Scan and Solve with PhotoMath

PhotoMath is a new app which allows users to scan a math expressions or equations using a phone camera in real time and solve them. As of this writing, the supported expressions/equations are the arithmetic operations (+, -, ×,÷), fractions, decimals, powers and roots, linear equations, powers and roots, quadratic equations, simple systems of linear equations. It also supports absolute value equations and inequalities. Below is a short introductory video about PhotoMath. PhotoMath from MicroBLINK on Vimeo. PhotoMath is available as an iOS, Android, Amazon and Windows Phone application.

Understanding the Concept of Inverse Functions

Let us consider the functions

f(x) = x^3  and g(x) = \sqrt[3]{x}.

The table on the left shows the ordered pairs (x,f(x)). We used f(x) and substitute them to x in the second table.

inverse functions

As we can see, all the values of g(x) are the same as those of x in the first table. For example,  if we have x = 3 in the first table, applying f, we get  27 as output. On the other hand, if we apply g to 27, the value returns to 3» Read more

Why the Area of a Rhombus is Half the Product of its Diagonals

A rhombus is a parallelogram with four congruent sides. Since it is a parallelogram, it has also all the properties of a parallelogram. One of these properties is that the diagonals bisect each other. That is, they divide each other into two equal parts.

Another property of a rhombus is that the diagonals are perpendicular. So, summarizing all the properties above, if we have rhombus ABCD, then,

\overline{AB} \cong \overline{BC} \cong \overline{CD} \cong \overline{DA}.

and

\overline{AC} \perp \overline{BD}. » Read more

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