What is the scale for 3 cm on the map correspond to 120 km in the actual distance?
2 answers:
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Assume the first even integer is x.
The next even integer will be 2 digits after this digit. So the next even integer will be x+2.
The reciprocals of these two even integers can be written as
and 
respectively.
The sum of their reciprocals is 7/24. So we can set up the equation as:
Taking LCM on left hand side:
Cross Multiplying the denominators:
Using the quadratic formula to solve the above equation:
Since, the value of x can only be an integer, we discard the fractional value and keep x=6
So the first even integer is 6 and the next even integer is 8. The sum of reciprocals of 6 and 8 is 7/24
The next even integer will be 2 digits after this digit. So the next even integer will be x+2.
The reciprocals of these two even integers can be written as
The sum of their reciprocals is 7/24. So we can set up the equation as:
Taking LCM on left hand side:
Cross Multiplying the denominators:
Using the quadratic formula to solve the above equation:
Since, the value of x can only be an integer, we discard the fractional value and keep x=6
So the first even integer is 6 and the next even integer is 8. The sum of reciprocals of 6 and 8 is 7/24
Check the picture below.
the slope goes by several names
• average rate of change
• rate of change
• deltaY over deltaX
• Δy over Δx
• rise over run
• gradient
• constant of proportionality
however, is the same cat wearing different costumes.
well, by the definition of a derivative, the slope at the point is f'(a), and any tangent line going through it will also have the same exact slope, keeping in mind that a straight line has a constant slope.
