30% of the water consumption is industrial use and 11% is personal use so (30% - 11%) = 19% more water is used for industrial purposes. 35,000 gallons are consumed daily so industry consumes \( \frac{19}{100} \) x 35,000 gallons = 6,650 gallons.

To divide terms with exponents, the base of both exponents must be the same. In this case they are so divide the coefficients and subtract the exponents:

\( \frac{-5y^7}{9y^3} \)
\( \frac{-5}{9} \) y^{(7 - 3)}
-\(\frac{5}{9}\)y⁴

To simplify a radical, factor out the perfect squares:

\( \sqrt{32} \)
\( \sqrt{16 \times 2} \)
\( \sqrt{4^2 \times 2} \)
4\( \sqrt{2} \)

Use PEMDAS (Parentheses, Exponents, Multipy/Divide, Add/Subtract):

4 + (4 + 3) ÷ 2 x 2 - 3²
P: 4 + (7) ÷ 2 x 2 - 3²
E: 4 + 7 ÷ 2 x 2 - 9
MD: 4 + \( \frac{7}{2} \) x 2 - 9
MD: 4 + \( \frac{14}{2} \) - 9
AS: \( \frac{8}{2} \) + \( \frac{14}{2} \) - 9
AS: \( \frac{22}{2} \) - 9
AS: \( \frac{22 - 18}{2} \)
\( \frac{4}{2} \)
2

To simplify this fraction, first find the greatest common factor between them. The factors of 20 are [1, 2, 4, 5, 10, 20] and the factors of 68 are [1, 2, 4, 17, 34, 68]. They share 3 factors [1, 2, 4] making 4 their greatest common factor (GCF).

Next, divide both numerator and denominator by the GCF:

\( \frac{20}{68} \) = \( \frac{\frac{20}{4}}{\frac{68}{4}} \) = \( \frac{5}{17} \)