Calculate the ratio of H+ ions to OH– ions at a pH = 6. Find the concentration of H+ ions to OH– ions listed in Table B of your Student Guide. Then divide the H+ concentration by the OH– concentration. Record this calculated ratio in Table A of your Student Guide. Compare your approximated and calculated ratios of H+ ions to OH– ions at a pH = 6. Are they the same? Why or why not? Record your explanation in Table A. What is the concentration of H+ ions at a pH = 6? mol/L What is the concentration of OH– ions at a pH = 6? mol/L What is the ratio of H+ ions to OH– ions at a pH = 6? :1

Fft review: linspace, fs, fftshift, nfft 1. generate one second of a cosine of w,-10hz sampled at f, = 100hz and assign it to x. define a tt as your time axis 2. take 64 points fft. 3. as you remember, the dft (which the fft implements) computes n samples of s2t where k-0,1,2, n -1. plot the magnitude of this 64-points fft at range 0 to 63, what do you think of this graph? 4â·to get the x-axis into a hz-frequency form, plot this 64-points fft between-50 to 50 (the 100hz sampling rate) and have n-points between them. 5. according to your figure, what frequency is this cosine wave at? 6. remember that the fft is evaluating from 0 to 2ď€. we are used to viewing graphs from-ď€ to ď€. therefore, you need to shift your graph. 7. now according to your shifted graph. what frequency is this at? 8. note that the spikes have long drop-offs? try a 1024-point dft. note that the peak is closer to 10 and the drop-off is quicker. although, now sidelobes are an issue

Power can be defined as a. the distance over which work was done. b. how much work can be done in a given time. c. all the work in an given area. d. the energy required to do work.

Explain how the energy of rubber ball is tranforned as it roll down a ramp. give evidence that the energy of the og the ball remains the same at all points on the ramp