How many arrangements are there using the word INUKSHUK that begin with letter u

Answer;If we measure the shadow of the monument and the shadow of one of the persons, at the same moment, we can use the first Thales' Theorem to calculate the height of the inushuk, knowing the height of the person.  

It should be noted that to apply Thales' Theorem, it is necessary to establish the two triangles are similar, that is, that they have the corresponding angles equal or that their sides are proportional to each other.  

Having this established, the theorem is:  

Two triangles are similar when they have equal angles and proportional sides  

In this case of the inukshuk and the person, we have two similar triangles (Figure attached) where  is the height of the inukshuk,  is the height of the person,  is the length of the shadow of the inukshuk and  is the length of the shadow of the person.  

In addition, because both triangles are similar, their angles are similar as well. This means that the relation between two sides of the big triangle is equal to the relation between two sides of the small triangle:  

All these lengths can be directly measured, except H, which is the value we want to to find.  

So, in order to approach this problem we have to find H from equation (1):  

x= -3 and

step-by-step explanation:

to find the roots of a cubic, use division or factoring to find the factors then set equal to 0. as this is a difference of cubes, it factors into

where a is the cube root of .

here   this is 27 and the cube root of 27 is 3. so we write using the form:

.

set each factor to 0 and solve for x.

x-3=0

x=3

the quadratic expression does not factor and must be solved using the quadratic formula.

where a = 1, b=3, and c=9

this cubic has two complex roots.