MHB Solving Algebra Problems: 2.(c,i),(c,ii),(c,iii) Exam Paper

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The discussion focuses on solving specific algebra problems from a past exam paper. For question 2.(c,i), the correct approach involves rewriting the equation as rx² - tx - h = 0 and solving it as a quadratic. In question 2.(c,ii), the response confirms that the expression -1/6(x+6)(x-6) is incorrect, and the correct form is h = 2x - (x²/6). Lastly, for question 2.(c,iii), the answer of 4.96m is validated as correct when substituting the height of 1.9 into the equation. Overall, the thread provides clarifications and corrections for the algebraic problems presented.
pretzel1998
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Hiya.

Im having problems with Questions 2.(c,i),(c,ii) and (c,iii) question on this past exam paper. http://www.nzqa.govt.nz/nqfdocs/ncea-resource/exams/2014/91261-exm-2014.pdfCan someone check my answers and explain the questions where I face planted? Thanks!

2. (c,i). I got h/(rx-t) = x, I know this is wrong because there is 2 x's in the equation which I am pretty sure is not correct. I factored out the x and divided both sides by (rx-t), where did I go wrong?
2. (c,ii). I got -1/6(x+6)(x-6), I'm pretty confident about this one, but can someone please check it anyways? I'm often wrong when I am confident hahaha.
2. (c,iii). I got 4.96m (rounded to 2 dp), I substituted in 1.9 as the height and solved the equation found in the above question to find the width of the lane. Did I do it right?

Thanks!
 
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Hi pretzel, and welcome to MHB!

pretzel1998 said:
Hiya.

Im having problems with Questions 2.(c,i),(c,ii) and (c,iii) question on this past exam paper. http://www.nzqa.govt.nz/nqfdocs/ncea-resource/exams/2014/91261-exm-2014.pdfCan someone check my answers and explain the questions where I face planted? Thanks!

2. (c,i). I got h/(rx-t) = x, I know this is wrong because there is 2 x's in the equation which I am pretty sure is not correct. I factored out the x and divided both sides by (rx-t), where did I go wrong?
Write the equation as $\color{red}{rx^2 - tx - h = 0}$, and solve it as a quadratic in $\color{red}x$.

2. (c,ii). I got -1/6(x+6)(x-6), I'm pretty confident about this one, but can someone please check it anyways? I'm often wrong when I am confident hahaha.

I got $\color{red}{h = 2x - \dfrac{x^2}6}$. Notice that $\color{red}h$ must be 0 when $\color{red}x$ is 0 or 12.

2. (c,iii). I got 4.96m (rounded to 2 dp), I substituted in 1.9 as the height and solved the equation found in the above question to find the width of the lane. Did I do it right?
I agree with the answer 4.96m (rounded to 2 dp)

Thanks!
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