Answer:
The rate at which both of them are moving apart is 4.9761 ft/sec.
Step-by-step explanation:
Given:
Rate at which the woman is walking,
= 3 ft/sec
Rate at which the man is walking,
= 2 ft/sec
Collective rate of both,
= 5 ft/sec
Woman starts walking after 5 mins so we have to consider total time traveled by man as (5+15) min = 20 min
Now,
Distance traveled by man and woman are
and
ft respectively.
⇒ 
⇒ 
As we see in the diagram (attachment) that it forms a right angled triangle and we have to calculate
.
Lets calculate h.
Applying Pythagoras formula.
⇒
⇒ 
Now differentiating the Pythagoras formula we can calculate the rate at which both of them are moving apart.
Differentiating with respect to time.
⇒ 
⇒ 
⇒
...as 
⇒ Plugging the values.
⇒
...as
ft/sec
⇒
ft/sec
So the rate from which man and woman moving apart is 4.9761 ft/sec.
When two lines cross, there are four angles at the place where they cross.
Two angles that do NOT share a side are vertical angles. There are two pairs
of vertical angles where the lines cross.
Also, by the way, vertical angles are always equal to each other. It's often
very helpful to know that.

By taking <span>logarithmic of base 10
∴ </span><span>

∴ x log 4 = log 64
∴

note: we don't need to write the base in case of the base =10
∴ The correct choice is
</span><span>x = log base 10 of 64, all over log base 10 of 4</span>