Problem 1 - The Square Root of 2 For any square, the Pythagorean Theorem reveals that the ratio between its diagonal and side length is Root 2. In the diagram below, this means that D/a = Root 2.

a) Using the Pythagorean theorem, mathematically prove that D/a = Root 2 for any square with side length a and diagonal length D.

b) Use a ruler to measure a and D. Write your measurements in your solution, and explain how you chose how many digits to report for each measurement.

c) Use your measurements to estimate the value of Root 2.

In the nineteenth century, gregor mendel first determined some basic rules of genetics that have been observed throughout all types of life. no observations have disproved these basic rules of genetics. charles darwin developed the idea of biological evolution around the same time, but he was unaware of mendel’s discoveries in genetics. over a century later, darwin’s idea of evolution was modified in order to incorporate mendel’s rules of genetics along with the other evidence that darwin had used. what is most likely the relationship between mendel’s rules of genetics and darwin’s idea of biological evolution? a.)mendel’s genetics states laws that are now part of the theory of biological evolution. b.)biological evolution states laws that are part of mendel’s theory of genetics. c.)mendel’s genetics replaced darwin’s entire concept of biological evolution. d.)biological evolution is a law that explains why all genetics exist.