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2 years ago

How many x intercepts does the polynomial function y=(x-8)(x+3)^2

Mathematics

1 answer:

guajiro [1.7K]2 years ago

4 0

Answer:

The answer is 2 x-intercepts

Step-by-step explanation:

To determine the x-intercepts we set y to zero and solve for x:

y=0

(x-8)(x+3)^2=0

The product of 2 factors is 0 means that one of them must be 0:

x-8=0 ⇒ x=8 →first x-intercept

or (x+3)^2=0 ⇒ x+3=0 ⇒ x=-3 →second x-intercept

Therefore the polynomial function two roots, so it has two x-intercepts x=8 and x=-3

Hope this helps :)

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At the beginning of a population study, the population of a large city was 1.65 million people. Three years later, the populatio

Maksim231197 [3]

Answer:

C. 1.8027

Step-by-step explanation:

The exponential population growth model is given by:

$P(t) = P_{0}e^{rt}$

In which P(t) is the population after t years, $P_{0}$ is the initial population and r is the growth rate.

At the beginning of a population study, the population of a large city was 1.65 million people. Three years later, the population was 1.74 million people.

This means that $P_{0} = 1.65, P(3) = 1.74$

Applying this to the equation, we find r. So

$P(t) = P_{0}e^{rt}$

$1.74 = 1.65e^{3r}$

$e^{3r} = \frac{1.74}{1.65}$

$e^{3r} = 1.0545$

Applying ln to both sides

$\ln{e^{3r}} = \ln{1.0545}$

$3r = \ln{1.0545}$

$r = \frac{\ln{1.0545}}{3}$

$r = 0.0177$

$P(t) = 1.65e^{0.0177t}$

What would be the population of the city 5 years after the start of the population study?

This is P(5).

$P(t) = 1.65e^{0.0177t}$

$P(5) = 1.65e^{0.0177*5}$

$P(5) = 1.8027$

So the correct answer is:

C. 1.8027

6 0

3 years ago

Between 1896—when the Dow Jones index was created— and 2012, the index rose in 65% of the years. Based on this information, and

forsale [732]

Answer:

a) P(x) = 0.67

b) P(y) = 0.67

c) P(x=4) = 0.3325

d) P( x = 0 ) = 0.0039

e) The fact that the rise and fall of the stock market relies on market sentiments violates independence used in Binomial distribution and the years are independent

Step-by-step explanation:

A) The probability that the stock market will rise next year = P(x) = 0.67

assuming next year to be X

B) Probability that the stock market will rise the year after next year

= P(y) = 0.67 and this is because the probability is independent of that of the previous years

C) Probability that the stock market will rise in four of the next five years

= P(x=4) = 0.3325

D) probability that the stock market will rise in none of the next five years

= P( x = 0 ) = 0.0039

E) The fact that the rise and fall of the stock market relies on market sentiments violates independence used in Binomial distribution and the years are independent