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Cos 2x=0.32
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:
Is this funtion linear? if so, rewrite in y=b+mx. g(w)= 1-12w/3
Solution:
- g(w)=1-12w/3
- g(w)=1 + (-4)w
- In the above example, y=g(w), b=1 and m=-4. If we replace each of the terms we can rewrite the above as y=b+mx
What is the difference b/w relation and function. It would be great if you could give some real life example.
Solution:
A relation is a set of ordered pairs, such as { (0,1) , (55,22), (3,-50) } (http://www.mathwarehouse.com/algebra/relation/math-function.php). A function is a special kind of relation in which each x value has only one y value.
For example:
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?
Solution:
- Start with 48
- Lost 6 (1/8 of 48 =s 6)
- Gave 8 to a friend (1/6 of 48 is 8)
- 48 – 6 – 8
- = 48 – 14
- = 34
Has to do with triangle, saw of cosine and sin, etc. I have to draw a polygon with 6-10 sides, and provide enough info for someone to be required to find 3 or more missing angles and 3 or more missing sides. Solve and find the area of the polygon.
Solution:
We’ll try the case of a six-sided polygon and will show that if we provide 3 angles, 3 sides and 5 spokes, we can expect someone to figure out the size of the three unknown angles and the lengths of the three unknown sides.
Here’s an example of a six-sided polygon, an irregular hexagon:
As you can see, this is an irregular shape – it’s not a regular hexagon where the sides and angles are of the same size.
Let’s now draw a central point and spokes, where you know the length of each spoke and all but one of the angles between the spokes:
You can calculate the unknown angle (we can call it “F”) because we know that all the angles need to add up to 360° (F = 360 – A – B – C – D – E). Since we know the length of two sides and one angle of each triangle that is formed (i.e. side-angle-side, … read more
Is this funtion linear? if so, rewrite in y=b+mx. g(w)=-12w/3
- g(w)=1-12w/3
- g(w)=1+(-4)w
- In the above example, y=g(w), b=1 and m=-4. If we replace each of the terms we can rewrite the above as y=b+mx
With Calculus Tutoring boost your child’s learning capabilities
It has been observed that with gradual increase in the burden of studies, children start lacking in grasping math concepts and formulae. The level of studies start becoming difficult as the child reaches the higher grades. Concepts such as calculus and trigonometry are always found to be difficult for students to understand at the first go. This is where online assistance of calculus tutoring helps students a lot with making them grasp these difficult looking concepts easily.
Studying calculus is considered to be vital for any field. Be it engineering or any other field of science, calculus somehow links to life of everybody. Only learning the formulae and solving the problems does not help in the long run and it should be done for understanding the concept. Calculus tutoring is what helps in understanding the basics of Calculus. The approach followed here is to make student grasp the fundamentals of calculus in interesting and interactive ways so that he does not forget them easily … read more
Online Homework Help is Not Cheating
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 … read more
How much homework help from friends and family is appropriate?
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 … read more
When does “homework help” cross the line and become “cheating”?
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 … read more
-2x < 3/7
Solution:
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languageChangeHandler: function(defaultev) { var dropdown = document.getElementById('languageDropDown'); var selOpt = dropdown.options[dropdown.selectedIndex]; var selectedLang = selOpt.value; if (!selectedLang.match("Turn")) { Transliterate.transliterationControl.setLanguagePair(google.elements.transliteration.LanguageCode.ENGLISH, selectedLang); Transliterate._controlDiv.title = 'Type in '+selOpt.title + '. Click on the checkbox to turn on/off the language setting.'; if(!defaultev){ Transliterate.setCookie('Transliterate_LANG', selectedLang); } Transliterate.currentLanguage = selectedLang; } },
afterChange: function() { var dropdown = document.getElementById('languageDropDown'); var selOpt = dropdown.options[dropdown.selectedIndex]; var selectedLang = selOpt.value; if (selectedLang.match… read more
What is the Volume of a Sphere the Radius of Six?
Solution:
- The formula for the volume of a sphere is
- r = 6
- =
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languageChangeHandler: function(defaultev) { var dropdown = document.getElementById('languageDropDown'); var selOpt = dropdown.options[dropdown.selectedIndex]; var selectedLang = selOpt.value; if (!selectedLang.match("Turn")) { Transliterate.transliterationControl.setLanguagePair(google.elements.transliteration.LanguageCode.ENGLISH, selectedLang); Transliterate._controlDiv.title = 'Type in '+selOpt.title + '. Click on the checkbox to turn on/off the language setting.'; if(!defaultev){ Transliterate.setCookie('Transliterate_LANG', selectedLang); } Transliterate.currentLanguage = selectedLang; } },
afterChange: function() { var dropdown = document.getElementById('languageDropDown'); var selOpt … read more
What is an Inverse Function?
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.… read more
Work out the grap y =x^-3
