Algebra Answers

use pascals triangle to expand the binomical expression (1+2x)^3?

Carl and Dennis are brothers. The sum of their ages is 29. In 6 years' time Carl will be the same age as Dennis was 3 years ago.

3+x² =-3

Multiply out (3x³ + 4x - 5)(2x³ - 8x² + 2) using polynomial long multiplication.

3.Four men are walking late at night. Together they have one flashlight with a weak battery, so that it can only light the immediate vicinity. They come to a bridge, which is so rickety that only two can cross at the same time. Thus, in order to get to the other end of the bridge, two must cross with the flashlight and one must walk back across the bridge to return the flashlight (they cannot risk throwing it), until all are over. The men can walk at different maximum rates. The slowest needs 10 minutes to cross the bridge, the next 5 minutes, the next 2 minutes and the quickest 1 minute. When two walk together, they must proceed at the pace of the slower. They need to get everyone across the bridge in 17-minutes. Can they do it? How?

Solve each of the following problems using the problem solving strategies.

1.This is known as the "Die Hard Problem" because it appears in the film Die Hard with a Vengeance, shown in 1995. But in fact, this and other similar problems. are very old and have been the subject of much study, particularly by computer scientists who have developed various strategies for solving all water-jug problems. In the film, the characters played by Bruce Willis and Samuel L. Jackson must disarm a bomb by placing exactly four gallons of water on a scale. They have water since they are at a fountain, but they have only two jugs, one of which holds five gallons and the other three gallons. Can you solve the problem, and how quickly can you do it?

A town has a population of 17000 and grows at 4% every year. What will be the population after 12 years, to the nearest whole number?

An element with mass 820 grams decays by 26.8% per minute. How much of the element is remaining after 18 minutes, to the nearest 10th of a gram?

Use the Upper and Lower Bounds Theorem to show that the real zeros of

(i) P (x) = 7x^8+2x^5+x^2-2

lie between −1 and 1.