A directed line segment on a gridded map shows the path of a hot-air balloon from A(0, 0) to B(8, 4). Each grid unit represents 1 mile. The balloon traveled at a constant speed of 20 miles per hour. Point V divides AB in the ratio 6 to 2. What are the coordinates of V? Round to the nearest tenth if necessary. Mary states that the distance from A to V is 6 miles. What is Mary’s mistake? What is the correct distance?

Step-by-step explanation:

The x position changed  8 - 0 = 8 miles

The y position changed 4 - 0 = 4 miles

A ratio of 6 to 2 means the fractional distance from the origin is

6 / (6 + 2) = 3/4

V has an x coordinate of 3/4(8) = 6 miles

V has a y coordinate of 3/4(4) = 3 miles

V = (6, 3)

Mary only considered the x dimension in her result.

d = √(6² + 3²) = √45 ≈ 6.7 miles

question: how many people can she serve?

answer: she can serve 16.66666667 people. so she can only give 16 people a complete serving.

question: does she have enough ice cream for her guests?

answer: no. explanation: she only has enough for 16 people to have a full serving. however, she can give a 17th person a partial serving.

an

y = 6x -3y -12

y +3y +12 = 6x

=> . x = { 2y / 3 +2 } this is equation of line in terms of x

=> . if line meets the x-axis the co-ordinates of meeting point would be ( x , 0 )

=> . x = 2 ( 0 ) / 3 + 2

=> . x = 2

so, the point is ( 2 , 0 )