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3 years ago

Which of the following numbers are rational?

Mathematics

1 answer:

ololo11 [35]3 years ago

6 0

Answer:

402

Step-by-step explanation:

2(109) plus 2(92) equals 402

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A colony of bacteria is growing at a rate of 0.2 times its mass. Here time is measured in hours and mass in grams. The mass of t

11Alexandr11 [23.1K]

Answer:

Question 1: $dm/dt=0.2m$

Question 2: $m=Ae^{(0.2t)}$

Question 3: $m=10e^{(0.2t)}$

Question 4: $m=10g$

Explanation:

Question 1: Write down the differential equation the mass of the bacteria, m, satisfies: m′= .2m

a) By definition: $m'=dm/dt$

b) Given: $rate=0.2m$

c) By substitution: $dm/dt=0.2m$

Question 2: Find the general solution of this equation. Use A as a constant of integration.

a) Separate variables

$dm/m=0.2dt$

b) Integrate

$\int dm/m=\int 0.2dt$

$ln(m)=0.2t+C$

c) Antilogarithm

$m=e^{0.2t+C}$

$m=e^{0.2t}\cdot e^C$

$e^C=A\\\\m=Ae^{(0.2t)}$

Question 3. Which particular solution matches the additional information?

Use the measured rate of 4 grams per hour after 3 hours

$t=3hours,dm/dt=4g/h$

First, find the mass at t = 3 hours

$dm/dt=0.2m\\\\4=0.2m\\\\m=4/0.2\\\\m=20g$

Now substitute in the general solution of the differential equation, to find A:

$m=Ae^{(0.2t)}\\\\20=Ae^{(0.2\times 3)}\\\\A=20/e^{(0.6)}\\\\A=10.976$

Round A to 1 significant figure:

A = 10.

Particular solution:

$m=10e^{(0.2t)}$

Question 4. What was the mass of the bacteria at time =0?

Substitute t = 0 in the equation of the particular solution:

$m=10e^{0}\\\\m=10g$

3 0

3 years ago

Given 9______

34kurt

7____ is the one that couldn't used to complete a table of eqiuvalent ratios

7 0

3 years ago

Read 2 more answers

Equivalent express15n+5n

makkiz [27]

♥ Let's solve:

15n+5n can be known as 15+5.

15+5=20 now add n.

Final answer: 20n

6 0

3 years ago

Read 2 more answers

What is 1.08 to the power of <img src="https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B5%7D" id="TexFormula1" title="\frac{1}{5}" alt="

OlgaM077 [116]

Answer:

$about \: 1.01551$

Step-by-step explanation:

No it isn't, because:

${1.08}^{ \frac{1}{5} } = { \frac{108}{100} }^{ \frac{1}{5} } = { \frac{27}{25} }^{ \frac{1}{5} } = \sqrt[5]{ \frac{27}{25} } = 1.01551$

6 0

3 years ago

There were 26 balloon in the party room, 12 red and 14 blue. Half of the blue balloon

Nostrana [21]

Answer:

There would be 19 ballons left

Step-by-step explanation:

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3 years ago