Sir Mike Ambrose is the author of the question.
AB exactly is;
= 16tan(3acos(8/9)) - 2√(17)
= 2(8tan(3acos(8/9))-√(17)) cm
= 102.760478669 cm
Sir Mike Ambrose is the author of the question.
P(2, (16√(5)/5))
Gradient of the curve at the tangent is;
= 24/5√(5)
Therefore;
Gradient of the curve at the normal is;
= -5√(5)/24
It i...
y = e, x = e²
dy/dx at the tangent is;
= 1/(y+2yIny) for y = e.
dy/dx at the tangent = 1/3e
Therefore;
dy/dx at the normal = -3e
It implies;
(e-P)/(e²-0) = -3e
P (height of triangle yellow)...
Area Orange exactly in square cm is;
Area trapezium with parallel sides 10 cm and 5 cm, and height 5 cm - Area triangle with height ½(5) cm and base ⅓(10) cm.
= ½*10(10+5) - ½*½(5)*⅓(10)
= 5(15) -...
(AD)² = 14²+48²
AD = 50 units.
Notice;
AD = AC
It implies;
CE = 14+50
CE = 64 units.
It implies, CD, diameter of the semi circle is;
(CD)² = 64²+48²
CD = 80 units.
½(CD) = BC = BD = radius of...
6² = 4²+6²-2*6*4cosa
48cosa = 52-36
cosa = 16/48
a = acos(⅓)
a = 70.5287793655°
b = 180-70.5287793655
b = 109.4712206345°
c = 180-2(70.5287793655)
c = 38.942441269°
d = ½(180-70.52877...
a = 180-60
a = 120°
b = 180-120-45
b = 15°
(1/sin15) = (c/sin45)
c = 2.7320508076 units.
d² = 2.7320508076²+2²-2*2*2.7320508076cos60
d = 2.4494897428 units.
It implies;
Calculating angle x.
(2...
Equation of the curve is;
y = ¼(x²)+4
Shaded area exactly in square units is;
Area triangle with height 8 unit and base 4 unit - Area sector with radius 4√(5) unit and angle (2atan(0.5))° + Area...
Area orange exactly in square units is;
Area triangle with height ⅓(10√(2)) unit and base 5sin45 unit - Area triangle with height (8/3) unit and base 2√(2)sin45 unit - Area triangle with height ⅔√(...
Sir Mike Ambrose is the author of the question.
Let the side of the square be 2 units.
Therefore;
a = 3√(5)/5 unit
b = 2√(5)/5 unit
c = √(5)/5 unit
d = 2√(5)/5 unit
It implies;
a² = b² + c² + d²...
