Do the given vectors form an orthogonal basis for ℝ3? v1 = 1 0 −1 , v2 = 2 4 2 , v3 = 3 −3 3 Yes, the given set does form an orthogonal basis for ℝ3. No, the given set does not form an orthogonal basis for ℝ3. You are given the theorem below. Let {v1, v2, , vk} be an orthogonal basis for a subspace W of ℝn and let w be any vector in W. Then the unique scalars c1, , ck such that w = c1v1 + + ckvk are given by ci = w · vi vi · vi for i = 1, , k. Use the theorem to express w as a linear combination of the above basis vectors. Give the coordinate vector [w]basis B of w with respect to the basis basis B = {v1, v2, v3} of ℝ3. w = 1 1 1 [w]basis B =

The? half-life of a radioactive substance is 20 years. if you start with some amount of this? substance, what fraction will remain in 120 ? years

Desmond wants to sell his car that he paid $8,000 for 2 years ago. the car depreciated, or decreased in value, at a constant rate each month over a 2-year period. if x represents the monthly depreciation amount, which expression shows how much desmond can sell his car for today? 8,000 + 24x 8,000 - 24x 8,000 + 2x 8,000 - 2xdesmond wants to sell his car that he paid $8,000 for 2 years ago. the car depreciated, or decreased in value, at a constant rate each month over a 2-year period. if x represents the monthly depreciation amount, which expression shows how much desmond can sell his car for today? 8,000 + 24x 8,000 - 24x 8,000 + 2x 8,000 - 2x

There are 3232 forwards and 8080 guards in leo's basketball league. leo must include all players on a team and wants each team to have the same number of forwards and the same number of guards. if leo creates the greatest number of teams possible, how many guards will be on each team?