Respuesta :
Answer:
tanФ = 2.6363636
Step-by-step explanation:
To find the tangent of the angle in-between the lines we will follow the steps below:
We are going to use the formula;
tanФ = |m₂ - m₁ / 1 + m₁m₂|
We can get the slope m₁ from the first equation
2x+3y–5=0
we will re-arrange it in the form y=mx + c
3y = -2x + 5
Divide through by 3
y = -[tex]\frac{2}{3}[/tex]x + [tex]\frac{5}{3}[/tex]
comparing the above equation with y=mx + c
m₁ = -[tex]\frac{2}{3}[/tex]
We will proceed to find the second slope m₂ using the second equation
5x=7y+3
we will re-arrange it in the form y=mx + c
7y = 5x -3
divide through by 7
y = [tex]\frac{5}{7}[/tex] x - [tex]\frac{3}{7}[/tex]
comparing the above with y=mx + x
m₂ = [tex]\frac{5}{7}[/tex]
we can now go ahead and substitute into the formula
tanФ = |m₂ - m₁ / 1 + m₁m₂|
tanФ = | [tex]\frac{5}{7}[/tex] - (-[tex]\frac{2}{3}[/tex] ) / 1 + (-[tex]\frac{2}{3}[/tex]₁)( [tex]\frac{5}{7}[/tex])|
tanФ = | [tex]\frac{5}{7}[/tex] +[tex]\frac{2}{3}[/tex] / 1 - [tex]\frac{10}{21}[/tex]|
tanФ = | [tex]\frac{29}{21}[/tex] / [tex]\frac{11}{21}[/tex]|
tanФ = | [tex]\frac{29}{21}[/tex] × [tex]\frac{21}{11}[/tex]|
21 will cancel-out 21
tanФ =[tex]\frac{29}{11}[/tex]
tanФ = 2.636363
