Suppose that the graph of y = 100 - x^2/400 represents....

[aznxschoolboi24]

Okay, well I was assigned a few calculus problems for homework and I have some answers but I don't know the correct work. So I was wondering, can someone do them really fast or perhaps tell me how to do them? please! =)



click to enlarge

i just need help starting the problem.

Sample Examination 1, Section II, Part B

Suppose that the graph of y = 100 - x²/400 represents a hill rising from level ground represented by the x-axis as shown in the figure [in the linked graphic]. Let x and y be measured in feet. A 16-foot tower, TR [with R at the top of the parabola and T above R on the y-axis], stands on top of the hill.

a) Determine the equation of line-segment TQ [where Q is on the positive x-axis], the line of sight from the top of the tower tangent to the hill. Justify your answer.

b) From the top of the tower, the ground between P [being the positive x-intercept] and Q is blocked by the hill and cannot be seen. Find the distance between P and Q to the nearest foot.

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Edited by stapel -- Reason for edit: copying text from graphic

 

[galactus]

For the first part, you have a line tangent to \(\displaystyle \L\\y=100-\frac{x^{2}}{400}\) that passes through (0,116). Find the equation of the line.

Use \(\displaystyle \L\\y-y_{1}=m(x-x_{1})\)

m is the derivative of y, y1=116, x1=0. Set it up and solve for x.

Once you have that you have all you need to find the equation of the line.

I see it says you can't use a calculator, but you can check to see what it looks like.

Here it is. You find the equation of the line.

For the second part, once you have the line equation, you can find where it crosses the x-axis by setting the equation equal to 0 and solving for x.
Then, find where the parabola crosses the x-axis by setting it equal to 0 and solving for x. Subtract the two results.