Suppose w is a subspace of set of real numbers r ℝn spanned by n nonzero orthogonal vectors. explain why w equals = set of real numbers r ℝn. the goal is to show that the subspace w is actually all of set of real numbers r ℝn. in general, when are two subspaces known to be the same space?

George is putting trim around his rectangular deck, including the gate. he will need 44 feet of trim to do the entire deck. if the deck is 13 feet long, how wide is the deck?

Which description is represented by a discrete graph? kiley bought a platter for $19 and several matching bowls that were $8 each. what is the total cost before tax? the temperature at 9 a. m. was 83° f and is heating up at an average rate of 6°f per hour. what is the temperature x hours later? juan ate an egg with 78 calories and some cereal with 110 calories per serving for breakfast. what is the total amount of calories he consumed? a bottle contained 2,000 ml of liquid and is being poured out at an average rate of 300 ml per second. how much liquid is left in the bottle after x seconds?

Suppose the equation ||x-a|-b|=2008 has 3 distinct real roots and a not =0. find the value of b.