Algebra Problems

pretzel1998

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Jan 4, 2015
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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.pdf
Can 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 im 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? Im often wrong when im 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!:D
 
For those who may not want to have to plow through a lengthy document which may soon go offline, here is the exercise:

QUESTION TWO:

(a) Factorise and solve 12a2 – 11a – 15 = 0

(b) (i) Write as a single fraction: \(\displaystyle \dfrac{3}{x\, -\, 2}\, -\, \dfrac{4x}{x\, +\, 1}\)

(ii) Solve the equation: \(\displaystyle \dfrac{x^2\, +\, 2x\, -\, 8}{x^2\, -\, x\, -\, 2}\, =\, 3\)

(c) (i) The height h metres of a tunnel is modelled by a function of the form h = rx2 - tx where r and t are constants. Make x, the distance in metres from the left side of the tunnel, the subject of the equation.

(ii) The shape of the tunnel can be modelled by a parabola. The maximum height of the tunnel is 6 m, and at ground level its width is 12 m. Find the equation of the parabola.

(iii) There are two lanes of equal width through the tunnel. The outside edge of each lane is marked by a line so that a car of height 1.8 m would have a minimum clearance of 0.1 m vertically from the top of the car to the tunnel roof. (Ignore the width of the line.) Find the width of each lane.
 
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For those who may not want to have to plow through a lengthy document which may soon go offline, here is the exercise:

QUESTION TWO:

(a) Factorise and solve 12a2 – 11a – 15 = 0

(b) (i) Write as a single fraction: \(\displaystyle \dfrac{3}{x\, -\, 2}\, -\, \dfrac{4x}{x\, +\, 1}\)

(ii) Solve the equation: \(\displaystyle \dfrac{x^2\, +\, 2x\, -\, 8}{x^2\, -\, x\, -\, 2}\)

This should be \(\displaystyle \frac{x^2+ 2x- 8}{x^2- x- 2}= 3\)

(c) (i) The height h metres of a tunnel is modelled by a function of the form h = rx2 - tx where r and t are constants. Make x, the distance in metres from the left side of the tunnel, the subject of the equation.

(ii) The shape of the tunnel can be modelled by a parabola. The maximum height of the tunnel is 6 m, and at ground level its width is 12 m. Find the equation of the parabola.

(iii) There are two lanes of equal width through the tunnel. The outside edge of each lane is marked by a line so that a car of height 1.8 m would have a minimum clearance of 0.1 m vertically from the top of the car to the tunnel roof. (Ignore the width of the line.) Find the width of each lane.
 
(c) (i) The height h metres of a tunnel is modelled by a function of the form h = rx2 - tx where r and t are constants. Make x, the distance in metres from the left side of the tunnel, the subject of the equation.
You can try solving for x using any method that you learned to solve quadratic eqs. Maybe try using the quadratic formula with a=r, b=... and c=...

(ii) The shape of the tunnel can be modelled by a parabola. The maximum height of the tunnel is 6 m, and at ground level its width is 12 m. Find the equation of the parabola.
Your answer is correct

(iii) There are two lanes of equal width through the tunnel. The outside edge of each lane is marked by a line so that a car of height 1.8 m would have a minimum clearance of 0.1 m vertically from the top of the car to the tunnel roof. (Ignore the width of the line.) Find the width of each lane.
Comments above
 
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