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4 years ago

For the function f(x) = −2(x + 3)2 − 1, identify the vertex, domain, and range.

Mathematics

1 answer:

Jet001 [13]4 years ago

4 0

Answer:

Vertex: (-3, -1)

Domain: All real numbers or (-∞, ∞)

Range: (-∞, -1]

Step-by-step explanation:

Quadratic Function: f(x) = a(bx - h)² + k

(h, k) is vertex

Step 1: Find vertex

f(x) = -2(x + 3)² - 1

h = -3

k = 1

Vertex = (-3, 1)

Step 2: Graph

When we graph, we should see our domain and range.

Domain is all x-values that can be inputted into the function.

Range is all y-values that can be outputted from the function.

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During optimal conditions, the rate of change of the population of a certain organism is proportional to the population at time

Lana71 [14]

Answer:

The population is of 500 after 10.22 hours.

Step-by-step explanation:

The rate of change of the population of a certain organism is proportional to the population at time t, in hours.

This means that the population can be modeled by the following differential equation:

$\frac{dP}{dt} = Pr$

In which r is the growth rate.

Solving by separation of variables, then integrating both sides, we have that:

$\frac{dP}{P} = r dt$

$\int \frac{dP}{P} = \int r dt$

$\ln{P} = rt + K$

Applying the exponential to both sides:

$P(t) = Ke^{rt}$

In which K is the initial population.

At time t = 0 hours, the population is 300.

This means that K = 300. So

$P(t) = 300e^{rt}$

At time t = 24 hours, the population is 1000.

This means that P(24) = 1000. We use this to find the growth rate. So

$P(t) = 300e^{rt}$

$1000 = 300e^{24r}$

$e^{24r} = \frac{1000}{300}$

$e^{24r} = \frac{10}{3}$

$\ln{e^{24r}} = \ln{\frac{10}{3}}$

$24r = \ln{\frac{10}{3}}$

$r = \frac{\ln{\frac{10}{3}}}{24}$

$r = 0.05$

$P(t) = 300e^{0.05t}$

At what time t is the population 500?

This is t for which P(t) = 500. So

$P(t) = 300e^{0.05t}$

$500 = 300e^{0.05t}$

$e^{0.05t} = \frac{500}{300}$

$e^{0.05t} = \frac{5}{3}$

$\ln{e^{0.05t}} = \ln{\frac{5}{3}}$

$0.05t = \ln{\frac{5}{3}}$

$t = \frac{\ln{\frac{5}{3}}}{0.05}$

$t = 10.22$

The population is of 500 after 10.22 hours.

7 0

3 years ago

Statements :

3241004551 [841]

Answer:

" $e^x$ is irrational for every nonzero integer x"

Step-by-step explanation:

The original statement is

" $e^x$ is rational for some nonzero integer x."

The negation is technically:

"It is NOT true that $e^x$ is rational for some nonzero integer x."

So it's expressing that it's false that $e^x$ can be rational for some nonzero integer x.

This just means that $e^x$ is always irrational when x is a nonzero integer.

Which can be worded as

" $e^x$ is irrational for every nonzero integer x"

4 0

3 years ago

Answer the question and answer it down below

Sergio039 [100]

Answer:

4:24 p.m.

Step-by-step explanation:

Figure out how often the buses leave at the same time. This is the same as the least common multiple (LCM) of how often they leave the stadium.

The LCM is found by multiplying the maximum number of each prime factor found in any of the numbers.

The prime factors of a number are found by dividing it by whole numbers until the factors are all prime. Prime numbers only have the factors 1 and itself.

6 = 2 X 3

8 = 2 X 2 X 2

The greatest times 2 repeats is three times.

The greatest times 3 repeats is one time.

2 X 2 X 2 X 3 = 24

The LCM is 24, and the buses have the same leaving times every 24 minutes.

Find 24 minutes after 4:00 p.m. Change the minutes only, which are the numbers right of the colon : .

The buses will next leave together at 4:24 p.m.

5 0

3 years ago

PLEASE HELP!!!!!!!!!! What is 2^4 AND <br> 3^5

shepuryov [24]

Answer:

2^4 is 16 and 3^5 is 243

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers

write a mixed number in simplest form to represent the number of pounds equivalent to each number of ounces . 66 oz = blank lb

sergiy2304 [10]

The answer would probably be 4 1/8 lb

5 0

3 years ago