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About Scotto
Expertise
Any kind of mathematics (calculus, analysis, game theory, linear approximation, finite differences, linear regression, linear programming, numerical analysis, probability, statistics, etc.). I also have answered some questions in Physics (mass, momentum, falling bodies), Chemistry (charge, reactions, symbols, molecules), and Biology.

Experience
Experience in the area: I have tutored students in all areas of mathematics for over 20 years. Education/Credentials: BSand MS in Mathematics from Oregon State University, where I completed sophomore course in Physics and Chemistry. I received both degrees with high honors. Awards and Honors: I have passed Actuarial tests 100, 110, and 135.

Publications
Maybe not a publication, but I have respond to well oveer 3000 questions on the PC. That's around 2,000 in basic math and 1,000 in advanced math.

Education/Credentials
I aquired well over 40 hours of upper division courses. This was well over the number that were required. I graduated with honors in both my BS and MS degree from Oregon State University. I was allowed to jump into a few junior level courses my sophomore year.

Awards and Honors
I have been nominated as the expert of the month several times. All of my scores right now are at least a 9.8 average (out of 10).

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My past clients have been students at OSU, students at the college in South Seattle, referals from a company, friends and aquantenances, people from my church, and people like you.

 
   

You are here:  Experts > Teens > Homework/Study Tips > Calculus > Calculus-Related Rates

Calculus - Calculus-Related Rates


Expert: Scotto - 7/15/2008

Question
I tried to work on these problems but I'm not completely sure how to start it and if I was doing it right.

A car passes over a bridge at 15.0 m/s at the same time a boat passes under the bridge at a point 10.5m directly below car. If the boat is moving perpendicularly to the bridge at 4.0m/s, how fast are the car and the boat separating 5.0s later?

A weather balloon leaves the ground 275m from an observer and rises vertically at 12.0m/s. How fast is the line of sight from the observer to the balloon increasing when the balloon is 450m high?

Answer
The car is moving one way at 15 m/s and the boat is moving 4 m/s.
Multiply the speed by 5 seconds to get how far they have gone.
Let c = car distance, b = boat distance, k = diagonal.

The equation would be b^2 + c^2 = k^2.  Take the derivative with respect to t with b, c, and k all functions of t.  The variables b and c were calculated, and then k can be found.  db/dt and dc/dt were given.  The equatioin is 2b(db/dt) + 2c(dc/dt) = 2k(dk/dt).  Solve for dd/dt.

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