Applications And Problem Solving

Applications And Problem Solving-82
\[t = \frac = 10.09998\hspace\hspace\hspace\,\,\,\,\,\,\,\,\,\,\,t = \frac = - 8.539011\] As with the previous example the negative answer just doesn’t make any sense.So, it looks like the car A traveled for 10.09998 hours when they were finally 300 miles apart. Due to the nature of the mathematics on this site it is best views in landscape mode.

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Let \(t\) be the amount of time it takes the first machine (Machine A) to stuff a batch of envelopes by itself.

That means that it will take the second machine (Machine B) \(t 1\) hours to stuff a batch of envelopes by itself.

So, let’s convert to decimals and see what the solutions actually are.

\[x = \frac = 7.2892\hspace\hspacex = \frac = - 10.2892\] So, we have one positive and one negative.

Machine B will need 4.5616 hours to stuff a batch of envelopes by itself.

Again, unlike the first example, note that the time for Machine B was NOT the second solution from the quadratic without the minus sign.\[\begin625 & = 90000\ 625 400 - 1600t 1600 & = 90000\ 1025 - 1600t - 88400 & = 0\end\] Now, the coefficients here are quite large, but that is just something that will happen fairly often with these problems so don’t worry about that.Using the quadratic formula (and simplifying that answer) gives, \[t = \frac = \frac = \frac\] Again, we have two solutions and we’re going to need to determine which one is the correct one, so let’s convert them to decimals.Also, as we will see, we will need to get decimal answer to these and so as a general rule here we will round all answers to 4 decimal places.So, we’ll let \(x\) be the length of the field and so we know that \(x 3\) will be the width of the field.From the stand point of needing the dimensions of a field the negative solution doesn’t make any sense so we will ignore it. The width is 3 feet longer than this and so is 10.2892 feet. In this case this is more of a function of the problem.Notice that the width is almost the second solution to the quadratic equation. For a more complicated set up this will NOT happen.Working separately, it will take the second machine 1 hour longer than the first machine to stuff a batch of envelopes.How long would it take each machine to stuff a batch of envelopes by themselves?Statics can be applied to a variety of situations, ranging from raising a drawbridge to bad posture and back strain.We begin with a discussion of problem-solving strategies specifically used for statics.


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