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Give written (and legible) answers to the following question...

Give written (and legible) answers to the following questions. Whenever you are asked to give an algorithm for a problem, you should present the following: the algorithm, a justification of its correctness, and a derivation of its running time. Write clear and convincing pseudo-code for your algo...

1. (12 pts) In the diagram below, chords AB and CD are perpe...

1. (12 pts) In the diagram below, chords AB and CD are perpendicular. Let the diameter of the circle be given by d. Prove that AX² + BX² + CX² + DX² = d2! C A X D B I will start you off. Construct all of the following: diameter CF, as well as segments AD, BC, and BF. Cont...

1. (10 pts) Suppose a circle is given, along with a chord of...

1. (10 pts) Suppose a circle is given, along with a chord of the circle that is not a diameter. Prove that if a line I passes through the center of the circle and also bisects the chord, then l is perpendicular to the chord. 2. (10 pts) Two circles of different sizes are given below, both with th...

2)Let 2 be a position vector of a traveling particle. a)Fi...

2)Let 2 be a position vector of a traveling particle. a)Find the curvature vector KN at t=7 b)find the radius of the oscutating circk at t=7. 3)Let T6)=2t(+14t}-k - Find the principle normal? tn 27 3t ^ 4) Let R(+)=8ej+gk A be a position vector of a traveling particle . - Find the OUT cur...

1. (8 pts each) In the diagram below, ^ABC has a right angle...

1. (8 pts each) In the diagram below, ^ABC has a right angle at C, and the altitude from C is constructed. Side lengths are labeled (and in case it's not clear, C= AB). C b a h A B X D y c (a) Use similar triangles to prove h - ab (b) Use the Pythagorean Theorem, and NOT similar triangl...

A scientist is studding a very symmetrical spider web made b...

A scientist is studding a very symmetrical spider web made by a Latin American spider. The spider web is a regular pentagon as shown in the figure. 1 cm 2 cm 3 cm 4 cm Explore how the area covered by the spider web varies with the length of the side. Express your findings as a general rule. ...

2. Triangles ABC and A'B'C' have respectively equal: one sid...

2. Triangles ABC and A'B'C' have respectively equal: one side (BC = B'C'), the medians to that side (AM = A'M'), and the altitutes to that side (AD = A'D'). Prove that triangles ABC and A'B'C' are congruent. A A' B M D C B¹ M D' c I 3. Two circles with centers O1 and O2 are tangent ...

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