Hello, could please you help me with this exercice?
Species of wood - Density (g/cm3)
Cedar - 0.40
Chestnut - 0.86
Buis - 0.90
Sea pine - 0.55
Pine - 0.90
1) A wooden cube of 6.2 cm of ridge has a mass of about 205 g.
Is the wood used to make it pine or chestnut?
2) A cube with a whole number of centimetres on the side, made in
wood of a single species, has a mass of 68.75 g.
Determine the species of wood used in its manufacture and the length of the wood the edge of the cube.
could you please explain it step by step, i do not speak english fluently, thank you so much.

1) Chestnut

2) Sea pine

Step-by-step explanation:

1)

In this problem, we have to calculate the density of the cube.

The density of an object is given by:

where

m is the mass of the cube

V is the volume of the cube

For the wooden cube in this problem, we have:

m = 205 g is the mass

L = 6.2 cm is the length of one side

So, its volume is:

Therefore, its density is

And by comparing this value with the table, we see that this wood is used to make chestnut.

2)

In this problem, we have another cube with a mass of

m = 68.75 g

We also know that the cube has a side measuring a whole number of centimeters.

Let's call the length of one side as L.

We have to try several attempts to find the correct value of L.

Let's start with 6 cm:

L = 6 cm

So the volume is

In this case, the density would be

This value is lower than all the values in the table, so we have to try with a smaller volume.

The next lower integer  length for the cube is

L = 5 cm

which leads to a volume of

In this case, the density is

Which matches with the density of sea pine.

solution:

the given function is ,

      =

the three roots of this quadratic function is , 0 ,8 and 10.all the roots are real and rational.

if a quadratic equation is of the form ,

sum of the roots = a + b +c= 0+8+10=18=  

product of roots taken two at a time = a b + b c+ c a = 0+80+0=80 =  

product of roots = a b c = 0=  

there are 11 doors in a hall starting from 0 to 11.the entry in the hall is permitted through gate number 0 and exit is allowed through only gate number 8 and 10.so, three roots(0,8,10) of quadratic function is given by entry and exit route of this hall.