40,-20,10,-5,__,__,__
What are the next three numbers.

Imagine a new pasture with grass growing on it. every day after the seeds have germinated, the number of blades of grass in the pasture triples. after 18 days, the entire pasture is completely covered in grass. how many days did it take for the pasture to be one-third covered in grass?

On a string instrument, the length of a string varies inversely as the frequency of its vibrations. an 11-inch string has a frequency of 400 cylces per second. find the frequency of a 10-icnch string.

To diagonalize an nxn matrix a means to find an invertible matrix p and a diagonal matrix d such that a pdp d p ap or [1 3 dh epap 3 let a=-3 -5 -3 3 3 1 step 1: find the eigenvalues of matrix a "2's" step 2: find the corresponding eigenvectors of a step 3: createp from eigenvectors in step 2 step 4 create d with matching eigenvalues.