# -2x < 3/7

Monday, September 6th, 2010

# Cos 2x=0.32

Monday, September 6th, 2010

### Solution:

First let’s apply the reverse cosine function to both sides of the equation:

cos-1(cos(2x)) = cos-1 (0.32) = cos-1 ()

Now if you take the inverse cosine the  cosine of 2x, you get 2x…so:

2x = cos-1 ()

2x 71.34°

x 35.67°  (which is approximately the same as 0.622 radians)

This looks like it might be the final answer, but actually it’s only one of the many correct answers. One way to see this is by graphing y=cos(2x) and seeing where it intersects the line y=0.32. If you do this, you will see that the intersections occur at multiple points:

As you can see, the intersections occur at x 0.622 radians, 2.519 radians, 3.764 radians, 5.660 radians, etc. The general form of the solution set is as follows:

# What is the Volume of a Sphere the Radius of Six?

Saturday, September 4th, 2010

### Solution:

1. The formula for the volume of a sphere is
2. r = 6

# What is an Inverse Function?

Saturday, September 4th, 2010

If you have a function called ƒ, let’s call its inverse ƒ–1 (i.e. ƒ–1 is the inverse function of ƒ).

By definition, the property of ƒ–1 is that if ƒ(a)=b, then ƒ–1(b)=a. Wikipedia (http://en.wikipedia.org/wiki/Inverse_function) has a good example:

A function ƒ and its inverse ƒ–1. Because ƒ maps a to 3, the inverse ƒ–1 maps 3 back to a. In mathematics, if ƒ is a function from a set A to a set B, then an inverse function for ƒ is a function from B to A, with the property that a round trip from A to B to A (or from B to A to B) returns each element of the initial set to itself.

# I had 48 marbles in my jar. I lost 1/8 and gave 1/6 to my best friend. How many marbles were left in my jar?

Friday, July 23rd, 2010

### Solution:

2. Lost 6  (1/8 of 48 =s 6)
3. Gave 8 to a friend   (1/6 of 48 is 8)
4. 48 – 6 – 8
5. = 48 – 14
6. = 34

# Online Homework Help is Not Cheating

Thursday, February 25th, 2010

Today’s curriculum is vast. Consequently, students often need help in doing their homework. Teachers in school are not always able to provide help when the students most need it. This is where the online homework help comes in.

Many people believe that this is a form of cheating, but this is far from the truth. Students seek help from online teachers just like they do when they are in their class. The difference being that the online teachers are available to them at any hour of the day and not just during school hours. Online homework help is just the thing that many students need to excel, as it enables them to avoid “getting stuck” and helps them focus on areas where they need practice.

Technology is helping students perform well in their studies. If you need help with homework, there are many sources of online homework help, including one-on-one academic coaching. By dong some research, you may also find some free resources for online homework help.

# How much homework help from friends and family is appropriate?

Thursday, November 19th, 2009

This is a question that parents are faced with as long as their children are in school. There is no simple of answer. It depends on many factors, such as the number of children you have, the amount of time the parent can set aside for the child, the child’s IQ level, the child’s interest level in studies, the child’s ability to absorb educational inputs, etc. However, the bottom line would be that as the student graduates from elementary school to middle school and to high school, the number of hours of time spent helping him with homework should steadily come down. Parents should encourage children to be able to handle their work  on their own (to the extent possible), and look for help only when it is absolutely essential.

One positive method of helping children with homework is to position oneself as a dependable resource to answer specific questions. Parents should make an effort to answer the child’s questions. In addition, parents may wish to consider engaging a tutor to fill in knowledge gaps and plan the student’s work.

However, under no circumstances should parents do any part of the child’s homework, such as project work, even if it helps them receive high grades or accolades. When parents do some part of the child’s homework, the child will begin to increasingly depend on parental assistance. The child would begin to expend less and less physical and mental effort on homework. Also, when an elder sibling does a child’s homework, it would be unfair to the other children in the class who would be taking pains to do the work on their own, as they may not get the high grades or accolades that they rightfully deserve. The student would miss out in terms of learning about the importance of ‘fair play’ in life, and could also damage a student’s self confidence. That would be a setback in the growth and development of the student.

# When does “homework help” cross the line and become “cheating”?

Thursday, November 19th, 2009

It is quite common for friends and relatives of a student to help him or her with homework. Getting homework help in order to do homework is generally not considered cheating. In fact, it is considered essential in many cases.  Some students use study guides to to help them with their homework. So, if all these sources of assistance are considered necessary, when does it cross the line to become cheating?

Let’s look at the case of family members (e.g.  parent or elder siblings) helping out with a student homework. When the teacher explicitly states that certain work has to be done by the student, without the help of anyone else, getting help would definitely be cheating. Even if there is no one to monitor whether the student has taken the help of others or not, a teacher who knows the student well can often tell whether he or she has received help.

There are other potential forms of cheating with respect to homework. These include getting answers from homework guides, getting answers from older students who have done the same homework in a previous year, etc. In all these cases, there is little in the ‘legal’ sense to say that one has cheated. Rather the difference is subtle. In most cases, the choice is left to the student, who has the option of using or not using a source of superior information. Using such superior sources of information, which are not available to others, might be considered cheating. Teachers should monitor the quantum of help that each of their students get, and take that into account when assigning grades.

When does “homework help” cross the line and become “cheating”?

Generally, parents/elder siblings help out children/younger siblings with their homework. Taking the help of these elders to do proper and error-free homework is not considered cheating. In fact, it is considered essential in most instances. Even teachers monitor the quantum of assistance given by the elders in the family to the children. Sometimes, children are required to use the Internet to do their homework. So, if all these sources of assistance are considered necessary, when does it cross the thin line to become cheating?

Let’s look at the case of parents/elder siblings helping out with the homework of their children/younger siblings, which slips into the realm of cheating. Where the teacher explicitly states that certain work has to be done by the student, without the help of anyone else, in such cases taking the help of others would definitely be cheating. This is so, since there is no one to monitor whether the student has taken the help of others or not.

In the case where the student has to take the help of the Internet to gather certain information and draw his or her own conclusions from the information, if the student takes the help of the Internet to find out the optimum conclusion, it would be termed as cheating.

There are various other forms of cheating in ‘homework’. These include getting answers from Guides, getting answers from older batches that have done the same work in the previous year, el al.

In all these cases, there is little in the ‘legal’ sense to say or charge that one has cheated. Rather the difference is subtle. In most cases, the choice is left to the student who has the option of using or not using a source of superior information, which is not be available to other students of his/her batch. Using such superior source of information, which is not available to others, would be considered cheating.