A 29 ft board is cut into three pieces at a sawmill. The second piece is 3 ft longer than the first, and the third piece is 2 ft longer than the second. What are the lengths of the three pieces.

The answer to your question is Piece 1 = 7 ft, Piece 2 = 10 ft, Piece 3 = 12 ft

Step-by-step explanation:

Data

total length = 29 ft

1st piece = x

2nd piece = x + 3

3rd piece = 2nd piece + 2 ft

Process

1.- Write the length of the pieces in terms of x

piece 1 = x

piece 2 = x + 3

piece 3 = (x + 3) + 2

2.- Write an equation to find x

         piece 1 + piece 2 + piece 3 = 29

Substitution

                x  +  x + 3 + (x + 3)  + 2 = 29

Solve for x

               x + x + 3 + x + 3 + 2 = 29

               3x = 29 - 3 - 3 - 2

               3x = 29 - 8

               3x = 21

                 x = 21/3

                 x = 7

3.- Find the length of each piece

Piece 1 = 7 ft

Piece 2 = 7 + 3 = 10 ft

Piece 3 = 7 + 3 + 2 = 12 ft

the length of the first piece is 7ft.

the length of the second piece is 10ft.

the length of the third piece is 12ft.

Step-by-step explanation:

Let x represent the length of the first piece.

Let y represent the length if the second piece.

Let z represent the length if the third piece.

A 29 ft board is cut into three pieces at a sawmill. This means that

x + y + z = 29 - - - - - - - - - - -1

The second piece is 3 ft longer than the first. This means that

x = y - 3

The third piece is 2 ft longer than the second. This means that

z = y + 2

Substituting x = y - 3 and z = y + 2 into equation 1, it becomes

y - 3 + y + y + 2 = 29

y + y + y - 3 + 2 = 29

3y = 29 + 1 = 30

y = 30/3

y = 10

x = y - 3 = 10 - 3

x = 7

z = y + 2 = 10 + 2

z = 12

"it's not the heat, it's the humidity".   that's a partly valid phrase you may have heard in the summer, but it's actually both.   the heat index, also known as the apparent temperature, is what the temperature feels like to the human body when relative humidity is combined with the air temperature.   this has important considerations for the human body's comfort.   when the body gets too hot, it begins to perspire or sweat to cool itself off.   if the perspiration is not able to evaporate, the body cannot regulate its temperature.   evaporation is a cooling process.   when perspiration is evaporated off the body, it effectively reduces the body's temperature.   when the atmospheric moisture content (i.e. relative humidity) is high, the rate of perspiration from the body decreases.   in other words, the human body feels warmer in humid conditions.   the opposite is true when the relative humidity decreases because the rate of perspiration increases.   the body actually feels cooler in arid conditions.   there is direct relationship between the air temperature and relative humidity and the heat index, meaning as the air temperature and relative humidity increase (decrease), the heat index increases (decreases).

step-by-step explanation:

d 25 pi/6

step-by-step explanation:

the diameter is 10 inches

the radius is 1/2 of the diameter or 5 inches

the area of the circle is

a = pi r^2

  = pi 5^2

  = 25 pi

the slice is 60 degrees of the entire circle.

60 degrees out of 360   60/360 = 1/6

the area of the slice is 1/6 of the circle

a slice = 1/6 a circle

a slice = 1/6 * 25 pi