Let z denote the set of all integers with addition defined in the usual way, and define scalar multiplication, denoted o, by:
alpha o k = [[alpha]].k for all k in z

where [[alpha]] denotes the greatest integer less than or equal to alpha, for example,
2.25 o 4 = [[2.25]].4 =2..4 = 8
show that z, together with these operations, is not a vector space. which axioms fail to hold?

Distributivity of scalar multiplication with respect to field addition 

(a + b)v = av + bv 

Compatibility of scalar multiplication with field multiplication

 a(bv) = (ab)v

answer: the answer is (b) amie should have multiplied

step-by-step explanation: given a sphere and a cylinder with same radius and height.

let, 'r' be the radius of the cylinder and sphere and 'h' be the height of the cylinder. according to the question,

r = h.

now, the volume of the sphere will be

and the volume of the cylinder will be

therefore, we have

thus, ammie should have multiplied the volume of the sphere

step-by-step explanation:

hans did not square the 40-unit side; he merely multiplied it by 2.   incorrect.