An ant needs to travel along a 20cm × 20cm cube to get from point A to point B. What is the shortest path he can take, and how long will it be (in cm)?

1. Along a diagonal, and then along an edge.

2. 48.28 cm.

Step-by-step explanation:

Assume points A and B are at diagonally opposite corners, as in the diagram below.

1. Shortest path

The shortest path is to go along the diagonal AC and continue along the edge CB.

2. Distance

The distance travelled is

d = AC + CB  

According to Pythagoras,

AC² = AD² + CD² = 20² + 20²  = 400 + 400 = 800

AC = √800 = 20√2

d = AC + CB = 20√ 2+ 20 ≈ 2 × 1.414 + 20 = 48.28 cm

The ant travels 48.28 cm.

answer:

sometimes

*i think

step-by-step explanation:

let

we know that

the y-intercept is the y-coordinate of the point when the value of x is equal to zero

so

the y-coordinate of the point a is the y-intercept

the answer part a) is

the value of y-intercept is

part b) find the slope m

we know that

the value of the slope is equal to

substitute the values

therefore

the answer part b) is

the value of the slope is equal to

the general answer is

the slope is

the value of y-intercept is