9. T = \sqrt{\frac{w}{d}} w = 5.6 \times 10^5 d = 1.4 \times 10^4 (a) Work out the value of T - Edexcel - GCSE Maths - Question 10 - 2018 - Paper 3

Lottie's assertion is incorrect because the relationship between T, w, and d is more complex due to the nature of how they interact in the formula. While both w and d are indeed increased, the value of d in the denominator causes T to be affected differently by these changes.

To illustrate this, we can calculate the new values of w and d after their respective increases:

• If w is increased by 10%, then: $w_{new} = w + 0.1w = 1.1 \times 5.6 \times 10^5 = 6.16 \times 10^5$
• If d is increased by 5%, then: $d_{new} = d + 0.05d = 1.05 \times 1.4 \times 10^4 = 1.47 \times 10^4$

Now, we can calculate the new value of T:

$T_{new} = \sqrt{\frac{6.16 \times 10^5}{1.47 \times 10^4}}$

This yields a lower value for T compared to its original calculation, as the ratio of w to d has changed. Thus, even though both variables are increased, the overall effect on T can be a decrease due to the greater increase in d outweighing the increase in w.