1. michael's father bought a 13 foot board to cut into shelves for his
bedroom. michael plans to cut the board into 11 equal size lengths for his
shelves,
a. the saw blade that michael will use to cut the board will change the length of the board
by -0,2 inches for each cut. how will this affect the total length of the board? (hint:
draw a picture.)
b. after making his cuts, what will be the exact length of each shelf?
me

Lee has $1.75 in dimes and nickels. the number of nickels is 11 more than the number of dimes. how many of each coin does he have?

Find the solution on the interval [0, 2pi)

Xtax=1. determine their canon- 1. write the following quadratic forms as v(x) ical forms, find the modal matrices (i.e. the matrices of unit eigenvectors) of the corresponding transformations and write down explicite expressions for canonical coordinates (y1, 2, y3) in terms of the original coordinates (x1, x2, x3). state what surfaces these quadratic forms correspond to: = > (a) -a x + 4x12 4x1x38x231; (b) 3-33 + 4xrj224x3122a3= 1; (c) 4a7 2x1 2x1x36x2a3 = 1. 2. solve the following systems of differential equations using the matrix exponential technique 3x 4 (a) x(0) = 5, y(0) = 1; 4x-3y 3.x y(0) = 9, y(0) = 3; -2x 6x2y