Answer:
Step-by-step explanation:
Given


Required
Function from K to F
This implies that, we calculate F(k)
Given that:

Substitute c(k) for c

Substitute: 

Hence:

1) Find the derivative

and

.
2) The equation of the tangent line is

, so at point (2,6):

and


-the equation of the tangent line at point (2,6).
The answer is 99.2u squared y squared
Using the normal distribution, it is found that 25.14% of the batteries will last more than 420 hours.
<h3>Normal Probability Distribution</h3>
The z-score of a measure X of a normally distributed variable with mean
and standard deviation
is given by:

- The z-score measures how many standard deviations the measure is above or below the mean.
- Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.
In this problem, we have that the mean and the standard deviation are given, respectively, by:
.
The proportion of the batteries will last more than 420 hours is <u>one subtracted by the p-value of Z when X = 420</u>, hence:


Z = 0.67
Z = 0.67 has a p-value of 0.7486.
1 - 0.7486 = 0.2514.
0.2514 = 25.14% of the batteries will last more than 420 hours.
More can be learned about the normal distribution at brainly.com/question/24663213
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The answer would be 25/54