Question

3. . A rectangular shipping container must have a volume of 84 cubic meters. The client tells the manufacturer that, because of the contents, the length of the container must be one meter longer than the width, and the height must be one meter greater than twice the width. What should the dimensions of the container be? Embed your description of the dimensions in a sentence. In addition to showing the calculations that lead to your solution, write a synopsis of the tactic(s) you used to arrive at your solution to this question

4. An Egyptian mummy is discovered in which the amount of Carbon-14 present is only about twentynine fiftieths the amount found in living human beings. Show how you used the decay constant for Carbon-14 to determine the half-life of Carbon-14 (accurate to the fifth decimal place). About how long ago did the Egyptian die? (DO NOT USE THE FORMULA, ln(0.5) 0 ( ) t A t A e T  .) If this is a royal tomb, which Pharaoh is in the sarcophagus? The Pharaoh’s name, dynasty, and regnal years should be given in sentence form. In addition to showing the calculations that lead to your solution, write a synopsis of the tactic(s) you used to arrive at your solution(s) to this series of questions. Use clear and concise sentence structure and grammar. Your answer should be labelled with appropriate units and reflect the context used in this question.

Answer 1

volume of 84 cubic meters.

length of the container must be one meter longer than the width, and the height must be one meter greater than twice the width

Lets start with width be w .

Length = w+1

Height = 2*w+1

So, Equation becomes : w*(w+1)*(2w+1) = 84

Solve the equation for w :

Multiply the terms to expand the bracket : w( 2w^2 + 3w +1) = 84

2w^3 + 3w^2 + w = 84

2w^3 + 3w^2 + w - 84 =0

Ignore complex roots .So width = 3 mt

height = 2w+ 1 = 6+1 = 7 mt

length = w+1 = 4 mt