Liam is a tyre fitter. it takes him 56 minutes to fit 4 tyres to a van.

Answer:

                          π

V-foam = 4r³( 2 - ----- )

                             3

Step-by-step explanation:

Let r denote the radius of the sphere. The volume of the sphere is expressed as

V = (4/3)(π)(r³).

Next, understand that the cube's side length is 2r, hence the cube's volume is

V = (2r)³, which equals 8r³.

The volume of the foam is derived from the cube's volume subtracting that of the sphere:

V-foam = 8r³ - (4/3)(π)(r³). This can be simplified to

                          π

V-foam = 4r³( 2 - ----- )

                             3

Answer:

The solution to your inquiry can be found below

Step-by-step explanation:

First method

                      20 = 5(-3 + x)                   expanding this equation

                     20 = -15 + 5x                    combine like terms

                     5x = 20 + 15

                     5x = 35                            dividing by 5

                     5x/5 = 35/5

                     x = 7

Second method

                     20/5 = 5/5 (-3 + x)          divide both sides by 5

                     4  = -3 + x                        adding 3 to both sides

                     4 + 3 = -3 + 3 + x            simplifying

                     7 = x

Answer:

1) (2.2, -1.4)

2) (1.33, 1)

Detailed solution:

Question 1)

We are provided with two linear equations representing lines, and we need to find the intersection point that solves the system.

The lines given are:

Line 1 equation:

This line passes through points (0, 2.5) and (2.2, -1.4).

Line 2 equation:

The second line goes through (0, -3) and (2.2, -1.4).

According to the graph and data, the solution to the system is the coordinate where both lines intersect.

The solution to a system of linear equations is the coordinate pair common to both lines, i.e., the intersection point.

Here, both lines share the point (2.2, -1.4), indicating it is their intersection and the solution.

Therefore, the solution for question 1 is (2.2, -1.4).

Question 2)

The equations given are:

y = 1.5x - 1               Equation 1

y = 1                           Equation 2

The method of substitution can be used to find the solution.

Replacing y from Equation 2 into Equation 1 gives:

1 = 1.5x - 1

Add 1 to both sides:

2 = 1.5x

Dividing both sides by 1.5 yields:

x = 2/1.5

x = 1.33

y = 1

Thus, the solution of the system is (1.33, 1).

x = lowest height

<x+25 highest height

x=55