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3 years ago

Please help me with this

Mathematics

2 answers:

Inga [223]3 years ago

7 0

1. 23
2. 8 lbs
3. 4
4. 10 lbs

saveliy_v [14]3 years ago

6 0

23 pumpkins, 8 pounds, 4 pumpkins, 10 pounds.

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Aaron, Ben and Caleb all have grabbed some lollies from a jar. Ben has twice as

Thepotemich [5.8K]

Answer:

Aaron=12 Ben=24 Caleb=29

Step-by-step explanation:

Aaron=x

Ben=2x

Caleb=2x+5

x+2x+2x+5=65

5x+5=65

-5 on both sides

5x=60

divide by 5 on both sides

x=12

You then substitute this answer with ben and Caleb

ben= 2x (2*12) =24

caleb= 2x+5 (24+5)=29

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35 out of 100 play soccer...
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Answer:

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Step-by-step explanation:

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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