallel sides (16/√(17)) units and (4/√(17)) units, and height (16/√(17)) units - Area triangle with height (16/√(17)) units and base (4/√(17)) units - Area triangle with height (16/√(17)) units and base 3.1067961165sin(atan(13/16)) units. = ½*(16/√(17))((16/√(17))+(4/√(17))) - ½*(16/√(17))(4/√(17)) - ½*(16/√(17))*3.1067961165sin(atan(13/16)) =...

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