Suppose you work on a tree farm and you need to find the height of each tree. You know that the length of an object with its height. Find the constant of variation

The answer is below

Step-by-step explanation:

Suppose you work on a tree farm and you need to find the height of each tree. You know that the length of an object varies directly with its height. a) Find the constant of variation b) find the height of the tree

Solution:

a) Let y represent the length of an object and x represent the height of the object. Given that y ∝ x. Let k be the constant of variation, therefore the relationship between y and x is:

y = kx

y = 2 ft 2 in = 13/6 ft (1 ft = 12 in)

x = 6 ft

Substituting gives:

13/6 = k(6)

k = 13/6 ÷ 6

k = 13/36

b) y = (13/36)x

Given that y = 8ft 4 in = 25/3 ft

Substituting:

y = (13/36)x

25/3 = (13/36)x

x = 25/3 ÷ (13/36)

x= 300/13 ft ≈ 23 ft

a_n = a_1 + (n - 1)d

the first term is 6.

the common difference d = ?

when you find d, replace n with 7 and d with the common difference to find your answer.