A and b are positive integers and a-b=2 ... Evaluate the following: a) 2^a/2^b
b) 5^a/5^b
c) 4^0.5a/2^b

A) = 4.

B) = 25.

C) = 4.

Step-by-step explanation:

We are given that a and b are positive integers and that:

And we want to evaluate the following expressions.

Expression A)

We have:

This is equivalent to:

Therefore:

Substitute and evaluate:

Expression B)

We have:

This is equivalent to:

Again, substitute and evaluate:

Expression C)

Lastly, we have:

Note that 4 = 2². Hence:

Simplify:

Using the previous result:

hope this !

step-by-step explanation:

d = distance between moon and sun, which in this problem is the hypotenuse of a right triangle.  

the distance y is the side opposite to angle x in the right triangle.   use the definition of the sine function from basic trigonometry.

sin(x) = y/d ⇒

d = y/sin(x)