Answer:
has units of distance
has units of distance over time
has units of distance over 
has units of distance over 
Explanation:
Since the expression for the distance is:

then:
has units of distance
has units of distance over time
has units of distance over 
has units of distance over 
because we are supposed to be able to add all of the terms and get a distance. So the products on each term that contains factors of time (t) should be cancelling those time units with units in the denominator of the multiplicative constant s that accompany them.
Answer:
k_max = 31.82 w/mk
k_min = 17.70 w/mk
Explanation:
a) the maximum thermal conductivity is given as

where k_m is thermal conductvitiy of metal
k_p is thermal conductvitiy of carbide
v_m = proportion of metal in the cement = 0.17
v_p = proportion of carbide in the cement = 0.83
= 66*0.17 + 28*0.83
k_max = 31.82 w/mk
b) the minimum thermal conductivity is given as

= \frac{28+66}{28*0.17 +66*0.83}
k_min = 17.70 w/mk
Answer:
1.190390345 degrees.
Explanation:
As stated in the problem that the angle between the two curves is also the angle between slopes of the two cures at the point of intersection, which is 1 (when we set two equation equal and solve for x).
We know, if you don't you could verify it for yourself and it will be a nice mathematical exercise for you, that when there are two lines with slopes
and
then the angle between them and their two slopes has following relationship.
where
is angle between the two lines.
As it is clear that we can easily get the angle between the two curves if we know slopes at that point, which you will see in second is very straight forward to calculate.
Slopes are simply derivatives evaluated at the point of intersection and the two derivatives are
16x and
, substituting x =1 we get,
and
.
Now put
and
in this relationship, rearrange and solve for angle, it will come out to be
= 1.190390345 degrees.
that is our angle that we want to know between the two cures at the point of their intersection.