3 years ago

A competition

Mathematics

1 answer:

qwelly [4]3 years ago

4 0

Answer:

2049.

Step-by-step explanation:

2045 - 1983 = 62 years.

So the competition will take place in 1983 + 60 = 2043.

After 2045 the competition takes place in 2049.

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If 32^2c= 8^c+7, what is the value of c

Leona [35]

$\bf 32^{2c}=8^{c+7}~~ \begin{cases} 32=2\cdot 2\cdot 2\cdot 2\cdot 2\\ \qquad 2^5\\ 8=2\cdot 2\cdot 2\\ \qquad 2^3 \end{cases}\implies (2^5)^{2c}=(2^3)^{c+7} \\\\\\ 2^{5(2c)}=2^{3(c+7)}\implies \stackrel{\textit{if the bases are the same, then so are the exponents}}{5(2c)=3(c+7)\implies 10c=3c+21} \\\\\\ 7c=21\implies c=\cfrac{21}{7}\implies c=3$