Arectangular tank with a square base, an open top, and a volume of 864 ft cubed is to be constructed of sheet steel. find the dimensions of the tank that has the minimum surface area. let s be the length of one of the sides of the square base and let a be the surface area of the tank. write the objective function.

Tank dimensions:

s = 12 ft

h = 6 ft

Step-by-step explanation:

s = lenght side of the square base

A the total area of of the tank  ( this area is the area of the base plus  the lateral area (4) times

h  = the height of the tank

V  = 864 ft³             V  =  s² * h    ⇒   h = V/s²  ⇒ h = 864/ s²

Then we have :

A (total) =  Base area + 4 * lateral area

Area of the base is  s²

Lateral area is  s * h  but we have 4 wall  so lateral area = 4*s*h

Then Objective function is :

A(s) = s² + 4*s * V/s²           ⇒    A(s) = s²  + 4*864/s     ⇒   A(s) = s²  + 3456/s

Taken derivative of the objective function:

A´(s) = 2s - 3456/ s²

Solving for s

2s - 3456/s²  = 0     ⇒  2*s³  - 3456 = 0   ⇒  s³  = 3456/2  ⇒ s³ =  1728

s = ∛1728      ⇒   s =  12 ft

So h = V/s²       ⇒  h = 864 / 144       ⇒  h = 6 ft

introduction, methodology, results, discussion

step-by-step explanation:

an observational study is one which consists of actual observation to record data and then analyse the data.

there are a number of factors that should be analyzed before starting an observational study.

the main four factors are:

i) introduction:   this should be analysed to check whether the purpose of the study is correctly established and the data recorded are appropriate for the study

methodology:   the method of collecting the data, such as whether randomly selected, and whether sample size matches with the population to be studied, whether questions asked are easy to answer by common men, etc.

results: then results such as summary of data with comments should be studied thoroughly

discussion:   the last is the discussion, this can be either by management people or persons who are all interested , etc.

according to this law, when unemployment goes up by 1%, gdp drops by 2%. in the question, unemployment rate goes from 2% to 5%, meaning unemployment goes up by 3%, so the gdp drops by 6%. thus the effect is a drop in gdp by 6%.

step-by-step explanation: