9. $T = rac{w}{ ext{sqrt}(d)}$ $w = 5.6 imes 10^5$ d = 1.4 imes 10^4$ (a) Work out the value of $T$. Give your answer in standard form correct to 3 significant figures. $T = $ (b) Lottie says, "The value of T will increase because both w and d are increased." Explain why.

GCSE Edexcel Maths Real-Life Graphs: 9. $T = rac{w}{ ext{sqrt}(d)}

9. $T = rac{w}{ ext{sqrt}(d)}$ $w = 5.6 imes 10^5$ d = 1.4 imes 10^4$ (a) Work out the value of $T$ - Edexcel - GCSE Maths - Question 12 - 2018 - Paper 3

Question 12

$9.-$T-=--rac{w}{-ext{sqrt}(d)}$--$w-=-5.6--imes-10^5$--d-=-1.4--imes-10^4$--(a)-Work-out-the-value-of-$T$-Edexcel-GCSE Maths-Question 12-2018-Paper 3.png$

9. $T = rac{w}{ ext{sqrt}(d)}$ $w = 5.6 imes 10^5$ d = 1.4 imes 10^4$ (a) Work out the value of $T$. Give your answer in standard form correct to 3 signific... show full transcript

Worked Solution & Example Answer:9. $T = rac{w}{ ext{sqrt}(d)}$ $w = 5.6 imes 10^5$ d = 1.4 imes 10^4$ (a) Work out the value of $T$ - Edexcel - GCSE Maths - Question 12 - 2018 - Paper 3

Step 1

Work out the value of T.

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Answer

To calculate the value of $T$ , we substitute the values of $w$ and $d$ into the formula:

$T = rac{5.6 imes 10^5}{ ext{sqrt}(1.4 imes 10^4)}$

First, compute the square root of $d$ :

$ext{sqrt}(1.4 imes 10^4) = ext{sqrt}(1.4) imes ext{sqrt}(10^4) = ext{sqrt}(1.4) imes 10^2$

Using a calculator, we find that $ext{sqrt}(1.4) ext{ is approximately } 1.183$ . Therefore:

$ext{sqrt}(1.4 imes 10^4) ext{ is approximately } 1.183 imes 100 = 118.3$

Now, substituting back into the equation for $T$ :

$T = rac{5.6 imes 10^5}{118.3} ext{ which is approximately } 4.73 imes 10^3$

Correct to 3 significant figures, we have:

$T ext{ is } 4.73 imes 10^3$

Step 2

Explain why.

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Answer

Lottie's statement is incorrect. While both $w$ and $d$ increase, it is important to consider how $T$ is affected by these changes. The formula shows $T$ is inversely proportional to the square root of $d$ :

$T ext{ increases as } d ext{ decreases, and conversely, } T ext{ decreases as } d ext{ increases.}$

Since $d$ increases by 5%, the resulting effect on $T$ may outweigh the increase in $w$ . To confirm this mathematically, we can determine the new value of $T$ after increasing $w$ and $d$ :

New $w = 5.6 imes 10^5 imes 1.1$ (10% increase), and New $d = 1.4 imes 10^4 imes 1.05$ (5% increase). We'll see how these values influence the overall calculation of $T$ .

9. $T = rac{w}{ ext{sqrt}(d)}$ $w = 5.6 imes 10^5$ d = 1.4 imes 10^4$ (a) Work out the value of $T$ - Edexcel - GCSE Maths - Question 12 - 2018 - Paper 3

Worked Solution & Example Answer:9. $T = rac{w}{ ext{sqrt}(d)}$ $w = 5.6 imes 10^5$ d = 1.4 imes 10^4$ (a) Work out the value of $T$ - Edexcel - GCSE Maths - Question 12 - 2018 - Paper 3

Work out the value of T.

Explain why.

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