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Dafna1 [17]
3 years ago
14

A bacteria culture starts with 120 and after 3 hours the population consists of 200 bacteria. What is the rate of the increase t

o the nearest percent?
Mathematics
2 answers:
jenyasd209 [6]3 years ago
8 0
This is a continuous compounded growth:

P = A . eⁿˣ, where A is the original value, P, the yielded value after a growth of 
"x" during a time = n ( n = time = 3 hours : given)

200 = 120(e)³ˣ

200/120 = (e)³ˣ

5/3 = (e)³ˣ

ln(5/3) = ln[(e)³ˣ

0.5108 = 3x.ln(e) (ln(e) = 1)

x = 0.5108/3 = 0.17
 so the HOURLY growth rate = 0.17

posledela3 years ago
4 0
The rate of the increase to the nearest percent is 30 percent
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Two corresponding sides of similar triangles are 2 cm and 5 cm. What is the area of the second triangle if the area of the first
Stella [2.4K]

Answer:

(1) Area of second triangle= 50 cm^2.

(2) Area of ΔABC=98 cm^2.

   and Area of ΔDFG=175 cm^2.

Step-by-step explanation:

<em>" For two similar triangles the ratio of sides is equal to the ratio of square of their areas".</em>

i.e. if a,b are the corresponding sides of two similar triangles and let A and B denote the area of two triangles then we have the relation as:

\dfrac{a^2}{b^2}=\dfrac{A}{B}

(1)

for the first question:

we have a=2, b=5.

A=8 cm^2.

Hence,

\dfrac{2^2}{5^2}=\dfrac{8}{B}\\\\\dfrac{4}{25}=\dfrac{8}{B}

B=50 cm^2.

Hence, the area of second triangle is 50 cm^2.

(2)

In second option we have:

a=6 and b=5.

A-B=77 cm^2.

A=77+B

\dfrac{6^2}{5^2}=\dfrac{A}{B}\\  \\\dfrac{36}{25}=\dfrac{77+B}{B}\\  \\36B=25\times77+25B\\\\36B-25B=25\times77\\\\11B=25\times77\\\\B=25\times7\\\\B=175

Hence area of second triangle i.e. ΔDFG is 175 cm^2.

and area of first triangle i.e. ΔABC=175-77=98 cm^2.




8 0
2 years ago
(2x+5)+3(x-6)=90 what is x
snow_lady [41]
I don’t know if I’m 100% correct but I got

Exact form x= 103/5
Decimal form x=20.6
8 0
3 years ago
How many integers between 100 and 400 contain the digit 2?
Semenov [28]
102, 112, 120-129, 132, 142, 152, 162, 172, 182, 192, 200-299, 302, 312, 320-329, 332, 342, 352, 362, 372, 382, 392
2+10+7+100+2+10+7
138 integers.
8 0
3 years ago
Need help with Geometry homework.
solmaris [256]

Answer:

SU = 22

Step-by-step explanation:

SR = RU

4x - 1 = x + 8

3x - 1 = 8

3x = 9

x = 3

SR =  4(3) - 1 = 11

RU =  3 + 8 = 11

SU = 11 + 11 = 22

7 0
3 years ago
If it takes John 10 hours to paint the fence, how long will it take John and his two friends to do the job if they work at the s
VMariaS [17]

Answer:

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