Posted: March 7th, 2023

Problem 6

-What are the coordinates of the point (x,y

)?

-Give the equation for the path of the ball, showing all work. Explain why you do each step.

-Include a screenshot of the graph of your equation (use Desmos.com), verifying that it goes through the given points.

Problem 10

-The total time T (in hours) of the trip as a function of the distance x (in miles). Make sure you show all your work to come up with this equation, and explain each step and what it represents.

-The domain of the function. Explain why this domain makes sense, and show work as needed.

-Graph the function using the graphing utility on Desmos.com. Take a screenshot and make sure it is included in your document. The graph should be focused over the domain of the function.

-Find the value of x that minimizes T. Desmos.com will note this ordered pair for you automatically. If it does not, then you can click various points of the graph and it will display the ordered pair.

-What does the ordered pair of the minimum for T represent in our situation? I.E. what does the value of x tell us, and what does the value of T tell us? Write a brief paragraph interpreting these values.

10. Trip Time You are in a boat 2 miles from the nearest

point on the coast (see figure). You plan to travel to

point Q, 3 miles down the coast and 1 mile inland. You

row at 2 miles per hour and walk at 4 miles per hour.

2 mi

X

3-x

1 mi

Y

k3 mig

Not drawn to scale

(a) Write the total time T (in hours) of the trip as a

function of the distance x (in miles).

(b) Determine the domain of the function.

(c) Use a graphing utility to graph the function. Be sure

to choose an appropriate viewing window.

(d) Find the value of x that minimizes T.

(e) Write a brief paragraph interpreting these values.

11. Heaviside Function The Heaviside function

Place an order in 3 easy steps. Takes less than 5 mins.