If (8, 12) and (3, 4.5) belong to a proportional relationship, what is the constant of proportionality A:2.5 B:1.5 C:0.6 D:Not here

1.5

Step-by-step explanation:

k= y/x

y= 12-4.5 =7.5

x= 8-3 = 5

k = 7.5/5 = 1.5

A cardboard box without a lid is to have a volume of 32,000 cubic cm. Find the dimensions that minimize the amount of cardboard used

. ans: base 40 x 40, height = 20  

Solution:  

The typical box might look like the one below  

where . In addition we have xyz = 32000 ,so we need to minimize .  

We have,  

From the geometry of the problem  so y = x. So  or x = 40.  

Finally, y = x = 40 and z = 32000/(xy)=20.