Answered

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y
∝
√
x
If
y
=
45
when
x
=
81
find,
x
when
y
=
100

Sagot :

olayemiolakunle65

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.

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