The set of full binary trees can be de ned recursively: (a) The tree with only one vertex is a full binary tree. (b) If T1 and T2 are two disjoint full binary trees, there is a full binary tree, denoted as T1 T2, with T1 as its left subtree, T2 as its right subtree, and a new root r connecting to T1 and T2. Use structural induction to prove that the number of leaves is one more than the number of internal vertices in a full binary tree.

You receive an email from an impressive-sounding stranger, professor alexander rothschild renard iii, president of the american institute for scientific political statesmen. he urges you to vote for his presidential candidate choice. this social media red flag is known as

Ihave a singular monitor that is a tv for my computer. recently, i took apart my computer and put it back together. when i put in the hdmi cord and booted the computer to see if it worked, the computer turned on fine but the screen was blue with "hdmi no signal." i've tried everything that doesn't require buying spare parts, any answer is appreciated!

The volume v and paper surface area a of a conical paper cup are given by where r is the radius of the base of the cone and h is the height of the cone. a. by eliminating h, obtain the expression for a as a function of r and v. b. create a user-de ned function that accepts r as the only argument and computes a for a given value of v. declare v to be global within the function. c. for v ! 10 in.3 , use the function with the fminbnd function to compute the value of r that minimizes the area a. what is the corresponding value of the height h? investigate the sensitivity of the solution by plotting v versus r. how much can r vary about its optimal value before the area increases 10 percent above its minimum value?