Question

Find the rate of change of its elevation when x= 26

Answer 1

Step 1:

Write the displacement function

`y\text{ = }-(1)/(130)x^2\text{ }+\text{ 180}`

Step 2:

`\frac{d.\text{ x}}{d\mathrm{}y}\text{ = 5 ft/s}`

Step 3

`\begin{gathered} \frac{d.y}{d\mathrm{}x}\text{ = }(-2)/(130)x\text{ } \\ d.y\text{ = }(-1)/(65)xd.x \end{gathered}`

Step 4

`\begin{gathered} \frac{d.y}{d\mathrm{}t}\text{ = }(-1)/(65)\text{ }*\text{ }26\text{ }*\text{ }(d.x)/(d.t) \\ \\ \frac{d.y}{d\mathrm{}t}\text{ = }(-1)/(65)\text{ }*\text{ 26 }*\text{ 5} \\ =\text{ }(-130)/(65) \\ =\text{ -2 ft/s} \end{gathered}`

Final answer

Rate of change of the elevation = -2 ft/s