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2 years ago

PLEASE HELP!

Mathematics

1 answer:

Gennadij [26K]2 years ago

8 0

Answer:

x² + 6x + 9

Step-by-step explanation:

(x + 3)² = (x + 3)(x + 3)

Each term in the second factor is multiplied by each term in the first factor , that is

x(x + 3) + 3(x + 3) ← distribute parenthesis

= x² + 3x + 3x + 9 ← collect like terms

= x² + 6x + 9

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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

2 years ago

a railroad car container can hold 42,000 pounds. Mr.Evans wants to ship 90 ovens and some freezers in the same container. If eac

NeX [460]

The amount of freezers that can be shipped is 70. I'm not completely sure, because I do not know how many pounds the ovens are. But to get the answer, just simply divide 42000 by 600.

5 0

3 years ago

Read 2 more answers

A van travels 150 miles on 6 gallons of gas. How many gallons will it need to travel 325 miles?

shtirl [24]

<h3>Answer: C) 13 gallons</h3>

============================================================

Work Shown:

(150 miles)/(6 gallons) = (325 miles)/(x gallons)

150/6 = 325/x

150*x = 6*325 .... see note below

150x = 1950

x = 1950/150 .... divide both sides by 150

x = 13 gallons is the final answer

-----------

Note: in this step, I cross multiplied. The general template for cross multiplication is that we go from A/B = C/D to A*D = B*C. As the name implies, the "cross" refers to the "X" shape that forms when you multiply the terms.

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3 years ago

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If a= 2x - 3 and b= 2x+5<br> find the value of a+b <br> help pleaseeee i would really appreciate

Goshia [24]

Answer:

4x+2

Step-by-step explanation:

a= 2x - 3 and b= 2x+5

a+b = 2x-3 + 2x+5

Combine like terms

a+b = 4x+2

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1 year ago

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Percy use hose to wash pig sty for 11 minutes. The hose uses 7 liters of water every minute how many liters did percy pig use to

kykrilka [37]

Answer:

Percy used 77 liters to wash

Step-by-step explanation:

This question can be solved using a rule of three.

Each minute of washing costs 7 liters.

She washed for 11 minutes.

1 minute - 7 liters

11 minutes - x liters

x = 7*11 = 77

Percy used 77 liters to wash

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3 years ago