the maximum load, v, that can be safely supported by horizontal beam varies jointly with the width of the beam ,w, and the square of its depth ,x, and inversely with the length of the beam ,a, write an equation for the constant of variation ,k, in terms of v, w, x and a.

you know that

v = kwx^2/a

Now just solve for k

The maximum load, v , that can be safely supported by a horizontal beam varies jointly with the width of the beam, w , and the square of its depth, x , and inversely with the length of the beam, a .

Write an equation for the constant of variation, k, in terms of v, w, x, and a.

The given problem states that the maximum load, v, varies jointly with the width of the beam, w, and the square of its depth, x, and inversely with the length of the beam, a.

We can express this relationship mathematically as:

v = k * (w * x^2) / a

Where:
v = Maximum load
w = Width of the beam
x = Depth of the beam
a = Length of the beam
k = Constant of variation

Now, let's isolate the constant of variation, k, in terms of the other variables:

k = (v * a) / (w * x^2)

Therefore, the equation for the constant of variation, k, in terms of v, w, x, and a is:

k = (v * a) / (w * x^2)

To write the equation for the constant of variation, we need to express the relationship described in the problem as a mathematical equation.

According to the problem, the maximum load, v, that can be safely supported by the beam varies jointly with the width, w, and the square of its depth, x, and inversely with the length, a.

We can express this relationship as:

v = k * (w * x^2) / a

Where:
v is the maximum load supported by the beam
w is the width of the beam
x is the depth of the beam
a is the length of the beam
k is the constant of variation

Rearranging the equation, we can solve for k:

k = v * a / (w * x^2)

So, the equation for the constant of variation, k, in terms of v, w, x, and a is:

k = v * a / (w * x^2)