# Tutor profile: Rajasekhara K.

## Questions

### Subject: Geometry

Find the area of a triangle that is inscribed in a circle having its diameter as one of its sides. The area of the circle is 25$$\pi$$ and one of the sides of the triangle inscribed is 8?

This problem can be solved by using geometric axiom "The triangle inscribed in a semi-circle is always a right-angled triangle and the diameter of the semi-circle is the hypotenuse". Using the area of the circle given, we can calculate the radius and diameter of the circle. Therefore, area of circle is given by A= $$\pi$$*r$$^2$$, where 'r' is the radius of the circle. Therefore, 25$$\pi$$=$$\pi$$ $$*r^{2}$$. This implies r=5 and diameter d= 2r= 2*5=10. The diameter of the circle will be the hypotenuse of the right angle triangle inscribed. Using pythagoras theorem, $$c^{2}$$= $$a^2 + b^2$$, Here 'c' is the hypotenuse 10, 'a' is the side of the triangle which is 8 and 'b' is the other side of the triangle. Therefore, using Pythagoras theorem, b= $$\sqrt({c^{2}- a^{2}}$$). Substituting the values of 'c' and 'a' in the above equation gives b = $$\sqrt({10^{2}- 8^{2}}$$)= 6 Therefore the sides of the triangle are 10 (hypotenuse), 6, and 4 of the triangle. For the right-angled triangle the two sides other than hypotenuse will become the base and height of the triangle. Therefore the area of the triangle can be calculated by using 0.5*base* height=0.5*6*4= 12. Therefore, the area of the triangle is 12.

### Subject: Biochemistry

What is the molecular weight of the microbial protein corresponding to the DNA of size 2376 base pairs?

Here the size of DNA is 2376 base pairs (bp). Since it is a microbial protein there is no chance of alternate splicing and intron deletions. So after transcription and post-transcriptional modifications size of mRNA remains same, which is 2376 bp. Each 3 bp of mRNA code for one amino acid. By this calculation, corresponding protein should contain (2376/3 = 792) 792 amino acids. However last 3 bp of mRNA, code for STOP codon to stop the reaction only and do not code for any amino acid. So, this protein contains only 791 amino acids. The average size of each amino acid out of 23 amino acids is 110 kilodalton (kDa). Therefore, the possible molecular weight of the protein is ( 110X 791) kDa, which is 87010 kDa.

### Subject: Biological Engineering

Which method among negative staining and simple staining gives you more accurate size and shape of microbes?

Negative staining gives you more accurate shape and size of microbes compare to simple staining. In simple staining basic dyes like crystal violet, methylene blue was used to stain the microbial cells. Microbial cell wall contains a bilipid layer which is a negative charge and basic dyes are positively charged. Due to the ionic attraction, the basic dye penetrates the cell wall and cells will be colored with the dye. Hence, because of dye penetration cells were visible little enlarged. However, acidic dyes were used in negative staining which is negatively charged. Due to the repelled nature, acidic dyes stain the background of the cells and cells were visible as it is. Therefore, in negative stain, the shape, and size of the cell is more accurate than the simple stain.

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