16. y is directly proportional to $
abla{x}$
y = \frac{1}{6}$ when $x = 8$
Find the value of y when $x = 64$
(Total for Question 16 is 3 marks) - Edexcel - GCSE Maths - Question 16 - 2017 - Paper 1
Question 16
16. y is directly proportional to $
abla{x}$
y = \frac{1}{6}$ when $x = 8$
Find the value of y when $x = 64$
(Total for Question 16 is 3 marks)
Worked Solution & Example Answer:16. y is directly proportional to $
abla{x}$
y = \frac{1}{6}$ when $x = 8$
Find the value of y when $x = 64$
(Total for Question 16 is 3 marks) - Edexcel - GCSE Maths - Question 16 - 2017 - Paper 1
Step 1
Find the constant of proportionality
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Answer
Since y is directly proportional to ablax, we can express this relationship as:
y = k
oot{x} ext{ for some constant } k.
Using the given value y = \frac{1}{6}whenx = 8$:
[ \frac{1}{6} = k\sqrt{8} ]
Now, solving for k,
[ k = \frac{1/6}{\sqrt{8}} = \frac{1/6}{2\sqrt{2}/4} = \frac{2}{12\sqrt{2}} = \frac{1}{6\sqrt{2}} ]
Step 2
Calculate y for x = 64
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Answer
Now, substituting k back into the equation and finding y for x = 64:
[ y = \frac{1}{6\sqrt{2}}\sqrt{64} ]
Calculating the square root:
[ y = \frac{1}{6\sqrt{2}} \times 8 ]
[ y = \frac{8}{6\sqrt{2}} = \frac{4}{3\sqrt{2}} ]
