Calculate, correct to one decimal place, the acute angle between the lines 3x - 4y + 5 = 0 and 2x + 3y - 1= 0.

70.6°

Step-by-step explanation:

The angle between the 2 lines can be calculated using

tanΘ = | | ( Θ is the angle between the lines )

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Rearrange the 2 equations into this form to extract the slopes

3x - 4y + 5 = 0 ( subtract 3x + 5 from both sides )

- 4y = - 3x - 5 ( divide all terms by - 4 )

y = x + with m = ←

--------------------------------------------

2x + 3y - 1 = 0 ( subtract 2x - 1 from both sides )

3y = - 2x + 1 ( divide all terms by 3 )

y = - x + with m = - ←

Note it does not matter which slope is labelled or

Thus

tan Θ = |

          = | = | | = , then

Θ = ( ) ≈ 70.6° ( to 1 dec. place )

x/3-10=8

x/3=18

x=48

the population of other specie of birds will decline or other specie of birds will find some alternate source of food to survive.

explanation:

according to the competitive exclusion principle, which is also known as gause's law, two specie living in the same niche and feeding on the same resource cannot co-exist stably.

as we have well studied the theory of natural selection which states that only those organisms survive which have better tendency to compete for food and adapt to the environmental conditions.

coming towards the question, what wi ll happen when one species outcompetes the other for the small fish , the other specie will not get enough food and will start to die or decline in population. eventually either other specie needs to find another alternative food source for itself or migrate at some other location where there is less competition otherwise it will just not exist anymore at that niche.

hope it !