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3 years ago

I need help on this question

Mathematics

2 answers:

kompoz [17]3 years ago

5 0

Answer: A

Step-by-step explanation:

topjm [15]3 years ago

4 0

Answer:

Step-by-step explanation:

so you would want to get y on the same side for both systems.

for x + y = 3, you subtract x from both sides and get y = -x +3.

then you do the other one. 5x + 5y = 15. subtract 5 x from both sides.

5y= -5x + 15. then divide both sides by 5. y = -x +3. this means these two systems are referring to the same line. in this case, there are infinitely many solutions. so, answer c.

for no solutions, you would have parallel lines (lines with the same slope)

and for one solution, you would have two lines that intersected at one point

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GuDViN [60]

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

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

$y=200(2.718)=543.6=543.6$

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