Photo AI

y is inversely proportional to the square root of x - OCR - GCSE Maths - Question 15 - 2023 - Paper 4

Question 15

y is inversely proportional to the square root of x. y = 7 when x = 144. Find the value of y when x = 16.

Worked Solution & Example Answer:y is inversely proportional to the square root of x - OCR - GCSE Maths - Question 15 - 2023 - Paper 4

Step 1

96%

114 rated

Answer

Since y is inversely proportional to the square root of x, we can express this as:

$y = \frac{k}{\sqrt{x}}$

where k is a constant. We know that y = 7 when x = 144, so we can substitute these values in to find k:

$7 = \frac{k}{\sqrt{144}}$

Calculating the square root gives us:

$7 = \frac{k}{12}$

Thus, to find k, we multiply both sides by 12:

$k = 7 \times 12 = 84$

Step 2

99%

104 rated

Answer

Now that we have the constant k, we can find y when x = 16:

$y = \frac{84}{\sqrt{16}}$

Calculating the square root gives us:

$y = \frac{84}{4} = 21$

Thus, the value of y when x = 16 is:

y = 21

97% of Students

Report Improved Results

98% of Students

Recommend to friends

100,000+

Students Supported

1 Million+

Questions answered

;