Monica Capoor Solutions for Chapter: Enrichment Activities (Based on Chapters 20–25), Exercise 1: ENRICHMENT ACTIVITIES (Based on Chapters 20-25)

Factorize $3a^2+24a+36$.

Expressing $(3x+4y-z)(3x-4y-z)$ as a difference of two squares gives $(3\mathrm{x}-\mathrm{z}{)}^2-(\mathrm{k}{)}^2$. Find te value of $\mathrm{k}$.

What must be subtracted from $5a^3+3a^2+5a+3$ so that the resulting polynomial is exactly divisible by $a^2-2a+1$?

Vihaan rides a scooter at a constant speed of $45 \mathrm{km}/\mathrm{h}$. Draw a time-distance graph for this situation. Use it to find the time taken by Vihaan to cover $180 \mathrm{km}$.

Vihaan rides a scooter at a constant speed of $45 \mathrm{km}/\mathrm{h}$. Draw a time-distance graph for this situation. Use it to find the distance covered by Vihaan in $2 \mathrm{hours} 12 \mathrm{minutes}$.

Draw a graph for simple interest vs time, when principal and rate of interest is fixed.

Draw a graph for simple interest vs rate of interest, when time and principal are fixed.

The magic hexagon given in the figure below has a total of $19$ hexagons within it.

All sets of $3, 4$ and $5$ hexagons in a row add up to $38$. Fill in the missing figures. No number should be repeated.