The weight W that a horizontal beam can support varies inversely as the length L of the beam. Suppose that a 4-m beam can support 1000 kg. How many kilograms can a 17-m beam support?
Well, the weight W is inversely proportional to the length L of the beam. This means that as the length increases, the weight decreases. So, we can set up the equation W = k/L, where k is a constant.
To find the value of k, we can use the information given. When L = 4 m, W = 1000 kg. Plugging these values into the equation, we have:
1000 = k/4
To solve for k, we can multiply both sides by 4:
4000 = k
Now that we have the value of k, we can find the weight that a 17-m beam can support by plugging L = 17 into the equation:
W = 4000/17
Calculating this value gives us W ≈ 235.29 kg.
So, a 17-m beam can support approximately 235.29 kilograms. And hey, that's a pretty weighty topic!
To find the weight that a 17-m beam can support, we need to use the inverse variation formula.
Inverse variation formula: W = k/L
Where:
W = weight the beam can support
L = length of the beam
k = constant of variation
We are given that a 4-m beam can support 1000 kg. Let's use this information to determine the value of k.
W = 1000 kg
L = 4 m
Using the inverse variation formula, we have:
1000 kg = k/4 m
Let's solve for k by cross-multiplying:
1000 kg * 4 m = k
4000 kgm = k
Now that we know the value of k, we can find the weight that a 17-m beam can support.
W = k/L
L = 17 m
Substituting the values into the formula, we have:
W = 4000 kgm / 17 m
Simplifying, we find:
W = 4000/17 kg
Therefore, a 17-m beam can support approximately 235.29 kg (rounded to two decimal places).
To solve this problem, we need to use the inverse variation formula:
W = k/L,
where W is the weight, L is the length, and k is the constant of variation.
We can find the value of k by substituting the given values into the formula. When a 4-m beam can support 1000 kg:
1000 = k/4.
To solve for k, we multiply both sides of the equation by 4:
4000 = k.
Now that we have the value of k, we can find the weight W for a 17-m beam. Substituting the values into the formula:
W = 4000/17.
Calculating this division, we get:
W ≈ 235.29 kg.
Therefore, a 17-m beam can support approximately 235.29 kg.
W = k(1/L)
given: if L = 4m, W = 1000 kg
1000 = k(1/4)
k = 4000
so : W = 4000/L
if L = 17
W = 4000/17 = appr 235.29 kg
or
by ratio:
W1/W2 = L2/L1
1000/W2 = 17/4
17W2 = 4000
W2 = 4000/17 = 235.29 , as before