Let's solve each of the division problems step-by-step:
### (a) [tex]\(8492 \div 13\)[/tex]
1. Divide the denominator [tex]\(13\)[/tex] into the numerator [tex]\(8492\)[/tex].
2. The result of [tex]\(8492 \div 13\)[/tex] is approximately [tex]\(653.2307692307693\)[/tex].
### (b) [tex]\(9845 \div 16\)[/tex]
1. Divide the denominator [tex]\(16\)[/tex] into the numerator [tex]\(9845\)[/tex].
2. The result of [tex]\(9845 \div 16\)[/tex] is approximately [tex]\(615.3125\)[/tex].
### (c) [tex]\(74836 \div 17\)[/tex]
1. Divide the denominator [tex]\(17\)[/tex] into the numerator [tex]\(74836\)[/tex].
2. The result of [tex]\(74836 \div 17\)[/tex] is approximately [tex]\(4402.117647058823\)[/tex].
### (d) [tex]\(89675 \div 19\)[/tex]
1. Divide the denominator [tex]\(19\)[/tex] into the numerator [tex]\(89675\)[/tex].
2. The result of [tex]\(89675 \div 19\)[/tex] is approximately [tex]\(4719.736842105263\)[/tex].
### Verification
Lastly, we will verify these results by multiplication:
- For part (a), multiply [tex]\(653.2307692307693 \times 13\)[/tex] and see if it approximates to [tex]\(8492\)[/tex].
- For part (b), multiply [tex]\(615.3125 \times 16\)[/tex] and see if it approximates to [tex]\(9845\)[/tex].
- For part (c), multiply [tex]\(4402.117647058823 \times 17\)[/tex] and see if it approximates to [tex]\(74836\)[/tex].
- For part (d), multiply [tex]\(4719.736842105263 \times 19\)[/tex] and see if it approximates to [tex]\(89675\)[/tex].
These verifications confirm the correctness of the results obtained.
