The weight of a fish varies jointly as its girth and the square of its length. One fish weighed in at 24.6 lb and measured 35 in long with 24 in girth. How much would a fish 37 in long with 22 in in girth weigh?

w = kgl^2

plug in w,g,l to find k
Then evaluate with new g and l

To solve this problem, we can use the joint variation formula:

w = klg²

where w is the weight of the fish, l is the length of the fish, g is the girth of the fish, and k is the constant of variation.

Step 1: Find the value of k by substituting the given values from the fish weighed in, w₁, l₁, and g₁, into the joint variation formula:

24.6 = k(35)(24)²

Step 2: Solve for k:

k = 24.6 ÷ (35 × 24²)

Step 3: Substitute the value of k into the joint variation formula and solve for the weight, w₂, of the fish with the given length, l₂, and girth, g₂:

w₂ = k(l₂)(g₂)²

w₂ = (24.6 ÷ (35 × 24²))(37)(22)²

Step 4: Calculate the weight of the fish:

w₂ ≈ 12.64 lb

Therefore, a fish weighing 37 in long with 22 in girth would weigh approximately 12.64 lb.

To solve this problem, we can use the information given about the joint variation of weight, girth, and the square of length. The joint variation equation can be written as:

Weight = k * Length^2 * Girth

where k is the constant of variation.

We are given the weight, length, and girth of one fish (24.6 lb, 35 in, and 24 in, respectively). We can use these values to find the value of k:

24.6 = k * (35)^2 * 24
24.6 = k * 35^2 * 24
24.6 = k * 122,640
k = 24.6 / 122,640
k ≈ 0.0002

Now that we have the value of k, we can use it to find the weight of a fish with a different length and girth.

To find the weight of a fish 37 in long with 22 in girth, substitute the values into the joint variation equation:

Weight = k * Length^2 * Girth
Weight = 0.0002 * (37)^2 * 22
Weight = 0.0002 * 1369 * 22
Weight = 0.0002 * 30,118
Weight ≈ 6.02 lb

Therefore, a fish that is 37 in long with a girth of 22 in would weigh approximately 6.02 lb.

24.6lbs