32÷3/8 please explain

Mathematics

1 answer:

HACTEHA [7]3 years ago

6 0

Answer:

$\dfrac{256}{3} = 85 \dfrac{1}{3}$

Step-by-step explanation:

$32 \div \dfrac{3}{8} =$

$= 32 \times \dfrac{8}{3}$

$= \dfrac{32}{1} \times \dfrac{8}{3}$

$= \dfrac{32 \times 8}{1 \times 3}$

$= \dfrac{256}{3}$

$= 85 \dfrac{1}{3}$

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Read 2 more answers

If log2 5 = a, log2 3 = b and log2 7 = c, determine an expression for log2 (25/21) in terms of a, b, and c

Ilia_Sergeevich [38]

Answer:

$2a - b -c$

Step-by-step explanation: We know that:

$log_{2} 5 = a\\log_{2} 3 = b\\log_2 7 = c\\$

and we want:

$log_2 \frac{25}{21}$ .

We can form the numerator using just the first fact (since 5^2 is 25) and the denominator using the latter two (since 3*7 = 21).

$log_2 \frac{25}{21} = log_2 \frac{5^2}{3*7}.$

The logarithm of a division can be expanded by subtracting the numerator and denominator (while still keeping the log). The logarithm of a product can be expanded by adding the terms while keeping the log. If the logarithm is raised to a power, we can bring it down as a factor:

$log_2 \frac{5^2}{3*7} = log_2(5)^2 - log_2 (3*7) = 2 log_2(5) - (log_2 3 + log_2 7)$