Two Lagrangian Toads spot my cat Pythagoras simultaneously. They both run directly away from Pythagoras immediately. The first is initially 5 m from Pythagoras and runs at a rate of 2 m/s and the second is initially 1 m from Pythagoras and runs at a rate of 3 m/s. If the angle of the line of sight from Pythagoras to each of these Lagrangian Toads is 30°, then how fast is the distance between these Lagrangian Toads increasing after 4 seconds?

Explanation:

In the triangle formed , the third side , that is distance between two toads can be calculated with the help of following formula

Cos C = a² + b² - c² / 2ab

c² = a² + b² - 2abcosC

c² = 5² + 1² - 2 x 5 x 1 cos 30

= 26 - 8.66

= 17.34

c = 4.16 m

c² = a² + b² - 2abcosC

differentiating with respect to time

2 c x dc / dt = 2a da/dt + 2 b db/dt - 2 cosC ( a db/dt + b da/dt )

c x dc / dt = a da/dt +  b db/dt -  cosC ( a db/dt + b da/dt )

4.16 dc/dt = 5 x 2 + 1 x 3 - .866 ( 5 x 3 + 1 x 2 )

= 13 - 14.722

= - 1.722

dc / dt = - 1.722 / 4.16

= -  .414 m /s .

The distance between the two will decrease at the rate above.

answer: the direction of the wind is expressed as the direction from which the wind is blowing. for example, easterly winds blow from east to west, while westerly winds blow from west to east.

explanation:

from

explanation:

wind is defined by the direction it blows from.   for example, a wind blowing from north to south is called a northerly wind.