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RideAnS [48]
3 years ago
8

1.12. the time rate of change of an alligator population p in a swamp is proportional to the square of p. the swamp contained a

dozen alligators in 1988, and two dozen in 1998. when will there be four dozen alligators in the swamp? what happens thereafter?

Mathematics
1 answer:
yaroslaw [1]3 years ago
6 0
<h3>Given</h3>

p'(t) = kp²

p(0) = 12; p(10) = 24

<h3>Find</h3>

a) p(t)

b) t such that p(t) = 48

c) the behavior of p(t) after the time of part b

<h3>Solution</h3>

a) The differential equation is separable, so can be solved by separating the variables and integrating.

\displaystyle\frac{d}{dt}p(t)=k\cdot p(t)^{2}\\\\\int{p^{-2}}\,dp=\int{k}\,dt\\\\-p^{-1}=kt+C\\\\p=\frac{-1}{kt+C}

Plugging in the given boundary conditions, we can solve for k and C to find

p(t)=\dfrac{240}{20-t}

b) The population doubles when the time to t=20 is cut in half. The first doubling occurred in 10 years; the second one will occur in half that time, 5 years. There will be 48 alligators in the swamp in 2003.

c) The population doubles again in half the time of the previous doubling, so is predicted to be infinite in 2008.

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PLEASE HELP!
Alexandra [31]

its the first one because for example [-12] and 4

the absolute value of -12 is 12 so its greater

8 0
3 years ago
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Vinil7 [7]
Real and rational and integer?
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3 years ago
Find the volume of the cubes or rectangular prisms in cubic centimeters.
DanielleElmas [232]

a) Volume of Rectangular prism is \frac{36}{125}\,\,cm^3

b) Volume of cube is \frac{8}{125}\,\,cm^3

c) Volume of cube is \frac{1}{125}\,\,cm^3

d) Volume of Rectangular prism is \frac{6}{125}\,\,cm^3

Step-by-step explanation:

Part a)

Volume of rectangular prism with

length= \frac{3}{5}\,\,cm

width= \frac{4}{5}\,\,cm

height = \frac{3}{5}\,\,cm

The formula used to find Volume of rectangular prism is:

Volume\,\,of\,\,rectangular\,\,prism=length*width*height

Putting values:

Volume\,\,of\,\,rectangular\,\,prism=\frac{3}{5} *\frac{4}{5} *\frac{3}{5}\\Volume\,\,of\,\,rectangular\,\,prism=\frac{36}{125}\,\,cm^3

So, Volume of Rectangular prism is \frac{36}{125}\,\,cm^3

Part b)

Volume of cube with side length of \frac{2}{5}\,\,cm

The formula used to find Volume of cube is:

Volume\,\,of\,\,cube=length^3

Putting value of length and finding volume:

Volume\,\,of\,\,cube=length^3\\Volume\,\,of\,\,cube=(\frac{2}{5})^3\\ Volume\,\,of\,\,cube=\frac{8}{125}\,\,cm^3

So, Volume of cube is \frac{8}{125}\,\,cm^3

Part c)

Volume of cube with side length of \frac{1}{5}\,\,cm

The formula used to find Volume of cube is:

Volume\,\,of\,\,cube=length^3

Putting value of length and finding volume:

Volume\,\,of\,\,cube=length^3\\Volume\,\,of\,\,cube=(\frac{1}{5})^3\\ Volume\,\,of\,\,cube=\frac{1}{125}\,\,cm^3

So, Volume of cube is \frac{1}{125}\,\,cm^3

Part d)

Volume of rectangular prism with

length= \frac{1}{5}\,\,cm

width= \frac{2}{5}\,\,cm

height = \frac{3}{5}\,\,cm

The formula used to find Volume of rectangular prism is:

Volume\,\,of\,\,rectangular\,\,prism=length*width*height

Putting values:

Volume\,\,of\,\,rectangular\,\,prism=\frac{1}{5} *\frac{2}{5} *\frac{3}{5}\\Volume\,\,of\,\,rectangular\,\,prism=\frac{6}{125}\,\,cm^3

So, Volume of Rectangular prism is \frac{6}{125}\,\,cm^3

Keywords: Volume

Learn more about Volume at:

  • brainly.com/question/6443737
  • brainly.com/question/12497249
  • brainly.com/question/12613605

#learnwithBrainly

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3 years ago
The average person laughs 15 times per day.
drek231 [11]
Really? i didn’t know.
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3 years ago
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The half-life of the isotope Osmium-183 is 12 hours. Choose the equation below that gives the remaining mass of Osmium-183 in gr
raketka [301]

The given equations are incomprehensible, I'm afraid...

You're given that osmium-183 has a half-life of 12 hours, so for some initial mass <em>M</em>₀, the mass after 12 hours is half that:

1/2 <em>M</em>₀ = <em>M</em>₀ exp(12<em>k</em>)

for some decay constant <em>k</em>. Solve for this <em>k</em> :

1/2 = exp(12<em>k</em>)

ln(1/2) = 12<em>k</em>

<em>k</em> = 1/12 ln(1/2) = - ln(2)/12

Now for some starting mass <em>M</em>₀, the mass <em>M</em> remaining after time <em>t</em> is given by

<em>M</em> = <em>M</em>₀ exp(<em>kt </em>)

So if <em>M</em>₀ = 590 g and <em>t</em> = 36 h, plugging these into the equation with the previously determined value of <em>k</em> gives

<em>M</em> = 590 exp(36<em>k</em>) = 73.75

so 73.75 ≈ 74 g of Os-183 are left.

Alternatively, notice that the given time period of 36 hours is simply 3 times the half-life of 12 hours, so 1/2³ = 1/8 of the starting amount of Os-183 is left:

590/8 = 73.75 ≈ 74

6 0
3 years ago
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