Calculate the width of the gutter where the depth is 6cms

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To calculate the width of the gutter where the depth is 6 cm, the quadratic equation y = (4/11)x^2 - 4x + 11 must be solved for x when y equals 6. The equation becomes (4/11)x^2 - 4x + 11 = 6. After simplifying, it is necessary to rearrange the equation to find the roots, which represent the width. The initial guess of 1.26 cm is questioned, indicating a need for clarification on the correct method to solve the quadratic. The discussion emphasizes the importance of correctly identifying the variables in the equation.
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Homework Statement


The cross-section of a gutter can be represented by the quadratic:
y=4/11x^2-4x+11 where x and y are measurements in cm. Calculate the width of the gutter where the depth is 6cms.


Homework Equations





The Attempt at a Solution


my answer was 1.26cm or 12.6mm but I'm pretty sure that's wrong so could someone please explain how to work it out?
 
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What did you try?
 
Paulo2014 said:

Homework Statement


The cross-section of a gutter can be represented by the quadratic:
y=4/11x^2-4x+11 where x and y are measurements in cm. Calculate the width of the gutter where the depth is 6cms.
It's impossible to say if you won't tells us which of x, y is the width and which is the depth! I might guess that x is twice the width and y the depth, so that you need to solve the equation (4/11)x^2- 4x+ 11= 6. My guess is partly based on the fact that if x is the depth, you would only need to evaluate that (4/11)(6)^2- 4(6)+ 11 and that is too easy!


Homework Equations





The Attempt at a Solution


my answer was 1.26cm or 12.6mm but I'm pretty sure that's wrong so could someone please explain how to work it out?
 
sorry guys... x is width and y is depth
 

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