The fish population in a certain part of the ocean (in thousands of fish) as a function of the water's temperature (in degrees Celsius) is modeled by: P(x)=-2(x-9)^2+200
What is the maximum number of fish?

200 thousands

Step-by-step explanation:

The fish population in a certain part of the ocean (in thousands of fish) as a function of the water's temperature (in degrees Celsius) is modeled by:

P(x)=-2(x-9)^2+200

P(x) = -2(x - 9)² + 200

Differentiating

d(px)/dx  = -2 * 2(x - 9)

=> d(px)/dx  = -4(x - 9)

d(px)/dx  = 0

=> -4(x - 9)  = 0

=> x = 9

d²(px)/dx ² = -4  < 0

=> x = 9 will give maximum value

Maximum number of fish = 200 thousands

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step-by-step explanation:

y = 5x + 17

step-by-step explanation:

a perpendicular line will be the opposite reciprocal slope of the given equation.   the slope given is -1/5 so the opposite reciprocal is 5

find b:

7 = 5 (-2) + b

7 = -10 + b

17 = b

write equation

y = 5x + 17