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联动变化
如果两个量在联动变化，我们如何把这两个量联系起来，理解其中一个量的变化如何影响另一个？
1. Introduction
Introduction
2. Using Graphs to Represent Relationships
Using Graphs to Represent Relationships
3. Using Algebra to Add Perspective
Using Algebra to Add Perspective
4. Summary
Summary
5. Quantities that change in the filling tank
A rectangular tank 4 ft long, 2 ft wide and 3 ft high is filled by a hose delivering 0.5 cubic feet per minute. Which list correctly separates the changing quantities from the fixed ones?
6. Describing the sketch of the tank
A correct labeled sketch of either tank while it is partly filled must show which of the following?
7. Volume after three minutes
In the aquarium the volume of water grows at 0.75 cubic feet per minute, so V = 0.75t. What is V when t = 3 minutes?
8. Shape of the depth graph
In a tank of constant cross-section, the water's volume and depth are related by V = 8h. How should the graph of depth h against time t appear while the tank fills at a constant rate?
9. Volume of a full spherical tank
A spherical tank of radius 3 feet starts completely full and drains at 1.2 cubic feet per minute. How many cubic feet of water does it hold when full? Round to one decimal place.
10. Time to drain the spherical tank
The same 36pi-cubic-foot sphere drains at 1.2 cubic feet per minute. How many minutes does it take to empty completely? Round to two decimal places.
11. Volume remaining after forty minutes
The sphere holds 36pi cubic feet at t = 0 and drains at 1.2 cubic feet per minute, so V = 36pi - 1.2t. What is the volume remaining after 40 minutes? Round to one decimal place.
12. The depth of a draining sphere falls at a constant rate
While the spherical tank drains at a constant volumetric rate, the water's depth h decreases at a constant rate.
13. The unusual sphere-and-chimney tank
A tank is a sphere of radius 3 feet topped by a cylinder of radius 1 foot and height 2 feet, filled at 1.25 cubic feet per minute. Which description of the height graph is correct?
14. A sphere filled at constant depth rate
A sphere of radius 6 feet is filled so that its water depth rises at a constant 0.4 feet per minute. How does the volume graph of V against t behave?
15. Reading the car's position data
A car's position s (thousands of feet) is recorded every two minutes: t = 0, 2, 4, 6, 8, 10 with s = 0, 1.5, 3, 3, 6.5, 10. What does the flat stretch from t = 4 to t = 6 tell you?