A child fills a pail by using a water hose. After finishing, the child plays in

Question

A child fills a pail by using a water hose. After finishing, the child plays in a sandbox for a while before tipping the pail over to empty it. If V (t) gives the volume of the water in the pail at time t, then the figure below shows V'(t) as a function of t. At what time does the child: Begin to fill the pail? t = Finish filling the pail? t = Tip the pail over? t = (What would the graph of V'(t) look like if the child filled the pail by using a play shovel to repeatedly scoop water from a larger bucket and dump it in the pail instead of using a hose?)

Explanation / Answer

begins to fill the pail at 3 seconds.

finish filling the pail at 9 seconds.

tips the pail over at 14 seconds.

this is because this is the derivative graph of the volume of the water. so when the gaph is above zero for the y value, (3-9 sec.) water will be getting added to the bucket. when the graph is at o for the y value, the bucket will not be losing any water or gaining any water. When the graph is a negative y-value, 14sec.-18sec., water will be leaving the bucket.

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.