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4 years ago

How many 28 oz bottles make 1 gallon?

Mathematics

1 answer:

adell [148]4 years ago

5 0

There are 128 oz in a gallon. Take 128 and divide it by 28 (which equals 4.57 rounded to 2 decimal places )

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The population of mosquitoes in a certain area increases at a rate proportional to the current population, and in the absence of

Alexandra [31]

Answer:

Population of mosquitoes in the area at any time t is:

$P(t) =504,943.26 -104,943.26e^{0.693t}$

Step-by-step explanation:

assume population at any time t = P(t)

population increases at a rate proportional to the current population:

⇒dP/dt ∝ P

$\implies \frac{dP}{dt} =kP$ ----(1)

where k is constant rate at which population is doubled

solving (1)

$ln|P(t)|=kt +C\\P(t)= e^{kt+C}\\P(t)=Ce^{kt}$

$t=0\\P(0) = P_{o}\\\implies C= P_{o}\\P(t) =P_{o}e^{kt}\\$ ---- (2)

initial population = 400,000

population is doubled every week

⇒P(1)=2P(0)

Using (2)

$P_{o}e^{k(1)} = 2P_{o} e^{k(0)}\\$

$e^{k} =2\\k=ln|2|\\$

In presence of predators amount is decreased by 50,000 per day

Then amount decreased per week = 350,000

In this case (1) becomes

$\frac{dP}{dt}=kP-350,000\\\frac{dP}{dt} - kP=-350,000\\$ ---(3)

solving (3) by calculating integrating factor

$I.F=e^{\int-k dt}$

Multiplying I.F with all terms of (3)

$e^{-kt}\frac{dP}{dt} - ke^{-kt}P =-350,000 e^{-kt}\\\frac{d}{dt}(e^{-kt}P) = -350,000 e^{-kt}$

Integrating w.r.to t

$e^{-kt}P(t)= \frac{350,000e^{-kt}}{k} +C$

$P(t) =\frac{350,000}{k} +Ce^{kt}\\$

$k=ln|2| =0.693$

$P(t) =504,943.26 + Ce^{0.693t}\\$

at t=0

$P(0) =504,943.26 + Ce^{0.693(0)}$

$400,000 =504,943.26 + C$

$C = -104,943.26$

So, population of mosquitoes in the area at any time t is

$P(t) =504,943.26 -104,943.26e^{0.693t}$

6 0

3 years ago

The interior of a regular polygon is 120°.How many sides has this polygon?

horsena [70]

Step-by-step explanation:

I had to take help from my brother for the solution as I'm not very good with solid geometry. Hope you got it and thanks for sharing questions like this. It helps me to learn more.

5 0

3 years ago

Steven and Brittney are both starting lawn mowing businesses to save money to buy a dog. Steven charges $20 a yard and $6 an hou

balandron [24]

Answer:

https:brainly.com/question/20068899

3 0

3 years ago

Solve the expression. use order of operations. 8x3+70/7-7

Assoli18 [71]

Anything divided by zero is one so the answer is 1

6 0

2 years ago

HELPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP

Alex17521 [72]

Answer:

76 in²

Step-by-step explanation:

Area of the figure

Area (top rectangle) + 2 x Area (bottom rectangle)
12 x (7 - 2) + 2 x 2 x 4
12 x 5 + 16
60 + 16
76 in²

7 0

3 years ago