The maximum load a beam will support varies directly with the square of the diagonal of the beam's cross section.A beam with diagonal 6 inch will support a maximum load of 108 pounds. What load will a beam with a 10 inch diagonal support?

translated:

load = k d^2
given: if d = 6, load = 108
108 = k(36)
k = 108/36 = 3

load = 3d^2
so when d = 10
load = 3(100) = 300 pounds

Show me all working out

Well, isn't it funny how the load of a beam relates to the diagonal of its cross section? It's like the bigger the diagonal, the bigger the load it can support. So, let's do some math here.

We know that the diagonal of the first beam is 6 inches, and it can support a maximum load of 108 pounds. But what about our second beam with a diagonal of 10 inches? Let's find out!

Since the load varies directly with the square of the diagonal, we can set up a proportion:

(6^2) : 108 = (10^2) : x

Simplifying that, we get:

36 : 108 = 100 : x

Now, cross-multiply and solve for x:

36 * x = 108 * 100

x = (108 * 100) / 36

x ≈ 300 pounds

So, if my calculations are correct (and I sure hope they are), a beam with a 10-inch diagonal will support a maximum load of around 300 pounds. Just imagine what you can do with that much weight! Maybe build a home gym or a catapult for launching watermelons into the neighbor's yard? The possibilities are endless!

To find the load a beam with a 10-inch diagonal will support, we can set up a proportion using the given information.

Let's denote the maximum load as L and the diagonal as d. According to the problem, the maximum load (L) varies directly with the square of the diagonal (d^2). We can express this as a proportion:

L / d^2 = k

Where k is the constant of variation.

Now, we can set up the proportion using the given information:

L1 / d1^2 = L2 / d2^2

L1 = 108 pounds (load supported by the beam with a diagonal of 6 inches)
d1 = 6 inches (diagonal of the beam supporting 108 pounds)
d2 = 10 inches (diagonal of the beam we want to find the load for)

Setting up the proportion:

108 / 6^2 = L2 / 10^2

108 / 36 = L2 / 100

Cross multiplying:

100 * 108 = 36 * L2

10,800 = 36 * L2

Divide both sides by 36:

300 = L2

Therefore, a beam with a 10-inch diagonal will support a maximum load of 300 pounds.

To find the load that a beam with a 10-inch diagonal will support, we need to use the concept of direct variation.

According to the given information, the maximum load a beam will support varies directly with the square of the diagonal of the beam's cross section.

Let's denote the maximum load as L and the diagonal as d.

Using the direct variation equation, we can write this relationship as:

L = k * d^2

Where k represents the constant of variation.

To find the value of k, we can use the information provided: when the diagonal is 6 inches, the maximum load is 108 pounds.

So, we have:

108 = k * 6^2

Simplifying this equation, we get:

108 = k * 36

To find the value of k, we divide both sides of the equation by 36:

k = 3 (108 ÷ 36 = 3)

Now that we know the value of k, we can use it to find the load for a beam with a 10-inch diagonal.

Using the equation:

L = k * d^2

L = 3 * 10^2

L = 3 * 100

L = 300 pounds

Therefore, a beam with a 10-inch diagonal will support a maximum load of 300 pounds.