Suppose you work for the Department of Forestry and have been called in to cut down a diseased tree at a summer camp. The tree is quite tall and is in an area surrounded by cabins. You measured the distance from the base of the tree to the nearby cabins, and you found that the cabins will be safe if the tree falls within 200.5 feet of its base. Is it safe to cut the tree at ground level?
If not, how high up the trunk must you cut to guarantee that the tip of
the tree will hit the ground within the safe zone?

In the early afternoon, you find that a 96-inch fence post casts a 36-inch shadow at the same time the diseased tree casts a 70.7-foot shadow.

Find the height of the tree and determine whether it is safe to cut the tree at ground level or not.

Which part of a 2-column proof is the hypothesis of the conjecture? a) given b) reasons c) prove d) statements ! i think it's b but i'm not quite

Describe how to determine the average rate of change between x = 4 and x = 6 for the function f(x) = 2x^3 + 4. include the average rate of change in your answer.

Suppose we have a set of small wooden blocks showing the 26 letters of the english alphabet, one letter per block. (think of scrabble tiles.) our set includes 10 copies of each letter. we place them into a bag and draw out one block at a time. (a) if we line up the letters on a rack as we draw them, how different ways coukl we fill a rack of 5 letters? (b) now suppose we just toss our chosen blocks into a pile, and whenever we draw a letter we already have, we put it back in the bag and draw again. how many different piles of 5 blocks could result? possible? piles will contain at least one repeated letter? (c) if we draw out 5 blocks wit hout looking at them, how many different piles are (d) if we draw out 5 blocks without looking at them, how many of the possible 2. (4) consider the following formula. 12 give two different proofs, one using the factorial formulas and the other combina torial.