Constructive Interference：Two or more crests (or two or more troughs) move towards each other and, when they meet, the resulting wave appears with a amplitude equal to the sum of the amplitudes of the crests/troughs.

Destructive Interference：A crest and a trough of identical amplitudes and wavelengths are moved towards one another, when they meet, they cancel each other, out of phase and continue in their movement.

Transverse wave: A wave that vibrates at a right angle. Shown by the pulling of the spring to one side at a right angle.

Longitudinal wave: several turns of the spring are compressed and let go; Disturbance is in the same direction as the direction of travel. Parts of the coil are compressed and released, this wave travels lengthwise down the coil.

design and building process/ construction of invention

day one:

1.design drawing

2. made holes on 3 bottles

day two: cut off bottom of two bottles

day three:connect 3 bottles together, and twine the tube around the bottle.(same like drawing design)

day four: mix water and ink. put the water into the bottle.

History

On a Sunday, Archimedes and his classmates went on a wooden boat, driving slowly on the Nile, and his eyes were dazzled by the charming scenery. Suddenly he saw a group of people carrying water in a bucket. “why do they carry water?” he asked.
“The river bed is low and the farmland is high, so the farmer has to carry the water.” A local student told him. “So the efficiency of carrying water is too low, and it is not sure how many barrels are to be carried by the water.” Archimedes had a sympathy for the peasants. The student said disapprovingly, “people do this. Do you have any good ideas?”
When Archimedes came back, he always had a picture of the farmer struggling with water. “Can you let the water run high?” Archimedes began to think about this problem. Gradually, in Archimedes’ mind, there was a vision: “make a big spiral and put it in a cylinder. In this way, when the spiral is turned, the water can be carried aloft along the spiral groove.
Archimedes immediately drew a sketch of the idea. He took this sketch to find the carpenter and asked the master to help him with a tool for pumping water. By Archimedes’s advice, the carpenter made a strange thing. Archimedes moved this thing to the river and put one end of it into the water, then gently shook the handle. The water was shaking the handle and coming out from the top of the thing. The water was flowing high.
The farmer, who came to see, was fascinated by this amazing thing. They praised Archimedes for doing a great deed for the peasants. Soon, the spiraling pumps were spreading in the Nile valley, even wider. This pump is called the archimedean screw pump. Until now, some modern factories still use this archimedean screw pump to move fluid and powder.

Explanation of physics involved

Produced by using mechanical rotating centrifugal force, make the water produces the speed, following the upward spiral pipe wall, in the water rushed to the pipe wall, the pipe wall will continue to generate thrust, making the water flow from the bottom to the top.

To move stationary water from one place to another, force has to be applied. The forces involved are gravitational and normal forces. When the screw turns a half rotation, it scoops up water and holds it in a fixed position. Because the angle of the screw (Archimedes’ screw cannot be vertical), gravity and the normal forces in the screw thread and wall cause the water to be in a stable equilibrium position (a state in which opposing forces are balanced).

This week in Pre-Calc we learned about Solving Quadratic Inequalities in One Variable, Graphing Linear Inequalities in Two Variables, and Solving Quadratic Systems of Equations.

When solving Quadratic Systems of Equations you would solve algebraically, either with substitution, or elimination. You could also graph, but if your point of intersection is not on a prefect point, you will not be able to be completely accurate. To solve get everything equal to zero.

Example:

y = x^{2} – 5x + 7

y = 2x + 1

Make both equations into “y=” format:

They are both in “y=” format, so Set them equal to each other

x^{2} – 5x + 7 = 2x + 1

Simplify into “= 0” format (like a standard Quadratic Equation)

Subtract 2x from both sides: x^{2} – 7x + 7 = 1

Subtract 1 from both sides: x^{2} – 7x + 6 = 0

Start with: x^{2} – 7x + 6 = 0

Rewrite -7x as -x-6x: x^{2} – x – 6x + 6 = 0

Then: x(x-1) – 6(x-1) = 0

Then: (x-1)(x-6) = 0

Which gives us the solutions x=1 and x=6

Use the linear equation to calculate matching “y” values, so we get (x,y) points as answers

Yes i was able to be an active listener and support & encourage others. At first my partner have no idea with what kind of mandalas does she want to do, so I share my ideas whit her. We did third one together, we mix our ideas.

I hear different points of view from others but I am not disagree. I am ok with use others opinions.

I share my ideas with my group, and did 2.5 mandalas(third one is I with another group member did)

All our mandalas are connected. And our opinion is same.

I took on a thinker role in my group, consider what kind of color or type.

This week in Pre Calculus 11 we learned about Graphing Linear Inequalities in two variables. The solutions to these inequalities are represented by a boundary line and shading one side of the line.

Ex:

key notes

choosing any coordinate (the easy one is 0,0) and seeing if the statement is true or false.