Answer:
x = 400 when y = 100
Step-by-step explanation:
This is a question in relation to direct variation.
y ∝ [tex]\sqrt{x}[/tex]
y = k [tex]\sqrt{x}[/tex]
Given that, y = 45, x = 81. Then;
45 = k [tex]\sqrt{81}[/tex]
45 = 9k
k = [tex]\frac{45}{9}[/tex]
k = 5
Thus the relationship among the variables is;
y = 5 [tex]\sqrt{x}[/tex]
If y = 100, then;
100 = 5 [tex]\sqrt{x}[/tex]
[tex]\sqrt{x}[/tex] = [tex]\frac{100}{5}[/tex]
[tex]\sqrt{x}[/tex] = 20
x = [tex](20)^{2}[/tex]
x = 400
Therefore, x = 400 when y = 100.
