Let's find the derivative of that hyperbola in order to find a slope formula to help us with this equation. We already have an x and y value. The derivative is found this way:

so

. The derivative supplies us with the slope formula we need to write the equation. Sub in the x value of 3 to find what the slope is:

. So in our slope-intercept equation, x = 3, y = 1, and m = -1/3. Use these values to solve for b.

so b = 2. The equation, then, for the line tangent to that hyperbola at that given point is
Answer:
12
Step-by-step explanation:
The range of a data set is just the difference between the largest and smallest values.
So, let's find the smallest value: it's 39. The largest value is 51.
Their difference is:
51 - 39 = 12
Thus, the answer is 12.
<em>~ an aesthetics lover</em>