A golf ball is manufactured so that if it is dropped from A feet above the ground onto a hard surface, the maximum height of eac
1 answer:
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Using the washer method, the volume is given by the integral
where 3 - 1 = 2 is the distance from <em>y</em> = 3 to the axis of revolution, and similarly (1 + sec(<em>x</em>)) - 1 = sec(<em>x</em>) is the distance from <em>y</em> = 1 + sec(<em>x</em>) to the axis. The integrand is symmetric about <em>x</em> = 0, so the integral "folds" in on itself, and the integral from -π/3 to π/3 is twice the integral from 0 to π/3.
So the volume is
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:
Answer:
20.78feet
Step-by-step explanation:
The question made us to understand that the man is standing and also there is angle of elevation, then we need to draw a right triangle having a base equal to 36 feet with an angle from the base to the top of the pole which is 30 degrees.
tan= opposite side / adjacent side
Let height of the pole =h
Tan(30)= h/36
But tan 30degree= 1/√3
h= 36 × 1/√3
h= 20.78feet
Therefore, the height of the pole= 20.78feet
CHECK THE ATTACHMENT FOR DETAILED FIGURE
