Ex 11.1, 5 - Chapter 11 Class 8 Direct and Inverse Proportions

Transcript

Ex 11.1, 5 A photograph of a bacteria enlarged 50,000 times attains a length of 5 cm as shown in the diagram. What is the actual length of the bacteria? If the photograph is enlarged 20,000 times only, what would be its enlarged length?Given, Length of bacteria is 5 cm if its photograph is enlarged 50,000 times Finding the actual length of bacteria Let the actual length of bacteria = x cm Since bacteria is englarged 50,000 times to 5 cm 50,000 × Actual Length = 5 cm 50,000 × 𝑥 = 5 𝒙 = 𝟓/(𝟓𝟎,𝟎𝟎𝟎) cm 𝑥 = 1/10,000 cm 𝑥 = 1/(10^4 ) cm 𝒙 = 𝟏 × 〖𝟏𝟎〗^(−𝟒) cm ∴ Actual length of bacteria is 𝟏×〖𝟏𝟎〗^(−𝟒) cm Now, our question is If the photograph is enlarged 20,000 times only, what would be its enlarged length? Finding the enlarged length Now, given that Length of bacteria is 5 cm if its photograph is enlarged 50,000 times Let y cm be the length of bacteria if the photograph is enlarged 20,000 times Thus, our table looks like As photograph is enlarged, The length of bacteria also increases, ∴ Length and enlarged photograph are in direct proportion. (𝟓𝟎,𝟎𝟎𝟎)/𝟓 = (𝟐𝟎,𝟎𝟎𝟎)/𝒚 10,000 = 20,000/𝑦 10,000 = 20,000/𝑦 10,000×𝑦 = 20,000 𝑦 = 20,000/10,000 𝒚 = 𝟐 ∴ The enlarged length of bacteria = 2 cm