Which expression represents the number of sides in the polygon for the nth member of the pattern?
1 answer:
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Answer:
See below
Step-by-step explanation:
π, pronounced as <em>pi</em> is the ratio between 2πr which is circumference to 2r which is diameter.
In word, π is circumference/diameter which has exact value of 3.14159... and it is also an irrational number too.
π is often used to be defined as 3, 3.14 or 22/7 [Keep in mind, these numbers are only approximation.] in some fields. In trigonometry, π is mostly used to refer as <u>π radians</u> or <u>π rad</u> which is equivalent to 180°.
Why do we need it? Because it’s useful in a field that requires rotation. If you notice, figure with circular base will always have π with it, the volume is an example.
In calculus, you need π to do solid of revolution method which is:
In trigonometry, you need it for measurement/angle.
So anything that’s related to revolution, rotation or related to circle must require π at least.
In general life, you do not use it but this is mostly applied in engineering field and anything related to science that involves with circle or revolve.
Let me know if you have any questions!
Answer:
Step-by-step explanation:
That will be a square with a diagonal of 20
side length of 20sin45
and area of (20sin45)² = 200 units²
prove it you say?
Area of a rectangle is base times height
A = bh
With a radius of 10, the diagonals of any rectangle inscribed will be 20 units
20² = b² + h²
h =
A = bh
A = b
Area will be maximized when the derivative is set to zero
dA/db = - b²/
0 = - b²/
b²/ =
b² = 400 - b²
2b² = 400
b² = 200
b =
h =
h =
h =
A = bh
A = •
A = 200 units²