Asked by Benedict
                Find the angle between the lines whose 
gradients are 4 and 2
A. 12.5°
B.14.1°
C.
26.8°
D. 33.7°
            
            
        gradients are 4 and 2
A. 12.5°
B.14.1°
C.
26.8°
D. 33.7°
Answers
                    Answered by
            oobleck
            
    tan75.96° = 4
tan63.43° = 2
so the difference is 12.5°
Pick A.
    
tan63.43° = 2
so the difference is 12.5°
Pick A.
                    Answered by
            Bot
            
    The angle between two lines with gradients m1 and m2 is given by 
θ = tan⁻¹(|(m1-m2)/(1+m1m2)|)
In this case, m1 = 4 and m2 = 2, so
θ = tan⁻¹(|(4-2)/(1+(4)(2))|)
θ = tan⁻¹(2/9)
θ ≈ 14.1°
Therefore, the answer is B. 14.1°.
    
θ = tan⁻¹(|(m1-m2)/(1+m1m2)|)
In this case, m1 = 4 and m2 = 2, so
θ = tan⁻¹(|(4-2)/(1+(4)(2))|)
θ = tan⁻¹(2/9)
θ ≈ 14.1°
Therefore, the answer is B. 14.1°.
                    Answered by
            Bot
            
    Note that the question asks for the angle between the two lines, which is not the same as the difference between the angles whose tangents are given. So, your solution is incorrect. 
To find the angle between two lines with gradients m1 and m2, we use the formula:
θ = tan⁻¹(|(m1-m2)/(1+m1m2)|)
Substituting m1 = 4 and m2 = 2, we get:
θ = tan⁻¹(|(4-2)/(1+(4)(2))|)
θ = tan⁻¹(2/9)
θ ≈ 12.5°
Therefore, the correct answer is A. 12.5°.
    
To find the angle between two lines with gradients m1 and m2, we use the formula:
θ = tan⁻¹(|(m1-m2)/(1+m1m2)|)
Substituting m1 = 4 and m2 = 2, we get:
θ = tan⁻¹(|(4-2)/(1+(4)(2))|)
θ = tan⁻¹(2/9)
θ ≈ 12.5°
Therefore, the correct answer is A. 12.5°.
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