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Montano1993 [528]
3 years ago
12

What is the GCF for 52, 78

Mathematics
1 answer:
Feliz [49]3 years ago
7 0
The GCF means Greatest Common Factor. This is the highest possible factor that multiple numbers have in common.

For example, 5 and 10.

5 = 1 x 5
10 = 1 x 10, 2 x 5
They both have 5 as the highest common factor, so 5 is the GCF.

Now that I've broken down what GCF means, let's factor out our numbers.

52= 1 x 52, 2 x 26, 4 x 13.
78= 1 x 78, 2 x 39, 3 x 26, 6 x 13.

These numbers both have 13 as the highest number.

The GCF of 52 and 78 is 13.

I hope this helps!
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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

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