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2 years ago

Please help me if you can

Mathematics

1 answer:

IRISSAK [1]2 years ago

8 0

Answer:

8π in

64π mm²

Step-by-step explanation:

The circumference of a circle is equal to 2πr, where r is the radius.

2π(4) = 8π ≈ 25.132

The area of a circle is equal to πr²

π(8)² = 64π ≈ 201.062

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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

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Answer:

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Step-by-step explanation:

Hey there!

This can be represented by an equation of a line, where the number of days is our x-values(d), and the price is our y-values(c).

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The points are (1, 45) and (4, 90).

We can first find the slope of the line:

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Please help me if you can ​

Please help me if you can