Question

4. Gold is very heavy compared to other substances. The graph below shows the proportional

relationship between the weight of gold, w, and its volume, v, with some points marked.
The relationship between w and v can be expressed
using the equation:
w = k·v
where k is the constant of proportionality.
(a) What is the value of k? Give both the value
and proper units.
Weight of Gold (grams)
100
90
80
70
W
40
30
20+
10+
(2, 38.6)
(1, 19.3)
(3, 57.9)
(5, 96.5)
(4,77.2)
1
2
3
4
Volume of Gold (cubic centimeters)
5
meters

Answer 1

Answer: 19.3

Explanation:

The equation given to express the relationship between the weight of gold, w, and its volume, v, is w = k·v, where k is the constant of proportionality.To find the value of k, we can use the given points on the graph. Let's choose any two points on the graph, (1, 19.3) and (2, 38.6), which represent the volume of gold (in cubic centimeters) and its corresponding weight (in grams).Using the equation w = k·v, we can substitute the values from the chosen points:19.3 = k·138.6 = k·2 From the first equation, we can solve for k:k = 19.3So, the value of k is 19.3. Since weight is measured in grams and volume is measured in cubic centimeters, the unit for k is grams per cubic centimeter (g/cm³).In summary, the value of k in the equation w = k·v is 19.3, with the unit of grams per cubic centimeter (g/cm³).