Question

11) Fishing is a serious environmental issue. It has been determined by the scientists that if the net of a trawler has mesh size x cm by x (square mesh) then the percentage of fish entering the net that is caught in the net is (100-0.02x^2-0.05x). For example, if the mesh size is zero 100% of the fish that enters the net will be caught. The trawler with the net with a square mesh that was suspected of using an illegal size net dropped its net to the ocean near the damans and coast guard officials arrested the crew. The scientists later looked at the size of the fish caught and estimated that the net used by the trawler at least 97.93% of the fish entering the net would be caught. What is the maximum value of x for the net by the trawler?a. 8.5b.9c. 11d. None of the answers

Answer 1

Answer:

The maximum value of x is 9 cm

Explanation:

Given the expression for the percentage of fish caught in the net of size x cm by x cm

$P=100-0.02x^2-0.05x$

When 97.93 % of fish is caught then

P = 97.93

Therefore

$97.93= 100-0.02x^2-0.05x$

or, $0.02x^2+0.05x= 2.07$

$\implies 2x^2+5x= 207$

$\implies 2x^2+5x-207=0$

$\implies 2x^2+23x-18 x-207=0$

$\implies x(2x+23)-9(2x+23) =0$

$\implies (2x+23)(x-9) =0$

$\implies x=9, -23/2$

But x cannot be negative

Therefore, x = 9

Therefore, the value of x is 9cm