Question

The numbers in each of the following equalities are all expressed in the same base, r . Determine the radix r in each case for the following operations to be correct. (a) 14/2 = 5 (b) 54/4 = 1

Answer 1

Answer:

a) r = 6

b) r = 0

Step-by-step explanation:

See it in the pic.

Answer 2

Answer:

a)r=6  b)r=0

Step-by-step explanation:

Before to get started, Let's to express each number in base r.

We should take in account that it process is similar to express numbers in  decimal base, except that in this case $10^{n}$ is  replaced by $r^{n}$.

a) 14=1x$1*r^{1} +4*r^{0} =r+4$

  $2=2*r^{0}$

  $5=5*r^{0}$

Replacing each number in base r  on the equalitie a.

$\frac{r+4}{2} =5$

Solving this equation

$(r+4)=10\\r=6$

b) $54=5*r^{1} +4*r^{0} =5r+4\\4=4*r^{0} \\1=1*r^{0}$

Replacing each number in base r  on the equalitie b.

$\frac{5r+4}{4}=1$

Solving this equation:

$5r+4=4\\r=0$