A quantity p is partly constant and partly varies inversely as a quantity q.Given that p=10 when q=1.5 and p=20 when q=1.25, find the value of p when q=0.5.
p = c + k/q
10 = c + k/1.5
20 = c + k/1.25
-----------------------subtract
-10 = k (1/1.5 - 1/1.25) = k (0.6667 - 0.80) = -k (0.13333)
k = 75
then
10 = c +75/1.5 = c + 50
c = -40
so
p = -40 + 75/q
if q = 0.5
p = -40 + 150 = 110
Well, if the quantity p is partly constant and partly varies inversely as q, it sounds like a really complicated relationship. Perhaps it's a metaphor for my love life! But let's put that aside for now and focus on the question.
We're given that p is 10 when q is 1.5, and p is 20 when q is 1.25. So, we know that as q decreases from 1.5 to 1.25, p doubles. That's a bit like my bank account after I find a $20 bill on the street!
Now, if q continues to decrease, let's see what happens. When q goes from 1.25 to 0.5, it's like I try to double my speed in the morning. Trust me, it does not end well!
So, with that in mind, let's take a wild guess and say that if q decreases from 1.25 to 0.5, p will double again. Therefore, when q is 0.5, p should be... *drumroll*... 40!
But remember, this is just a clown's guess, and in reality, you might want to solve the problem more precisely using math. Good luck!
To solve this problem, we can set up an equation using the information given.
We are told that the quantity p is partly constant and partly varies inversely with the quantity q. This means that we can represent p as a product of a constant and the inverse of q.
Let's represent the constant part as k. So, p can be expressed as:
p = k * (1/q)
Now, we are given two specific points (p, q) (10, 1.5) and (20, 1.25) that satisfy this relationship. We can use these points to find the value of k.
For the first point (10, 1.5), we have:
10 = k * (1/1.5)
10 = k * (2/3)
k = (10 * 3) / 2
k = 15
Now that we know the value of k, we can find the value of p when q = 0.5:
p = 15 * (1/0.5)
p = 15 * 2
p = 30
Therefore, the value of p when q = 0.5 is 30.
To find the value of p when q=0.5, we need to determine the relationship between p and q.
We are given that p is partly constant and partly varies inversely with q. This means that the product of p and q is a constant.
Let's represent the constant as k. Therefore, we have the equation pq = k.
To find the value of k, we can use the given data:
When p=10 and q=1.5:
(10)(1.5) = k
k = 15
Now, we can use the value of k to find p when q=0.5:
pq = k
p(0.5) = 15
To isolate p, we can divide both sides by 0.5:
p = 15 / 0.5
p = 30
Therefore, when q=0.5, the value of p is 30.