{9-[8-(1/3+1/4)×6]}÷[8(1/3+1/2)×6]
1 answer:
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Answer:
a. attached graph; zero real: 2
b. p(x) = (x - 2)(x + 3 + 3i)(x + 3 - 3i)
c. the solutions are 2, -3-3i and -3+3i
Step-by-step explanation:
p(x) = x³ + 4x² + 6x - 36
a. Through the graph, we can see that 2 is a real zero of the polynomial p. We can also use the Rational Roots Test.
p(2) = 2³ + 4.2² + 6.2 - 36 = 8 + 16 + 12 - 36 = 0
b. Now, we can use Briott-Ruffini to find the other roots and write p as a product of linear factors.
2 | 1 4 6 -36
1 6 18 0
x² + 6x + 18 = 0
Δ = 6² - 4.1.18 = 36 - 72 = -36 = 36i²
√Δ = 6i
x = -6±6i/2 = 2(-3±3i)/2
x' = -3-3i
x" = -3+3i
p(x) = (x - 2)(x + 3 + 3i)(x + 3 - 3i)
c. the solutions are 2, -3-3i and -3+3i
Cairo's cost is modeled by 45 + 24h
Tarantino's is modeled by 30h
For h = 6:
Cairo = 45 + 24*6 = 189
Tarantino = 180
For h = 7
Cairo = 45 + 24*7 = 213
Tarantino = 210
For h = 10
Cairo = 45 + 24*10 = 285
Tarantino = 300
Tarantino's is modeled by 30h
For h = 6:
Cairo = 45 + 24*6 = 189
Tarantino = 180
For h = 7
Cairo = 45 + 24*7 = 213
Tarantino = 210
For h = 10
Cairo = 45 + 24*10 = 285
Tarantino = 300