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Marianna [84]
2 years ago
12

5. find the missing value (s) so that the line segments are parallel.

Mathematics
1 answer:
Nastasia [14]2 years ago
3 0
The missing value will be (9,5)
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Suppose a population of rodents satisfies the differential equation dP 2 kP dt = . Initially there are P (0 2 ) = rodents, and t
WINSTONCH [101]

Answer:

Suppose a population of rodents satisfies the differential equation dP 2 kP dt = . Initially there are P (0 2 ) = rodents, and their number is increasing at the rate of 1 dP dt = rodent per month when there are P = 10 rodents.  

How long will it take for this population to grow to a hundred rodents? To a thousand rodents?

Step-by-step explanation:

Use the initial condition when dp/dt = 1, p = 10 to get k;

\frac{dp}{dt} =kp^2\\\\1=k(10)^2\\\\k=\frac{1}{100}

Seperate the differential equation and solve for the constant C.

\frac{dp}{p^2}=kdt\\\\-\frac{1}{p}=kt+C\\\\\frac{1}{p}=-kt+C\\\\p=-\frac{1}{kt+C} \\\\2=-\frac{1}{0+C}\\\\-\frac{1}{2}=C\\\\p(t)=-\frac{1}{\frac{t}{100}-\frac{1}{2}  }\\\\p(t)=-\frac{1}{\frac{2t-100}{200} }\\\\-\frac{200}{2t-100}

You have 100 rodents when:

100=-\frac{200}{2t-100} \\\\2t-100=-\frac{200}{100} \\\\2t=98\\\\t=49\ months

You have 1000 rodents when:

1000=-\frac{200}{2t-100} \\\\2t-100=-\frac{200}{1000} \\\\2t=99.8\\\\t=49.9\ months

7 0
2 years ago
16x&gt;2x-3<br> Solve the inequality for x and show the steps
Marysya12 [62]

Answer:

Step-by-step explanation:

16x > 2x - 3

Subtract 2x from both sides

14x > -3

Then divide; -3/14

3 0
3 years ago
Can someone please help me with this one question please??
Alenkasestr [34]
((5x2)+5.5+(6x3)+6.5+(7x5)+(7.5x4)+(8x4))/20
137/20
= 6.85
5 0
2 years ago
The transformation that can result in a figure that is NOT congruent to the original is:
ddd [48]
Dilation because the sides will not be the same size as the original
6 0
3 years ago
Read 2 more answers
Index notation simplify 4^9 x 4^3
LenKa [72]

Answer:

4^{12}

Step-by-step explanation:

Using the rule of exponents

a^{m} × a^{n} = a^{(m+n)} , then

4^{9} × 4^{3} = 4^{(9+3)} = 4^{12}

7 0
2 years ago
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