Assuming net value versus grade curve to be a straight line and mining cost of waste is INR 1000/m³; the correct representation of stripping ratio, SR (m³/tonne) versus Fe (%) grad... Assuming net value versus grade curve to be a straight line and mining cost of waste is INR 1000/m³; the correct representation of stripping ratio, SR (m³/tonne) versus Fe (%) grade curve is?
Understand the Problem
The question involves determining the correct representation of the stripping ratio (SR) based on the provided values for net value in relation to the percentage of iron (Fe). It requires analyzing options for the equation of SR given its relationship to Fe, and also includes a separate query about the curl of a vector field.
Answer
The equation for stripping ratio is $SR = -3250 + 125 \times Fe$.
Answer for screen readers
The correct representation of the stripping ratio (SR) is:
$$ SR = -3250 + 125 \times Fe $$
Steps to Solve
- Calculate the difference in net value To find the relation between the percentage Fe and net value, calculate the change in net value as the percentage Fe increases from 58% to 62%.
[ \Delta \text{Net Value} = 4500 - 4000 = 500 \text{ INR/tonne} ]
- Calculate the change in percentage Fe The change in percentage Fe is:
[ \Delta \text{Fe} = 62 - 58 = 4 % ]
- Determine the slope for the equation The slope ( m ) of the relationship can be calculated using the formula:
[ m = \frac{\text{change in net value}}{\text{change in Fe}} = \frac{500}{4} = 125 \text{ INR/tonne per % Fe} ]
- Formulate the stripping ratio (SR) equation Assuming that the SR is related linearly, we can express it in the slope-intercept form, where the intercept can be determined based on the net value for the lowest Fe percentage (58%).
[ SR = C + m \times \text{Fe} ]
- Calculate the intercept Using ( \text{Fe} = 58 ) and the corresponding net value of 4000:
[ 4000 = C + 125 \times 58 ]
Calculating ( 125 \times 58 = 7250 ):
[ C = 4000 - 7250 = -3250 ]
- Write the final equation for SR Thus, combining the slope and intercept, the equation of SR becomes:
[ SR = -3250 + 125 \times \text{Fe} ]
The correct representation of the stripping ratio (SR) is:
$$ SR = -3250 + 125 \times Fe $$
More Information
This equation indicates that as the percentage of iron (% Fe) increases, the stripping ratio decreases, meaning a more efficient extraction process.
Tips
- Miscalculating changes: Ensure you correctly calculate the difference in net value and the percentage Fe.
- Not using linear relation: Remember that the question assumes a linear relationship, which is essential for establishing the slope correctly.
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