4.09.2016

The equation a fraction

What if the equation of lead shot, and X is hidden in the denominator? We need to get rid of the denominator. What will happen with X? Do not worry. If you do everything correctly, he from the denominator goes into the numerator. Here you can recommend two ways to solve the equation.

The first method is to bring the expression to normal proportions. Then we use the proportion of the property - the multiplication of extreme terms in proportion equal to the multiplication of the average proportion of members. Denominator magically disappear. We get a simple equation, which can be easily solved. Consider an example.

The equation a fraction. Mathematics For Blondes.
The equation a fraction

The number did not work nicely. Make checks and look at the result. Substitute the original expression instead of X its value.


Checking equation. The equation a fraction. Mathematics For Blondes.
Checking equation

The audit showed that the equation is solved correctly.

The second method is to bring the expression to a common denominator. The denominator should be common to the left and right sides of the equation. In this case, we in good conscience can throw the denominator in the trash. We see an example of reduction to a common denominator.

The equation a fraction. Method is to bring the expression to a common denominator. Mathematics For Blondes.
The equation a fraction
The result was the same as in the first case.

4.01.2016

Law of cosines in general

To present the law of cosines in general need to go back to the beginning. If the expression for one side of the triangle the length multiplied by the same hand n-times, the equation does not change.

Conversion formulas. Law of cosines in general. Mathematics For Blondes.
Conversion formulas

If you add equal to three sides of the triangle, we obtain the law of cosines in general.

Law of cosines in general. Mathematics For Blondes.
Law of cosines in general


The law of cosines in general terms describes the relationship between the sides and angles of a triangle in a multidimensional space. If the given equation is satisfied, then the triangle is in the Euclidean space. Options description triangle in curvilinear spaces require further study. For the correct application of the law of cosines in solid geometry, spherical triangles side length should be unit of measurement in the same units of measurement, which is measured in planimetrics.