Determine if the function defines an inner product on r2, where u = (ul, u2) and v-(y, v2). (select all that apply.) (u, v) = u1v1 satisfies (u, v) - (v, u) does not satisfy (u, v)- (v, u) satisfies (u, v + , v) + ? u, w o does not satisfy (u, v + w) -(u, v) (u, w) d satisfies c(u, v? = ? cu, v o does not satisfy qu, , v) 0 satisfies (v, v? 2 0, and (v, v? = 0 if and only if v-o o does not satisfy (v, v) 2 0, and (v, v0 if and only if v- 0

The amount of money, in dollars, in an account after t years is given by a = 1000(1.03)^t. the initial deposit into the account was $_^a0 and the interest rate was _a1% per year. only enter numbers in the boxes. do not include any commas or decimal points^t. the initial deposit into the account was $__^a0 and the interest rate is % per year.

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?

Do some research and find a city that has experienced population growth. determine its population on january 1st of a certain year. write an exponential function to represent the city’s population, y, based on the number of years that pass, x after a period of exponential growth. describe the variables and numbers that you used in your equation.