Answer:
m^2-3m-180=0
m=15
Step-by-step explanation:
greater integer = m
small integer = n
we know that m = n+3 or n = m-3
we also know that n*m = 180
replace n for m-3
(m-3)*m=180
or
m^2-3m-180 = 0
(m-15)(m+12)=0
so m = 15 or -12, but since problem states positive, m=15
Answer:
Resultant vector of two vectors is (0, 0).
Step-by-step explanation:
in this question two vectors having ordered pair (-6, 5) and (6, -5) have been given.
We can represent these vectors in the form of

and 
Now the resultant of these vectors will be = A + A'
A + A' =
+ 
So the resultant vector = (0 + 0)
Therefore the resultant will be (0, 0)
Answer: option a.

Explanation:
A <em>shrink</em> of a function is a <em>shrink</em> on the vertical direction. It means that for a certain value of x, the new function will have a lower value, in the intervals where the function is positive, or a higher value, in those intervals where the function is negative. This is, the image of the new function is shortened in the vertical direction.
That is the reason behind the rule:
- given f(x), the graph of the function a×f(x), when a > 1, represents a vertical stretch of f(x),
- given f(x), the graph of the function a×f(x), when a < 1, represents a vertical shrink of f(x).
So, we just must apply the rule: to find a shrink of an exponential growth function, multiply the original function by a scale factor less than 1.
Since it <em>is a shrink of</em> <em>an exponential growth function</em>, the base must be greater than 1. Among the options, the functions that meet that conditon are a and b:

Now, following the rule it is the function with the fraction (1/3) in front of the exponential part which represents a <em>shrink of an exponential function</em>.
The distance between the trains is changing at the rate of (70 -60) = 10 mph. They will be in the same place (45 mi)/(10 mi/h) = 4.5 hours after they leave their respective cities. They will be 10 miles apart both 1 hour before that time and one hour after that time.
The trains will be 10 miles apart 3.5 hours after leaving.
They will be 10 miles apart the second time 5.5 hours after leaving.