To multiply terms with radicals, multiply the coefficients and radicands separately:

3\( \sqrt{8} \) x 5\( \sqrt{7} \)
(3 x 5)\( \sqrt{8 \times 7} \)
15\( \sqrt{56} \)

Now we need to simplify the radical:

15\( \sqrt{56} \)
15\( \sqrt{14 \times 4} \)
15\( \sqrt{14 \times 2^2} \)
(15)(2)\( \sqrt{14} \)
30\( \sqrt{14} \)

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:

\( \frac{-7c^5}{4c^2} \)
\( \frac{-7}{4} \) c^{(5 - 2)}
-1\(\frac{3}{4}\)c³

If the tiger has consumed 36 pounds of food in 6 days that's \( \frac{36}{6} \) = 6 pounds of food per day. The tiger needs to consume 60 - 36 = 24 more pounds of food to reach 60 pounds total. At 6 pounds of food per day that's \( \frac{24}{6} \) = 4 more days.

The area of a rectangle is width (w) x height (h). In this problem we know that the rectangle is twice as long as it is wide so h = 2w. The perimeter of a rectangle is 2w + 2h and we know that the perimeter of this rectangle is 6 meters so the equation becomes: 2w + 2h = 6.

Putting these two equations together and solving for width (w):

2w + 2h = 6
w + h = \( \frac{6}{2} \)
w + h = 3
w = 3 - h

From the question we know that h = 2w so substituting 2w for h gives us:

w = 3 - 2w
3w = 3
w = \( \frac{3}{3} \)
w = 1

Since h = 2w that makes h = (2 x 1) = 2 and the area = h x w = 1 x 2 = 2 m²

30% of the water consumption is industrial use and 12% is personal use so (30% - 12%) = 18% more water is used for industrial purposes. 10,000 gallons are consumed daily so industry consumes \( \frac{18}{100} \) x 10,000 gallons = 1,800 gallons.