If p varies jointly with q, r, and s, it means that the ratio of p to q, p to r, and p to s is always constant. In other words, the relationship between p, q, r, and s can be represented by the equation p = kqrs, where k is the constant of proportionality.
Based on the information given, we can determine the value of k by plugging in the known values for p, q, r, and s into the equation above. For example, we know that p = 80 when q = 10, r = 5, and s = 2, so we can substitute these values into the equation to get:
p = kqrs
80 = k(10)(5)(2)
Solving for k, we get:
k = 80 / (10 * 5 * 2)
k = 0.4
Now that we know the value of k, we can use it to determine the value of p when q = 10, r = 10, and s = 4. To do this, we simply substitute these values into the equation p = kqrs and solve for p:
p = kqrs
p = (0.4)(10)(10)(4)
p = 160
Therefore, when q = 10, r = 10, and s = 4, the value of p is 160.
Note: This solution assumes that the relationship between p, q, r, and s is truly a joint variation. If this is not the case, the solution above may not be correct.
Answers & Comments
Answer:
If p varies jointly with q, r, and s, it means that the ratio of p to q, p to r, and p to s is always constant. In other words, the relationship between p, q, r, and s can be represented by the equation p = kqrs, where k is the constant of proportionality.
Based on the information given, we can determine the value of k by plugging in the known values for p, q, r, and s into the equation above. For example, we know that p = 80 when q = 10, r = 5, and s = 2, so we can substitute these values into the equation to get:
p = kqrs
80 = k(10)(5)(2)
Solving for k, we get:
k = 80 / (10 * 5 * 2)
k = 0.4
Now that we know the value of k, we can use it to determine the value of p when q = 10, r = 10, and s = 4. To do this, we simply substitute these values into the equation p = kqrs and solve for p:
p = kqrs
p = (0.4)(10)(10)(4)
p = 160
Therefore, when q = 10, r = 10, and s = 4, the value of p is 160.
Note: This solution assumes that the relationship between p, q, r, and s is truly a joint variation. If this is not the case, the solution above may not be correct.