Answer:
A) y = 16/(x^2), B) 4/5
Step-by-step explanation:
For A, we can plug in some of the table values to check it. I will try 2 and 3
2. 4 = 16 / (2^2)
16/4 = 4
3. 16/9 = 16 / (3^2)
16/9 = 16/9
B) We can just input y into the formula 25 = 16 / (x^2)
This leaves us with +-4/5
Answer:
see explanation
Step-by-step explanation:
(a)
given y varies inversely as x² then the equation relating them is
y = [tex]\frac{k}{x^2}[/tex] ← k is the constant of variation
to find k substitute any ordered pair from the table into the equation
using (2, 4 ) , then
4 = [tex]\frac{k}{2^2}[/tex] = [tex]\frac{k}{4}[/tex] ( multiply both sides by 4 )
16 = k
y = [tex]\frac{16}{x^2}[/tex] ← equation of variation
(b)
when y = 25 , then
25 = [tex]\frac{16}{x^2}[/tex] ( multiply both sides by x² )
25x² = 16 ( divide both sides by 25 )
x² = [tex]\frac{16}{25}[/tex] ( take the square root of both sides )
x = ± [tex]\sqrt{\frac{16}{25} }[/tex] = ± [tex]\frac{4}{5}[/tex]
the positive value of x is x = [tex]\frac{4}{5}[/tex]
