What are the solutions to the inequality (x-3)(x+5)less than or equal to 0

-5 _> x  _< 3

Step-by-step explanation:

(x-3)(x+5)less than or equal to 0

(x -3)(x+5) <_ 0

x-3 _< 0  or x + 5_< 0

x _< 3  or x _<  -5

Therefore

-5 _> x  _< 3

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k = 1

P(t) = (t + 20)²

Step-by-step explanation:

P' = k√P = k P⁰•⁵

To solve for k,

P' = 10 rabbits/month

P = 100 rabbits

10 = k √100

10 = 10k

k = 1

To solve for P(t)

P' = dP/dt

(dP/dt) = kP⁰•⁵

dP/P⁰•⁵ = k dt

P⁻⁰•⁵ dP = k dt

∫ P⁻⁰•⁵ dP = ∫ k dt

2P⁰•⁵ = kt + c

At t = 0, P = 100

2(100)⁰•⁵ = 0 + c

2 × 10 = c

c = 20

2P⁰•⁵ = kt + c

2P⁰•⁵ = kt + 20

Recall, k = 1

2P⁰•⁵ = t + 20

P⁰•⁵ = (t + 20)

P(t) = (t + 20)²