Algebra Answers

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.

1. A man saves #100 in his first year of work and each year he saves #20 more than the proceeding year. In how many years will be save #5800.

2. A polygon has 25 sides, the lengths of which starting from the smallest sides are in A.P, if the perimeter of the polygon is 2100cm and the length of the largest side is 20times that of the smallest.find the length of the smallest side and the common difference of the A.P

Use the vertical line test to identify graphs in which y is a function of x.

2 A tunnelling machine drills 500 metres. Use your values from the

table to estimate the cost of drilling if the first metre costs £X and

each extra met

re costs £Y.

x=17

y=272

Write an equation to describe the variation. Use k for the constant of proportionality.

g  varies inversely as p 

Write an equation to describe the variation. Use k for the constant of proportionality.

r  varies directly as f

The intensity of light​ (in foot-candles) varies inversely as the square of​ x, the distance in feet from the light source. The intensity of light 2 feet from the source is 80 ​foot-candles. How far away is the source if the intensity of light is 5 ​foot-candles?