Consider the inner product on R3 defined as follow. For u = (U1, U2, U3) and v = (V1, V2, V3), (u, v) = U1V1 + 2u2V2 + 2u3V3 + U2V3 + U3V2. The vectors u = (-2, 2, 1) and v = (1, -2, 3) are orthogonal with respect to this inner product (as you may check if you wish). Find numbers a and b so that the linear combination au + bu best approximates the vector w = (-4, 5, -1) with respect to the inner product.

The height of a birch tree, f(x), in inches, after x months is shown in the graph below. how much does the birch tree grow per month, and what will be the height of the birch tree after 10 months? a. the birch tree grows 1 inch per month. the height of the birch tree will be 16 inches after 10 months. b. the birch tree grows 2 inches per month. the height of the birch tree will be 26 inches after 10 months. c. the birch tree grows 3 inches per month. the height of the birch tree will be 36 inches after 10 months. d. the birch tree grows 2 inches per month. the height of the birch tree will be 24 inches after 10 months.

Aquadrilateral has exactly 3 congruent sides davis claims that the figure must be a rectangle why is his claim incorrect.

For a house call, a veterinarian charges $70, plus $40 an hour. a. write an equation that represents the total fee y y (in dollars) the veterinarian charges for a visit lasting x x hours. equation: y= y= no response given b. find the x-intercept. x-intercept: