L varies partly inversely as m and is partly constant. When L=3,M=2 and when m=2 and when L=9,m=5.find M when L=1
L = k/m + b
3 = k/2 + b
9 = k/5 + b
------------- subtract
-6 = k/2 - k/5 = 5 k/10 - 2 k/10 = 3 k/10
k=-20
3 = -10 + b
b = 13
so
L = -20/m + 13
so put in 1 for L and see what you get for m
Well, well, well, looks like we have a little relationship conundrum here! L varies partly inversely as m... sounds complicated, doesn't it? But fear not, for I am here to unravel this equation with a touch of humor!
Let's break it down, shall we? "L varies partly inversely as m" means that as one quantity goes up, the other goes down. It's like a roller coaster of proportions!
Now, you mentioned that when L = 3 and M = 2, and when L = 9 and M = 5. Got it! These values give us a hint about the magical constant in this equation!
We can use the formula for partial inverse variation: L = k / m. Or in our case, we can write it as L = k * 1/m, because k is partly constant.
Now we can plug in the values: 3 = k * 1/2 and 9 = k * 1/5.
Solving the first equation for k, we get k = 6.
And now, with the magic of algebra, we can find M when L = 1! Oh, the suspense is killing me!
Plugging L = 1 into our equation (1 = 6 * 1/M), we can simply cross multiply.
1 * M = 6 * 1
M = 6
Ta-da! The solution emerges from the mist! When L = 1, M = 6! Keep that in your pocket, my friend, and amaze your mathematician friends with your newfound equation-solving skills.
To solve this problem, we can use the formula for variation:
L = k/m
where k is the constant of variation.
We are given two sets of values and can use them to find the value of k:
When L = 3 and m = 2:
3 = k/2
Solving for k:
k = 3 * 2 = 6
When L = 9 and m = 5:
9 = 6/5
To find M when L = 1, we can substitute the values into the formula:
1 = 6/M
Solving for M:
M = 6/1 = 6
To find M when L = 1, we need to determine the relationship between L and M by using the given information.
The problem tells us that L varies partly inversely as M and is partly constant. This means that the product of L and M remains constant.
Let's use the given values to find this constant. When L = 3 and M = 2, the product is 3 * 2 = 6. Similarly, when L = 9 and M = 5, the product is 9 * 5 = 45.
From these two examples, we can determine the constant (k) by taking the product of L and M at any point:
k = L * M
Now, we can find M when L = 1. Since the constant k remains the same,
k = L * M
Substituting the given values L = 1 and k = 6:
6 = 1 * M
Dividing both sides of the equation by 1, we get:
6 = M
Therefore, when L = 1, M = 6.