Answer:
[tex]\approx 13^\circ[/tex]
Step-by-step explanation:
Given two lines with the equations:
[tex]9x - y = 4\\ 8x + y = 6[/tex]
First of all, let us learn the formula for finding the angle between the two lines with given equations:
[tex]tan\theta = \dfrac{m_1-m_2}{1+m_1m_2}[/tex]
[tex]m_1, m_2[/tex] are the slopes of the two lines respectively.
Let us convert the given equation to point intercept form.
Point intercept form of a line is given as:
[tex]y = mx+c[/tex]
[tex]y = 9x-4\\y =-8x+6[/tex]
Comparing with slope intercept form, we get:
[tex]m_1 = 9\\m_2 = -8[/tex]
Using the above formula:
[tex]tan\theta =\dfrac{9 -(-8)}{1+9(-8)}\\\Rightarrow tan\theta = -\dfrac{17}{71}\\\Rightarrow \theta = -13.46^\circ\\[/tex]
Therefore, the acute angle between the two lines is [tex]\approx 13^\circ[/tex]
The acute angles between the equations is 13.46 degree.
To find the acute angles between the two equation, let's write out the individual slope of each equation.
Given Data
The given equations can be rearranged into equation of line.
[tex]9x-y=4\\ y=9x-4\\ slope=m_1=9[/tex]
The second equation can also be rearranged as and solving for the slope
[tex]8x+y=6\\ y=6-8x\\ y=-8x+6\\ slope = m_2 = -8[/tex]
Since we have the slopes of the two equation, we can now find the acute angle between them.
θ = [tex]tan^-^1[\frac{m_1-m_2}{1+m_1m_2}]\\ [/tex]
substituting the values and solving for the angle
[tex]x = tan^-^1[\frac{9-(-8)}{1+(9*-8)}]\\ x = tan^-^1[17/-71]\\ x=-13.46 = 13.46^0[/tex]
The acute angle between the equations is 13.46 degree
Learn more about acute angle in equations here;
https://brainly.com/question/6979153
