Explanation
We must the tangent line at x = 3 of the function:
The tangent line is given by:
Where:
• m is the slope of the tangent line of f(x) at x = h,
,
• k = f(h) is the value of the function at x = h.
In this case, we have h = 3.
1) First, we compute the derivative of f(x):
2) By evaluating the result of f'(x) at x = h = 3, we get:
3) The value of k is:
4) Replacing the values of m, h and k in the general equation of the tangent line, we get:
Plotting the function f(x) and the tangent line we verify that our result is correct:
Answer
The equation of the tangent line to f(x) and x = 3 is:
Answer:
25 minute
Step-by-step explanation:
Speed is the ratio of the total distance traveled to the total time taken to reach this distance. The formula for speed is:
Speed = total distance / total time taken
The total distance covered by the sloth = 60 ft, and the time taken = 5 minutes, hence:
Speed = total distance / total time taken
speed of the sloth = 60 ft / 5 minutes = 12 ft per minute.
We can calculate the time taken for the sloth to travel the length of the football field (i.e. 300 ft)
speed = distance / time
12 ft/minute = 300 ft / time
time = 300 ft / (12 ft/minute)
time = 25 minute
Hi there!
We can begin by making each fraction have a common denominator:
If we make each have a common denominator of ab, we get:
Simplify:
Multiply both sides by ab:
Move b to the opposite side:
Factor out b:
Divide by (ac - 1):
Answer:
$52.44
Step-by-step explanation:
Answer:
6
1, 50.3
Step-by-step explanation:
the second part for question two could be anywhere from 50.1-50.4
