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allsm [11]
3 years ago
15

No links or weird answers, please :(

Mathematics
1 answer:
garri49 [273]3 years ago
8 0
No because the x does not go with the y
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A solution initially contains 200 bacteria. 1. Assuming the number y increases at a rate proportional to the number present, wri
GuDViN [60]

Answer:

1.\frac{dy}{dt}=ky

2.543.6

Step-by-step explanation:

We are given that

y(0)=200

Let y be the number of bacteria at any time

\frac{dy}{dt}=Number of bacteria per unit time

\frac{dy}{dt}\proportional y

\frac{dy}{dt}=ky

Where k=Proportionality constant

2.\frac{dy}{y}=kdt,y'(0)=100

Integrating on both sides then, we get

lny=kt+C

We have y(0)=200

Substitute the values then , we get

ln 200=k(0)+C

C=ln 200

Substitute the value of C then we get

ln y=kt+ln 200

ln y-ln200=kt

ln\frac{y}{200}=kt

\frac{y}{200}=e^{kt}

y=200e^{kt}

Differentiate w.r.t

y'=200ke^{kt}

Substitute the given condition then, we get

100=200ke^{0}=200 \;because \;e^0=1

k=\frac{100}{200}=\frac{1}{2}

y=200e^{\frac{t}{2}}

Substitute t=2

Then, we get y=200e^{\frac{2}{2}}=200e

y=200(2.718)=543.6=543.6

e=2.718

Hence, the number of bacteria after 2 hours=543.6

4 0
4 years ago
−3(x + 3) = −3(x + 1) − 5
love history [14]
You have to simplify and then get x
5 0
3 years ago
Read 2 more answers
The diagram shows a solid metal cuboid.
Elodia [21]
Someone told me if I answer a question I can watch videos to unlock my answer sorry
3 0
3 years ago
Determine the price of a $35 basketball that is on sale for 50% off the regular price.
alexira [117]

Answer:

$17.5

Step-by-step explanation:

50 is 1/2 of 100, so just divide 35 by 1/2

6 0
3 years ago
PLEASE HELP ME
balandron [24]

9514 1404 393

Answer:

  • (3y)(2x^2 -1x -8xy +4y)
  • (3y)(x -4y)(2x -1)

Step-by-step explanation:

<u>Part A</u>: All of the coefficients have a common factor of 3. All of the variable products have a common factor of y, so the greatest common factor of all terms is 3y. The expression can be written as ...

  (3y)(2x^2 -1x -8xy +4y)

__

<u>Part B</u>: The remaining factor can be factored pairwise:

  3y(x(2x -1) -4y(2x -1)) = 3y(x -4y)(2x -1)

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3 years ago
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