Step 8: Does the direction of the graphed line correspond to the sign of the calculated slope?
2 answers:
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Answer:
Jogging 6th time.
Step-by-step explanation:
We have been given that Vicki started jogging the first time she ran she ran 3/16 mile the second time she ran 3/8 mile and the third time she ran 9/16 mile.
We can see that the distance Vicki covers each time forms a arithmetic sequence, where 1st term is 3/16.
We know that an arithmetic sequence is in form , where,
= nth term of sequence,
= 1st term of sequence,
n = Number of terms in sequence,
d = Common difference.
Let us find common difference of our given sequence as:
Since Vicki needs to cover more than 1 mile, so we nth term of sequence should be greater than 1.
Let us solve for n.
We can also write next terms of our sequence as:
Therefore, Vicki will run more than 1 mile when she is jogging for 6th time.
Answer:
1.49
Step-by-step explanation:
In order to find the slope of the tangent line to a given equation, and in a given point, we need to:
1. Find the first derivative of the given function.
2. Evaluate the first derivative function in the given point.
1. Let's find the first derivative of the given function:
The original function is
But remeber that the derivative of is
so,
2. Let's evaluate the first derivative function in the given point
The given point is (0.4,1.49) so:
Notice that the calculated slope of the tangent line is equal to the y-coordinate of the given point because f'(x)=f(x). In conclusion, the slope of the tangent line is equal to 1.49.