for each, list three elements and then show it is a vector space.

(a) the set of linear polynomials p1 = {a0 + a1x | a0, a1 ∈ r} under the usual polynomial addition and scalar multiplication operations.

(b) the set of linear polynomials {a0 + a1x | a0 − 2a1 = 0}, under the usual polynomial addition and scalar multiplication operations.

Can't gugys answer the ratio question. this is urgent the plans of a building is drawn toward scale of 1: 1000. kfc the foyer on the plans measures 62mm by 54mm, how large is the foyer in real life?

Brittany has designed four different birdcages, each with the same volume: a square pyramid, a cylinder, a cone, and a sphere. the zoo wants to use one of brittany’s designs but plans to change the volume of the cage. find the design change that would result in the birdcage with the greatest volume. increase the area of the base of the square pyramid by a factor of ten. increase the height of the cylinder by a factor of ten. increase the radius of the cone by a factor of ten. increase the radius of a sphere by a factor of ten. juan wants to build a greenhouse in his back yard. he needs to maximize the ratio of floor area to structure volume in order to provide the most room for plants while minimizing the area to be heated. find the description of the structure that best meets juan’s criteria. a cube with a side length of 12 feet a cone with a diameter of 12 feet and a height of 10 feet a square pyramid with a base side length of 12 feet and a height of 9 feet a hemisphere with a diameter of 12 feet marion has a bicycle that she is planning to take for a ride. the rim of the rear wheel lies 41 cm from the center of the wheel. the tire itself has a thickness of 3 cm.in order to marion to ride her bicycle 96,712 cm, approximately how many rotations will the rear wheel make? 350 15.9 376 5133 an isosceles trapezoid has perimeter of 42 inches. each of the congruent nonparallel sides is 5 inches long, and the trapezoid is 3 inches tall. how long are the two parallel sides? 10 inches and 16 inches 12 inches and 20 inches 16 inches and 16 inches 10 inches and 22 inches

The u-drive rent-a-truck company plans to spend $13 million on 320 new vehicles. each commercial van will cost $25 comma 000, each small truck $50 comma 000, and each large truck  $80 comma 000. past experience shows that they need twice as many vans as small trucks. how many of each type of vehicle can they buy?