plot a graph of the number of washers needed to sink the boat (y-axis) vs. volume of boat (x-axis)

Do not start your experiment until you read the background and answer all background questions.

Background: I often hear that the ship sank because of too many people on board. Today, you learn how scientists and engineers predict the maximum number of people on board. Before starting this project we need to confirm some basic concepts of buoyancy and density.

Represent density = mass / volume from class. To determine the density of an object, you must first find the mass and volume of the object. For a rectangular ship used in today's experiments, you need to use the volume = length x width x height formula. Please use triple beam balance to investigate the quality of the boat

Since the density of water is equal to 1 gram per cubic centimeter, the density of any object is greater than 1 gram per square centimeter. It will sink in the water. As long as the density is less than 1 gram per cubic centimeter, the object will float in the water. The reason for keeping objects floating is called buoyancy. This is the upward force of the fluid as the pressure of the fluid changes according to the depth. If the upward force is greater than the downward force, the object floats

Hypothesis: Discuss (and prove) the assumptions about the problem mentioned in the problem with your group.

1) Build five ships with aluminum foil. The height of each ship is 1 cm. The base of each ship should be square and the dimensions are as follows

Note: Please try building a ship without using minimal aluminum foil and Scotch tape. Please see the class notes. Remember the 3 x 3 x 1 cm boat. A 5 x 5 cm square aluminum foil is required. Then fold each side 1 cm at a time to make the boat's height 1 cm. Please discuss this with your group

2) Start with the smallest boat. Meet 1000 ml. Hydrate beaker 2/3 with water. Floating Boat Start adding pennies at once. Please be careful not to put all the pennies in one place on the ship.

Plot the graph with the number of gradient descent iterations on the x axis and the value of $ \ min _ {\ theta} J (\ theta) $ on the y axis and see how the latter changes as the number changes It can be visualized. Repeat. At some point, this curve becomes flat; this is the number of iterations that the gradient descent converges to a specific problem. You can expect this curve to resemble the curve above. If the slope falls sufficiently, $ min _ {\ theta} J (\ theta) $ decreases with the number of iterations. If not, you should use a smaller learning rate ($ \ alpha $). But again, please do not shrink too much. Convergence slows down.

You may be used to drawing a line graph using the X and Y axes. An X variable is also called an independent variable and a Y variable is called a dependent variable. Simple linear regression compares independent variable X with dependent variable Y. Strictly speaking, in regression analysis, an independent variable is called a predictor and a dependent variable is called a standard variable. However, many people only call them an independent variable and a dependent variable. For more sophisticated regression techniques (such as multiple regression) use multiple independent variables

Which variable is on the X axis? When a variable obviously depends on another variable (for example height depends on age, it is difficult to imagine the age according to height), customary the dependent variable on the Y axis, independent Draw a variable on the X axis. There may be no explicit arguments (leaf length and width: width depends on width, and vice versa). In these cases, there are no differences between which variable and which axis are mutually dependent. The Y diagram shows the relationship between them (one does not affect the other).