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:
n=9
Step-by-step explanation:
-5-4n=-41
+5 +5
---------------
-4n=-36
---------------
-4n/4=-36/-4
---------------
n=9
Answer:
The rate of change is 0.75 gallons per minute
Step-by-step explanation:
The rate of change of the linear relation is represented by the slope of the line which represents this relation
The rule of the slope of a line is
m = Δy/Δx, where
- Δy is the vertical change
- Δx is the horizontal change
From the given graph
∵ The line passes through points (0, 0) and (4, 3)
∴ Δx = 4 - 0 = 4
∴ Δy = 3 - 0 = 3
→ Use the rule of the slope above to find the slope of the line
∴ m = 
= 0.75
∵ The x-axis represents the time in minutes
∵ The y-axis represents the amount in gallons
∵ m represents the rate of change
∴ The rate of change = 0.75 gallons per minute
Answer:
Prove the lengths are the same
Step-by-step explanation:
When we say segments are congruent, we mean their lengths are the same.
__
Let's see if they are congruent.
AD = √((3-(-3))² +(2-2)²) = 6
BC = √((6-0)² +(6-6)²) = 6
AD ≅ BC . . . . their lengths are the same
What do you mean by that?
