MHB Solve System of Equations Related to Race Speeds

brinlin
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You seem to be under the impression that this is a site that will do your homework for you. It isn't! We don't know you and we don't dislike you enough to want you to fail this course. We will be happy to help you if you show enough of your own work that we can see what help you need.

The whole point of homework is for YOU to practice so you can pass the tests! I hope you want to pass the tests!

[I myself am a retired math professor. I once had a student who turned in perfect homework then failed every test. He complained bitterly when he received an "F" for the course. I have no idea who did his homework for him (he was a fraternity member if anyone thinks that is relevant) but clearly he didn't. They did him no favors!]
 
I'll help you get started. Let the distance each has to run be "x", the distance each has to swim "y", and the distance each has to cycle "z", all in miles, of course.

Velocity has units of mi/hr because it is "distance (mi.) divided by time (hr.)", v= d/t. Multiplying on both sides by t, vt= d. Dividing on both sides by v, t= d/v. I did that because this problem tells us velocities and I have assigned labels to the distances. I have those together on the right side of the equation.

Look at Amanda only, she ran a distance x miles at 10 mi/hr so took x/10 hours. She swam a distance y miles at 4 mi/hr so took y/4 hours. She cycled a distance z miles at 20 mi/hr so took z/20 hr. She took a total x/10+ y/4+ z/20 hours. The problem tells us she took 2 hours and 30 minutes which is 2.5 hours.

The equation is x/10+ y/4+ z/20= 2.5. If you don't like fractions (I don't!) multiply both sides by 20: 2x+ 5y+ z= 50.

Now you finish!
 
Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. In Dirac’s Principles of Quantum Mechanics published in 1930 he introduced a “convenient notation” he referred to as a “delta function” which he treated as a continuum analog to the discrete Kronecker delta. The Kronecker delta is simply the indexed components of the identity operator in matrix algebra Source: https://www.physicsforums.com/insights/what-exactly-is-diracs-delta-function/ by...
Fermat's Last Theorem has long been one of the most famous mathematical problems, and is now one of the most famous theorems. It simply states that the equation $$ a^n+b^n=c^n $$ has no solutions with positive integers if ##n>2.## It was named after Pierre de Fermat (1607-1665). The problem itself stems from the book Arithmetica by Diophantus of Alexandria. It gained popularity because Fermat noted in his copy "Cubum autem in duos cubos, aut quadratoquadratum in duos quadratoquadratos, et...
I'm interested to know whether the equation $$1 = 2 - \frac{1}{2 - \frac{1}{2 - \cdots}}$$ is true or not. It can be shown easily that if the continued fraction converges, it cannot converge to anything else than 1. It seems that if the continued fraction converges, the convergence is very slow. The apparent slowness of the convergence makes it difficult to estimate the presence of true convergence numerically. At the moment I don't know whether this converges or not.

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