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In what ways is the Pythagorean Theorem useful?
In real life its not useful, unless you're going to need geometry in the career you choose.
What is real life application of Basic proportionality theorem?
I guess, the BPT is used in Tiles & Painting and so on... It can be useful as paintings, tiles & many other things as such require precision & BPT helps to make sure that its in proportional. The theorem states that when a line is drawn parallel to one side of the triangle (inside it) it divides the other two sides of the same triangle in equal proportions. Similar is the Converse and it proves true. BPT stands for Basic Proportionality Theorem & was discovered by Thales. I hope this satisfies your question.
Why was algebra invented?
Algebra is a tremendously useful mathematical tool, without which modern science and technology would not have been possible. Algebra was invented as a tool for solving mathematical problems, and it has proved to be tremendously useful. Modern technology as we know it would have been impossible without the use of algebra. +++ More accurately, algebra is the set of symbols and rules used to construct mathematics. It is not a calculating tool to solve problems in its own right, but allows you to express the ways in which to solve those problems.
What is the analogy for utilitarian?
useful
Most useful for representing how one variable influences another variable?
A line graph is most useful for representing how one variable influences another variable.
