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sasho [114]
3 years ago
8

A common inhabitant of human intestines is the bacterium Escherichia coli. A cell of this bacterium in a nutrient-broth medium d

ivides into two cells every 20 minutes. The initial population of a culture is 60 cells. Find the relative growth rate.
Mathematics
1 answer:
qwelly [4]3 years ago
7 0

Answer:

Step-by-step explanation:

Given that,

Cells are divided into two cell every 20mins, this implies that the half-life is 20mins

Initial population growth is 60cells

Growth rate r?

Population growth is modeled as

P(t) = Po•exp(rt)

Where,

Po is the initial growth at t= 0

Po= 60

P(t) is population at any time t.

Since the population doubles every 20mins(⅓hr)

Then, P(⅓) = 2×60 =120

Then, P(t) = 120cells

So, applying the formula

P(t) = Po•exp(rt)

120 = 60•exp(⅓r)

120/60 = exp(r/3)

2 = exp(r/3)

Take In of both sides

In(2) = r/3

Cross multiply

r = 3In(2)

r = 2.079 /hour

The growth rate is 2.079/hour.

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kati45 [8]
4 rows and 6 seashells in each row. 
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Row 3: 0 0 0 0 0 0
Row 4: 0 0 0 0 0 0

You add all of them together 6+6+6+6=24 
Or you could do 6x4 and your answer would be 24
So the answer to the question is 24 seashells. 
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2 years ago
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Soloha48 [4]

Answer:whats the question

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2 years ago
What is PA <br> Enter your answer in the box
SSSSS [86.1K]

Answer:

3

Step-by-step explanation:

P is the in-center

⇒PA=PE=PD because they are in-radius of the in-circle

We know that, tangent segments drawn from a point outside the circle are always equal in length

⇒DK=EK=7.2

In right triangle PKE,

using Pythagoras' Theorem : PK^{2}=PE^{2}+KE^{2}

⇒PE^{2}=PK^{2}-KE^{2}

⇒PE=\sqrt{PK^{2}-KE^{2} }

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One<br> Find the product:<br> (n - 5)(n-1)
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4 0
3 years ago
Read 2 more answers
Solve<br><img src="https://tex.z-dn.net/?f=%5Csf%20%5Cdfrac%7B1%7D%7Bp%7D%20%2B%20%5Cdfrac%7B1%7D%7Bq%7D%20%2B%20%5Cdfrac%7B1%7D
Nostrana [21]

Answer:

\displaystyle   \begin{cases} \displaystyle  {x} _{1} =  - p \\   \displaystyle x _{2}   =  -  q \end{cases}

Step-by-step explanation:

we would like to solve the following equation for x:

\displaystyle  \frac{1}{p}  +  \frac{1}{q}  +  \frac{1}{x}  =  \frac{1}{p  + q + x}

to do so isolate \frac{1}{x} to right hand side and change its sign which yields:

\displaystyle  \frac{1}{p}  +  \frac{1}{q}    =  \frac{1}{p  + q + x}  -  \frac{1}{x}

simplify Substraction:

\displaystyle  \frac{1}{p}  +  \frac{1}{q}    =  \frac{x - (q + p +  x)}{x(p  + q + x)}

get rid of only x:

\displaystyle  \frac{1}{p}  +  \frac{1}{q}    =  \frac{  - (q + p )}{x(p  + q + x)}

simplify addition of the left hand side:

\displaystyle  \frac{q + p}{pq}     =  \frac{  - (q + p )}{x(p  + q + x)}

divide both sides by q+p Which yields:

\displaystyle  \frac{1}{pq}     =  \frac{  -1}{x(p  + q + x)}

cross multiplication:

\displaystyle    x(p  + q + x)  =   - pq

distribute:

\displaystyle    xp  + xq +  {x}^{2} =   - pq

isolate -pq to the left hand side and change its sign:

\displaystyle    xp  + xq +  {x}^{2} + pq =  0

rearrange it to standard form:

\displaystyle   {x}^{2} +    xp  + xq  + pq =  0

now notice we end up with a <u>quadratic</u><u> equation</u> therefore to solve so we can consider <u>factoring</u><u> </u><u>method</u><u> </u><u> </u>to use so

factor out x:

\displaystyle  x( {x}^{} +   p ) + xq  + pq =  0

factor out q:

\displaystyle  x( {x}^{} +   p ) +q (x + p)=  0

group:

\displaystyle  ( {x}^{} +   p ) (x + q)=  0

by <em>Zero</em><em> product</em><em> </em><em>property</em> we obtain:

\displaystyle   \begin{cases} \displaystyle  {x}^{} +   p  = 0 \\   \displaystyle x + q=  0 \end{cases}

cancel out p from the first equation and q from the second equation which yields:

\displaystyle   \begin{cases} \displaystyle  {x}^{}   =  - p \\   \displaystyle x  =  -  q \end{cases}

and we are done!

3 0
2 years ago
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