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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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Simplify<br><br> a+a+a=<br> 4b-b<br> 3x2+x2
Reika [66]
<h2>Good morning,</h2>

<em><u>__________________</u></em>

<em><u>Answer</u></em>:

a+a+a = 3a.

4b-b = 3b.

3x²+x² = 4x².

<u><em>explanation</em></u>

a+a+a = 3a.

4b-b = b(4 - 1) = b × 3 = 3b.

3x²+x² = x²(3 + 1) = x² × 4 = 4x².

_______________________________

:)

7 0
3 years ago
Li Na is going to plant 6363 63 tomato plants and 8181 81 rhubarb plants. Li Na would like to plant the plants in rows where eac
Whitepunk [10]

Answer: The greatest number of rows Li Na can plant is 9.


Step-by-step explanation:

Given: Li Na is going to plant 63 tomato plants and 81 rhubarb plants.

Li Na would like to plant the plants in rows where each row has the same number of tomato plants and each row has the same number of rhubarb plants.

To find the greatest number of rows Li Na can plant, we need to find the GCF of 63 and 81.

Since , 63=7\times9\ and\ 81=8\times9

Clearly, GCF(63,81)=9

Therefore, the greatest number of rows Li Na can plant is 9.

6 0
2 years ago
The cast of the play makes 275 programs for 5 shows. How many programs will be needed for 13 shows?
Advocard [28]
715 because 275/5= 55 then 55x13 will give you 715
8 0
3 years ago
If 3 is added to a number and multiplied the result by 5 gives 55 what is the number​
MakcuM [25]

Answer:24

Step-by-step explanation:Let the number we seek be X.

We are Given:

1). (5X+3 ) x (2) = 30

Expand and Rearrange.

(10X +6 ) = 30.

10X = 24.

2). X equals 2.4 . This is the answer for the number we seek.

Always check the answer.

This is Good Working Practice ALWAYS.

For Exams or similar remember:

Presentation (Neat & Tidy), Method & Layout (Show you understand), Accuracy.

All these count in most exams.

The first two points help greatly if your Answer is in error, but your METHOD Is CLEAR & CORECT.

Similarly, if the Check is wrong, mention this, but also, if the case, mention e.g. time ran out .. You may be credited as AWARE if your presentation and Method show you understood what to do and why.

CHECK: Substitute the answer for X into the original equation 1).

Equn. 1). (5X +3)*2 = 30.

Put in the value for X. Expand & Re-arrange.

(( 5 ).( 2.4 ) + ( 3 ).( 2 ) = 30.

( 12 + 6 ) = 30.

24 = 24. Checked & Agreed.

That’s about it.

6 0
3 years ago
What is the equation of a line that is parallel to y=2/3x+4 and passes through the point (3,7)
jeka57 [31]

Answer:

y=2/3x+5

Step-by-step explanation:

Parallel lines share the same slope so we already know the slope: 2/3.

Now we need to find the y-intercept for the equation. To do that, replace 4 with b. We have y=2/3x+b.

To find out what b is, we need to plug in the x and y values we are given into the current equation. We get 7=2/3(3)+b.

7=2+b

5=b

Now we can put all the information we have together.

y=2/3x+5

8 0
3 years ago
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