Solve: a 100-ml pitcher of lemonade is currently 90% water and 10% lemon concentrate. how much water must you add to change the ballance to 95% water and 5% lemon concentrate.

Must add 100 milliliters of water

Step-by-step explanation:

Let

x ----> milliliters of water to add

we know that

Originally

The milliliters of lemon concentrate is equal to the 10% of 100 mL

so

Now

The balance of lemon concentrate is equal to 5%

The milliliters of lemon concentrate is the same

so

solve for x

therefore

Must add 100 milliliters of water

y=mx+

1 number

if we use a graphing calculator, there is only one such number that satisfies the conclusion of the mean value theorem, that is, a number such that

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.