Question

Suppose the number of leaves z on a tree varies directly with the height of the tree y in yards and directly with the cube of the hours x of direct sunlight that the tree receives. If a tree that is 7 yards tall and receives 6 hours of direct sunlight has 6048 leaves on it, then how many leaves will be on a tree that is 2 yards tall but receives 11 hours of sunlight?

Answer 1

Answer:

The number of leaves are 10648

Step-by-step explanation:

By the given information,

number of leaves be= z

height of tree= y

hours of sunlight= x

by the given conditions,

$z = (k)(y)(x^{3})$

,where k is portionality constant.

now, z=6048, y=7 and x=6,

evaluating value of k using above conditions,

k=4

thus, using this value of k,

$z=(4)(2)(11^{3})$

z= 10648.