P is partly constant and partly varies inversely as Q.lf Q=9 when P=3 and Q=18 when P=9 find P when Q=12
P = k/Q + C
given:
P=3, Q=9
3 = k/9 + C
27 = K + 9C ***
P=9, Q = 18
9 = k/18 + C
162 = k + 18C **
subtract *** from **
135 = 9C
C = 15
in ***
k+135 = 27
k = -108
P = -108/Q + 15
so when Q = 12
P = -108/12 + 15 = 6
P=-108\12+ 15 =6
Multiply both side /no. With 12.
6 = 15 -108\12, you get
72 = 180 - 108
72 = 72, cross over 72 to the other side.
72-72 = 0
So, P = 0
Well, since P is partly constant and partly varies inversely as Q, it sounds like a complicated relationship. It's almost as complicated as trying to juggle rubber chickens while riding a unicycle!
But don't worry, I'll give it a shot! Let's break it down step by step.
First, we have the initial values: Q=9 when P=3 and Q=18 when P=9. These values help us establish a starting point.
If P is partly constant, then we know that for the given values, P will remain the same. So, we can conclude that when Q=9, P=3 remains constant.
Now, the problem says that P also varies inversely as Q. Inverse variation means that as Q increases, P decreases, and vice versa. It's kind of like when you try to fit into a small car – the more people you add, the less space there is for each person!
We can write this inverse variation relationship as P = k/Q, where k is a constant.
Using the second set of values, Q=18 when P=9, we can find k. So, 9 = k/18, which gives us k = 162.
Now that we know k, we can find P when Q=12. Plugging in the values, P = 162/12 = 13.5.
So, when Q=12, P would be equal to 13.5.
I hope that explanation didn't clown around too much! Let me know if you have any more questions!
To solve this problem, we need to understand that P is partly constant and partly varies inversely as Q.
Let's break down the given information:
When Q = 9, P = 3.
When Q = 18, P = 9.
From this information, we can deduce the following inverse relationship equation between P and Q:
P = k/Q,
where k is the constant of variation.
To find the value of k, we can use one of the given data points. Let's use the first data point:
3 = k/9.
To solve for k, we multiply both sides of the equation by 9:
27 = k.
Now that we have the value of k, we can use it to find P when Q = 12:
P = 27/12.
Simplifying this expression, we get:
P = 9/4.
Therefore, when Q = 12, P = 9/4 or 2.25.
To solve this problem, we can set up an equation involving the constant and the inverse variation.
We are given that P is partly constant and partly varies inversely as Q, which can be written as:
P = k · (1/Q)
Where k is the constant of variation.
First, we can find the value of k by using the given information. When Q is 9, P is 3, so we can substitute these values into the equation:
3 = k · (1/9)
To solve for k, we can multiply both sides of the equation by 9:
27 = k
Now that we know the value of k, we can find P when Q is 12. Substituting the values into the equation:
P = 27 · (1/12)
Simplifying this expression:
P = 27/12
P = 9/4
Therefore, when Q is 12, P is 9/4 or 2.25.