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y is directly proportional to the square of x - OCR - GCSE Maths - Question 13 - 2023 - Paper 5

Question 13

y is directly proportional to the square of x. Find the percentage decrease in y when x is decreased by 30%.

Worked Solution & Example Answer:y is directly proportional to the square of x - OCR - GCSE Maths - Question 13 - 2023 - Paper 5

Step 1

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Answer

Let the original value of x be represented as $x$ . When x is decreased by 30%, the new value of x is given by:

$x_{new} = x - 0.3x = 0.7x$

Step 2

99%

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Answer

Since y is directly proportional to the square of x, we write:

$y = kx^2$

for some constant k. Therefore, the original value of y is:

$y_{original} = kx^2$

Step 3

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Answer

Substituting $x_{new}$ into the equation for y, we have:

$y_{new} = k(0.7x)^2 = k(0.49x^2) = 0.49kx^2$

Thus, the new value of y is:

$y_{new} = 0.49y_{original}$

Step 4

98%

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Answer

The percentage decrease in y can be calculated as follows:

$ext{Percentage decrease} = rac{y_{original} - y_{new}}{y_{original}} imes 100$

Substituting the values we found:

$ext{Percentage decrease} = rac{y - 0.49y}{y} imes 100 = rac{0.51y}{y} imes 100 = 51\%$

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