Archimedes (ca. 287-212 b. c.) was able to use clever geometric means to determine the relative volumes of a cylinder and the cone and paraboloid that would fit snugly into it (1800 years before newton and leibniz). with calculus, you don't have to be a genius to reach the same conclusions. (a) determine the ratio of the volume of a (right circular) cone to the volume of a cylinder with the same height and base radius: (first you will need to determine the equation of the line which rotates to generate the cone.) vcone vcylinder = (b) determine the ratio of the volume of a paraboloid (a parabola rotated about the y axis) to the volume of a cylinder with the same height and base radius:

true

explanation:

x coordinate can be written by using the formula, x= x1 + 2/5(x2 - x1)

step-by-step explanation:

formula

x = x1 + p/w(x2 - x1)

let the line segment ab with a(x1,y1) and b(x2,y2)

a point(x,y) divide ab in the ratio, 2: 3 the x coordinate can be written as

x = x1 + p/w(x2 - x1)

here p=2 and w = 2+3

therefore,

x coordinate can be written by using the formula, x= x1 + 2/5(x2 - x1)

similarly y coordinate y = y1 + 2/5(y2 - y1)

you are playing an adventure game on your computer. you come across a troll who won't let you pass and there is no other way to get to the other side of the river except over the bridge he is guarding.

the troll is a nerd. he takes great delight in watching people struggle with his problems. very few get them. he only gives you one chance and then he changes the puzzle. you have to solve this one.

before you are four blocks. they are numbered 11,6, -7,21.

he tells that the answer he wants is minus and between -1 and - 2. you can use +, -, ×, ÷   ( and ) as many times as you like or no times at all. you don't like the way he's looking at you, but you need to cross the bridge. what do you do?