Use the method for solving equations of the form StartFraction dy Over dx EndFraction equals Upper G (ax plus by )dy dx=G(ax+by) to solve the following differential equation. StartFraction dy Over dx EndFraction equals StartRoot 6 x plus y EndRoot minus 6 dy dx=6x+y−6 Ignoring lost solutions, if any, an implicit solution in the form F(x, y)equals=C is nothingequals=C, where C is an arbitrary constant.

Asmall (but heavy) particle placed in a glass of water will follow a zigzag motion because the particle will bounce off of the water molecules it meets. this is called brownian motion. a physicist simulates this on a computer, by varying the distance a particle can travel (called the mean free length), on average, before it collides with a water molecule and assigning the change in motion to be one of 8 directions, each with a similar probability. by running the simulated particle (with the same mean free length) many times she determines that it should take 15 seconds, on average, for the particle to fall to the bottom, with a standard deviation of 1.5 seconds. next she lets a real particle fall through a glass of water and finds that it took 18 seconds. what does she conclude, and why?

Explain how you can use the associative property to evaluate (7x50)x4.

(05.02) mr. morris is going to save money and replace his sailboat's mainsail himself. he must determine the area of the mainsail in order to buy the correct amount of material. calculate the area of the parallelogram to determine how much material should be purchased. be sure to explain how to decompose this shape into rectangles and triangles. describe their dimensions and show your work.