l varies partly inversely as m and is partly constant when l=3,m=2 and when l=9,m=5.find m when l=1.
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L varies
partly inversely as M and is partly constant.
We can represent this relationship between L and M using the formula:
L = k(M/h)
where k and h are constants.
To find k and h, we can use the given information that when L=3 and M=2, and when L=9 and M=5:
3 = k(2/h)
9 = k(5/h)
We can solve for h in the first equation:
3h = 2k
h = (2/3)k
Substitute this into the second equation:
9 = k(5/((2/3)k))
9 = k(7.5)
k = 1.2
Now we can find h:
3 = 1.2(2/h)
h = 4
So the formula for L in terms of M is:
L = (1.2M/4)
L varies partly inversely as M and is partly constant when L=3,M=2 and when L=9,M=5 Fins M when L=1
We can use the formula L = k(M/h) to solve for the value of M when L=1.
From the given information, we know that when L=3 and M=2, and when L=9 and M=5:
3 = k(2/h)
9 = k(5/h)
We can solve for h in the first equation:
3h = 2k
h = (2/3)k
Substitute this into the second equation:
9 = k(5/((2/3)k))
k = 1.2
Now we know that:
L = (1.2M/4)
We can plug in L = 1 and solve for M:
1 = (1.2M/4)
M = (4/1.2)
M = 3.33 (rounded to two decimal places)
Therefore, when L=1, M is approximately equal to 3.33.
To find the value of m when l=1, we'll use the concept of the inverse variation equation.
In this case, l (length) varies partly inversely as m (measure). We can represent this relationship using the equation l = k/m, where k is the constant of variation.
We are given two scenarios with specific values of l and m:
1) When l = 3 and m = 2
2) When l = 9 and m = 5
Let's use these values to find the value of k, the constant of variation, and then plug it into the equation to determine m when l = 1.
First, substitute the values from the first scenario into the equation l = k/m:
3 = k/2
Next, substitute the values from the second scenario into the equation:
9 = k/5
Now we have two equations:
3 = k/2 ---(Equation 1)
9 = k/5 ---(Equation 2)
To isolate k, we can cross-multiply:
2 * 3 = k (from Equation 1)
5 * 9 = k (from Equation 2)
Simplifying the equations gives us:
6 = k
45 = k
Since we have two different values of k, we need to investigate further.
When l is constant, m is directly influenced by the value of k. So, we can observe that as l = 3 decreases to l = 9, m increases from 2 to 5. This tells us that as l increases, m decreases, indicating an inverse relationship.
From this, we can infer that the value of k should be larger when l is smaller. Therefore, k = 45 is the appropriate constant in this case.
Now, we can substitute the value of k into the inverse variation equation:
l = 45/m
To find m when l = 1, we substitute this new value into the equation:
1 = 45/m
Now, cross-multiply and solve for m:
m = 45/1
m = 45
Therefore, when l = 1, m is equal to 45.