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3 years ago

Solve for y, z, x or t: x/m-x=n if m≠1

Mathematics

1 answer:

andriy [413]3 years ago

5 0

X^2, y ....................:/.....

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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

3 years ago

<img src="https://tex.z-dn.net/?f=5%20%7B%7D%5E%7Bn%20%2B%201%7D%20%20%2B%205%20%7B%7D%5E%7Bn%20%2B%202%7D%20" id="TexFormula1"

alex41 [277]

Step-by-step explanation:

there 5^(n+1) + 5^(n+2) = 5^n x 5^1 + 5^n x 5^2 breaking them as x^(a+b) = x^a x x^b

then taking common 5^n from both terms

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3 years ago

Which equation can be used to determine p, the cost of s swimsuits

ch4aika [34]

is there more to the question? because in order find "s" I need to know the question but a majority of the time you would multiply the amount of money the suit cost by the quantity.

Im a math intern.

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3 years ago

3(32 − 4 + 6 )− (82 + + 3) ?<br> simpilyfy<br> plzz

IrinaVladis [17]

Answer:

17 is your answer

Step-by-step explanation:

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3 years ago

Read 2 more answers

The sum of an infinite geometric series is 1,280, while the first term of the series is 160. What is the common ratio of the ser

Arlecino [84]

The sum is 160/(1-r)=1280 where r is the common ratio,
1/(1-r)=1280/160=8
Inverting we get 1-r=1/8, r=7/8.

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3 years ago