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Soloha48 [4]
2 years ago
10

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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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
3 years ago
Find the sum of 5m 3n p, -5p 3n, and 2n - m. -4m 8n - 4p 4m 8n 4p 4m - 8n - 4p 4m 8n - 4p
Natali5045456 [20]
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The cost of renting a table at the flea market is based on a fixed price per day plus an initial registration fee. If it costs $
Simora [160]

Answer:

c = 15d + 30

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).

The price for one day ($45) and the price for 4 days($90) are specific points on that line.

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

We can first find the slope of the line:

  • As the price rises 45, the days increase by 3
  • Slope = rise/run
  • Slope = 45/3
  • Slope = 15

Now we can find the base price, by plugging the slope and a point into the equation y = mx + b.

Solve for b:

  • y = mx + b
  • 45 = 15(1) + b
  • 45 = 15 + b
  • 30 = b

The base price (b) is 30.

The equation is \text{\boxed{c = 15d + 30}}

6 0
1 year ago
The graph below represents the distance a pilot is from the home airport during a period of time. A graph titled Pilot's Distanc
Simora [160]

Answer:

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Step-by-step explanation:

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The answer is

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