Answer:
Part 1)
See Below.
Part 2)

Step-by-step explanation:
Part 1)
The linear approximation <em>L</em> for a function <em>f</em> at the point <em>x</em> = <em>a</em> is given by:

We want to verify that the expression:

Is the linear approximation for the function:

At <em>x</em> = 0.
So, find f'(x). We can use the chain rule:

Simplify. Hence:

Then the slope of the linear approximation at <em>x</em> = 0 will be:

And the value of the function at <em>x</em> = 0 is:

Thus, the linear approximation will be:

Hence verified.
Part B)
We want to determine the values of <em>x</em> for which the linear approximation <em>L</em> is accurate to within 0.1.
In other words:

By definition:

Therefore:

We can solve this by using a graphing calculator. Please refer to the graph shown below.
We can see that the inequality is true (i.e. the graph is between <em>y</em> = 0.1 and <em>y</em> = -0.1) for <em>x</em> values between -0.179 and -0.178 as well as -0.010 and 0.012.
In interval notation:

In the given question, it is given that ramp is 17 feet long, rises 8 feet above the floor, and covers a horizontal distance of 15 feet.
And we have to find the value of tan B.
And tangent of any angle is equal to the ratio of vertical by horizontal. That is:
tanB=8/15
And that's the required missing ratio for tan B.
Multiply the cost per hour by 60 to find the cost for a groundskeeper
cost = 12 × 60
cost = 720
The cost for each groundskeeper is $720
Find the cost for seven groundkeepers
Multiply cost for each groundskeeper by 7
cost = 720 × 7
cost = 5,040
The monthly labor cost for seven groundskeepers is $5,040
Answer:
15%
Step-by-step explanation:
To find the percent increase, use the equation:
percent of increase=<u>amount of increase</u>
original amount
The amount of increase is 92-80 = 12. The original amount of 80; this gives us
12/80 = 0.15 = 15%