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Geometry
Theorem
Let α(s) be parametrized by arc length. Then |α′(s)| =1. (Prove it)
Let α(s) be parametrized by arc length. Then |α′(s)| =1. (Prove it)
Geometry
Q.Find the length of the astroid x=acos3t, y=asin3t, [0, 2π].
Geometry
Q.Find the length of the Asteroid x=acos3t, y=asin3t.
Geometry
Show that if a and b are
in the same direction then |a + b| = |a| + |b|
in the same direction then |a + b| = |a| + |b|
Geometry
How to visualize unfamiliar geometrical curve?
Geometry
Q.Prove that If the tangent vector of the parameterized curve is constant, the image of the curve is (part of) a straight line.
Geometry
Q. What are the projections of helix (acost, asint, t) in all three coordinate planes xy-plane, yz-plane, xz-plane.
Geometry
A square sandbox has an area of 75 ft.² estimate the length of one of the sides of the sandbox
Geometry
Suppose that a rectangular classroom is 43 feet long, 19 feet wide and has a volume of 3,665 cubic feet. How high above the floor is the ceiling?
Geometry
ABCD is a plane quadrilateral and E is any point on AD.EF is drawn parallel to DB to meet AB in F, and EG is drawn parallel to DC to meet AC in G. Prove that FG is parallel to BC.
