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lina2011 [118]
3 years ago
9

Can you please solve the following equation?

Mathematics
1 answer:
AlladinOne [14]3 years ago
7 0

Answer:

x=3.903

Step-by-step explanation:

2^{x-3}.5^{x-1}=200\\2^x.2^{-3}.5^x.5^{-1}=200\\\frac{2^x}{2^3}.\frac{5^x}{5^1}=200\\\frac{2^x.5^x}{2^3.5}=200\\\frac{(2.5)^x}{8.5}=200\\10^x=200 \times 40\\10^x=8000\\log 10^x=log8000\\x=\frac {log8000}{log10}=log8000=log 8\times log1000=log 8+log 1000=log2^3+log10^3=3log2+3log10=3log2+3 \approx0.903+3 \approx3.903

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When studying radioactive​ material, a nuclear engineer found that over 365​ days, 1,000,000 radioactive atoms decayed to 973 co
HACTEHA [7]

Answer:

A. number of decayed atoms = 73.197

Step-by-step explanation:

In order to find the answer we need to use the radioactive decay equation:

N(t)=N0*e^{kt} where:

N0=initial radioactive atoms

t=time

k=radioactive decay constant

In our case, when t=0 we have 1,000,000 atoms, so:

1,000,000=N0*e^{k*0}

1,000,000=N0

Now we need to find 'k'. Using the provied information that after 365 days we have 973,635 radioactive atoms, we have:

973,635=1,000,000*e^{k*365}

ln(973,635/1,000,000)/365=k

-0.0000732=k

A. atoms decayed in a day:

N(t)=1,000,000*e^{-0.0000732t}

N(1)=1,000,000*e^{-0.0000732*1}

N(1)= 999,926.803

Number of atoms decayed in a day = 1,000,000 - 999,926.803 = 73.197

B. Because 'k' represents the probability of decay, then the probability that on a given day 51 radioactive atoms decayed is k=0.0000732.

4 0
3 years ago
Find the area of the shaded region
dsp73

Answer:

4

Step-by-step explanation:

I am not 100% sure but I really hope this helps you.

6 0
2 years ago
Simplify the following: (9x - 7) - (5x + 10)
lianna [129]
(9x - 7) - (5x + 10 )
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7 0
3 years ago
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Mamont248 [21]

Answer:

solution set are

(-3,0)

(1,8)

Step-by-step explanation:

we are given system of equation as

y=x^2+4x+3

y=2x+6

For finding solution set , we can draw graph of both equations

and then we can find intersection point

the intersection point will be our solution set

we get graph  as

So, solution set are

(-3,0)

(1,8)


4 0
2 years ago
What is equivalent to 1/4? 2/8, 1/3, 2/8, or 1/2
PolarNik [594]
2/8 is equivalent to 1/4, as it is directly proportional. 
7 0
3 years ago
Read 2 more answers
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