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Video 103. Class with Derick and Zino (year 7 and year 6 respectively) 03/10/2023...
Sir Mike Ambrose is the author of the question.
Calculating k.
3k² = 108
k = 6 units.
The equation of the curve is;
y = 4x-⅓(x²)
Area R is;
Area under the curve at x=0 and x=(6-3√(2)).
= 2(6-3√(2)...
Sir Mike Ambrose is the author of the question.
Let the side of the regular quadrilateral (square) be 4 units.
Area square is;
4²
= 16 square units.
Area Red is;
Area triangle with height 4.562952...
tana = 4/8
a = atan(½)°
b = (180-2atan(½))°
It implies;
Area Orange is;
Area triangle with base 8 units and height 4 units - Area square with side 4 units + Area quarter circle with radius 4 unit...
Sir Mike Ambrose is the author of the question.
Let the side of the square be 2 units.
Therefore;
Area square is;
2²
= 4 square units.
Radius of the inscribed circle, r is;
sin52.5 = r/1.044209537...
Sir Mike Ambrose is the author of the question.
Let the side of the regular hexagon be 2 units.
Therefore;
Area Green is;
Area regular equilateral triangle with side √(3) units.
½*√(3)*√(3)sin60
=...
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Sir Mike Ambrose is the author of the question.
Let the side of the regular octagon be 1 unit.
(a) Calculating alpha exactly. Let it be x.
x = atan(1/(√(2)+1)
x = 22.5°
(b) Calculating Area Yellow...
Sir Mike Ambrose is the author of the question.
Let the side of the regular hexagon be 2 units.
Area Regular hexagon is;
½(12)*(2/(2tan(180/6)))
= 6/tan30
= 6√(3) square units.
Area Shaded is;
A...
Sir Mike Ambrose is the author of the question.
Let the side of the inscribed regular pentagon be 2 units.
Therefore;
Length Red (AD) is;
2+2(2cos72)
= 2+4cos72
= 3.2360679775 units.
Ca...
