The value p varies directly with q^-1. If p=1/6 when q=5/8, what is the value of p when q=18?
A)864/5
B)7/24
C)5/864
D)-8/135
I did the p=kq, and found p to be 24/5 but that's not a choice. Help!!
p varies directly with q^-1
not
p varies directly with q^
p = k/q
so, pq = k, a constant. You want p such that
18p = (1/6)(5/8)
18p = 5/48
p = 5/864
Sure, I'd be happy to help!
First, let's use the information given to form an equation representing the direct variation between p and q. We're told that p varies directly with q^-1, which means that p is inversely proportional to q.
So, we have the equation p = k/q, where k is the constant of variation.
Now, let's plug in the values we have: p = 1/6 when q = 5/8. Substituting these into our equation, we get:
1/6 = k / (5/8)
To solve for k, we can multiply both sides of the equation by (5/8):
(5/8) * (1/6) = k
5/48 = k
Now that we have the value of k, we can use it to find the value of p when q = 18:
p = k / q
p = (5/48) / 18
p = (5/48) * (1/18)
p = 5 / (48 * 18)
p = 5 / 864
Therefore, the correct answer is C) 5/864.
I hope this helps! Let me know if you have any other questions.
To solve this problem, let's use the equation p = k/q where k is a constant.
We are given that p varies directly with q^-1, which means that p is inversely proportional to q. In other words, as q increases, p will decrease.
We also know that when q = 5/8, p = 1/6.
Using this information, we can find the value of k.
p = k/q
1/6 = k/(5/8)
1/6 = (8k)/5
5 = 48k
k = 5/48
Now that we have the value of k, we can find the value of p when q = 18.
p = (5/48) / 18
p = 5/48 * 1/18
p = 5/864
Therefore, the value of p when q = 18 is 5/864.
The correct answer is C) 5/864.
To solve this problem, we are given that the value of p varies directly with the inverse of q. In other words, we can write the relationship as p = k/q, where k is a constant.
We are also given a specific value for p and q at a certain point: p = 1/6 when q = 5/8.
To find the value of p when q = 18, we can substitute these values into the equation p = k/q and solve for k.
Using the given point (p = 1/6, q = 5/8), we have:
1/6 = k / (5/8)
To find the value of k, we can multiply both sides of the equation by (5/8):
(5/8) * (1/6) = k
5/48 = k
Now that we have the value of k, we can use it to find the value of p when q = 18:
p = k / q
p = (5/48) / 18
Simplifying further, we can divide the numerator by the denominator:
p = 5/48 * 1/18
p = 5/864
Therefore, the value of p when q = 18 is 5/864.
Hence, the correct answer is C) 5/864.