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zheka24 [161]
3 years ago
11

X + 2y = 33 x-y = 11

Mathematics
1 answer:
Tasya [4]3 years ago
7 0

Answer:

x=\frac{55}{3},\:y=\frac{22}{3}

Step-by-step explanation:

Solve by Substitution ;

\begin{bmatrix}x+2y=33\\ x-y=11\end{bmatrix}\\\\\mathrm{Isolate}\:x\:\mathrm{for}\:x+2y=33:\quad x=33-2y\\\\\mathrm{Subsititute\:}x=33-2y\\\\\begin{bmatrix}33-2y-y=11\end{bmatrix}\\\\Simplify\\\begin{bmatrix}33-3y=11\end{bmatrix}\\\\\mathrm{Isolate}\:y\:\mathrm{for}\:33-3y=11:\quad y=\frac{22}{3}\\\mathrm{For\:}x=33-2y\\\\\mathrm{Subsititute\:}y=\frac{22}{3}\\x=33-2\times\frac{22}{3}\\\\x=\frac{55}{3}\\\\x=\frac{55}{3},\:y=\frac{22}{3}

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Answer:

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V_{n} = {6*10^{-18}, 12*10^{-18},...}

a = 6*10^{-18}

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And the following arithmetic sequence that are the time(in hours).

T_{n} = {0,0.5,1,...}

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d = 0.5

T_{n} = 0.5n

How long will it take for a single bacterium to grow to fill a thimble with volume 1 cm3 ?

I am going to find the value of n for which V_{n} = 1cm^{3}, then i find the value at this position in the arithmetic sequence. So

1cm^{3} = 10^{-6}m^{3}

V_{n} = 6*10^{-18}*(2^{(n-1)})

10^{-6} = 6*10^{-18}*(2^{(n-1)})

\frac{10^{-6}}{6*10^{-18}} = 2^{(n-1)})

Obs: a^{b-c} = \frac{a^{b}}{a^{c}}

\frac{10^{12}}{6} = \frac{2^{n}}{2}

2^{n} = \frac{10^{12}}{3}

Now, we have to apply these following logarithim proprierties to find the value of n:

log a^{n} = n log a

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