Student Problem 7
1) What is this problem about?
This problem shows us how to convert repeating decimals into rational fractions. In this problem, our repeating decimal was 0.11111. So we can rewrite it out as 0.1+0.01+0.001 because they will add up together to equal the repeating decimal again. To find the value of r, we take the second term which was 0.01 and divide it by a sub 1(first term) which was 0.1. We find out that r is equal it 0.1 or 1/10. Now we take our infinite geometric series formula and plug in what we know. We already know that a sub 1 is 0.1 and the r-value is 1/10 or 0.1. So now the equation looks like S sub ∞=(1/10)/1-(1/10). We would solve it out and find out that our answer is 1/9.
2)What must the reader pay close attention to in order to not make a mistake?
Readers must remember to split up the repeating decimals into multiple terms. By doing that, we are able to form our a sub 1 and be able to find our r-value with those terms. Also remember that a # divided by a fraction is like a # multiplied to the fraction reciprocal. In this problem, we saw that the tens were diagonal from each other and were able to cancel them out to equal 1.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Student Problem 6
1) What is this problem about?
This problem is an example of how to solve partial fraction decomposition problems but with repeated factors. We are given one equation in which we have to split it up into multiple fractions with (+) and (-) signs between them.
2) What must the reader pay close attention to in order to not make a mistake?
The reader must at first know how to factor out the bottom polynomial into factors that have an x-variable to the power of 1 such as x or (x-2). Readers also must know from how many factors there are, there will be the same number of letters as numerators for the factors. Readers also must know how to find the LeastCommonDenominator but with this problem, he/she must pay really close attention to what to multiply to each equation. Because some fractions already have a variable such as (x+2) and (x+2)^2, so all you need to do is multiply with (x+2) to get the second power, you don't need to multiply (x+2)^2 to (x+2) cause that will get you a fraction to the third power. Readers also need to know how to solve a system of equations through elimination, substitution, or matrix, but with this equation we were lucky enough to only use substitution.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Student Problem 5
1) What is this problem about?
This problem is an example of how to solve partial fraction decomposition problems. We are given one equation in which we have to split it up into multiple fractions with (+) and (-) signs between them.
2) What must the reader pay close attention to in order to not make a mistake?
The reader must at first know how to factor out the bottom polynomial into factors that have an x-variable to the power of 1 such as x or (x-2). Readers also must know from how many factors there are, there will be the same number of letters as numerators for the factors. Readers also must know how to find the LeastCommonDenominator and know how to solve a system of equations through elimination or substitution.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Student Problem 4
1)What is this problem about?
This problem is an example of how to solve logarithmic equations but in this case, natural logs. We are given the equation and we have to determine what is the asymptote and also if the graph has a y-int and where the x-int is.
2) What must the reader pay close attention to in order not to make a mistake?
Readers must understand what the equation log sub (x-h) +k. The only part reader must know from this equation is the (x-h). Switch the operation sign that is in front of the h-value and that new value will be your x asymptote. If your x asymptote is 0 or higher, then you will know for sure that there will be no y-int. Readers also need to know how to exponentiate the (ln) with the letter (e)
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Student Problem 3
1)What is this problem about?
This problem is an example of how to solve exponential graphs. We are given the equation and we have to determine what is the asymptote and also if the graph goes left/right or stays above/below the asymptote.
2) What must the reader pay close attention to in order not to make a mistake?
Readers must understand what the equation a•b^(x-h)+k means. A determines if graph goes above/below asymptote and to determine, readers must remember positivism makes a person's mood go up so the graph will be above the asymptote and vice versa. B determines if graph will get close to the asymptote on the right or left side. If the absolute value of b is <1, then the graph will be closer on the right side and if absolute value of b is >1, then it will be closer on left side. (x-h) will shift the graph left or right, but we will be using a calculator to get the points that will shift the graph for us. Last is the k which represents the asymptote. Whatever k is, then y is the same(y=k)
No comments:
Post a Comment