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

[pretzel1998]

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!

 

[Opalg]

Hi pretzel, and welcome to MHB!

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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