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3 years ago

Use the grouping method to factor this polynomial completely. 3x3 + 12x2 + 2x + 8

Mathematics

1 answer:

dezoksy [38]3 years ago

3 0

Answer:

(3x^2 + 2)(x + 4).

Step-by-step explanation:

3x3 + 12x2 + 2x + 8

3x^2(x + 4) + 2(x + 4) The x + 4 is common to the 2 groups so we have:

(3x^2 + 2)(x + 4).

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3 years ago

In this example we modeled the world population from 1900 to 2010 with the exponential function P(t) = (1436.53) · (1.01395)t wh

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Answer:

a) Rate of increase = 26.66 millions per year

b) Rate of increase = 42.64 millions per year

c) Rate of increase = 79.53 millions per year

Step-by-step explanation:

We are given that population is modeled with the exponential function:

$P(t) = (1436.53).(1.01395)^t$

where t = 0 corresponds to the year 1900 and P(t) is measured in millions.

Rate of increase of world population =

$\displaystyle\frac{d(a^x)}{dx} = a^xln(a)\\\\P'(t) = (1436.53)(1.01395)^tln(1.01395)\\\\P'(t) = (1436.53)ln(1.01395)(1.01395)^t$

a) 1920

$P'(1920-1900) = (1436.53)(ln(1.01395))(1.01395)^{(1920-1900)}\\P'(20) = (1436.53)(ln(1.01395))(1.01395)^{(20)}\\P'(20) \approx 26.66$

Rate of increase = 26.66 millions per year

b) 1955

$P'(1955-1900)=(1436.53)(ln(1.01395))(1.01395)^{(1955-1900)}\\P'(55) = (1436.53)(ln(1.01395))(1.01395)^{(55)}\\P'(55) \approx 42.64$

Rate of increase = 42.64 millions per year

c) 2000

$P'(2000-1900) = (1436.53)(ln(1.01395))(1.01395)^{(2000-1900)}\\P'(100) = (1436.53)(ln(1.01395))(1.01395)^{(100)}\\P'(100) \approx 79.53$

Rate of increase = 79.53 millions per year

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2 years ago