Calculate, correct to one decimal place, the acute angle ...
Calculate, correct to one decimal place, the acute angle between the lines 3x - 4y + 5 = 0 and 2x + 3y - 1 = 0.
70.6°
50.2°
39.8°
19.4°
Correct answer is A
\(\tan \theta = \frac{m_{1} - m_{2}}{1 - m_{1}m_{2}}\)
\(m_{1} = \text{slope of 1st line } 4y = 3x + 5 \implies y = \frac{3}{4}x + \frac{5}{4}\)
\(m_{1} = \frac{3}{4}\)
\(m_{2} = \text{slope of 2nd line} 3y = 1 - 2x \implies y = \frac{1}{3} - \frac{2}{3}x\)
\(m_{2} = -\frac{2}{3}\)
\(\tan \theta = \frac{\frac{3}{4} - (-\frac{2}{3})}{1 - ((\frac{3}{4})(-\frac{2}{3}))} = \frac{\frac{17}{12}}{\frac{1}{2}}\)
\(\tan \theta = \frac{17}{6}\)
\(\theta \approxeq 70.6°\)
Given that \(R = (4, 180°)\) and \(S = (3, 300°)\), find the dot product...
The function \(f : F \to R\) = \(f(x) = \begin{cases} 3x + 2 : x > 4 \\ 3x - 2 : x = 4 \\ ...
If √5 cosx + √15sinx = 0, for 0° < x < 360°, find the values of x. ...
Find the value of \(\cos(60° + 45°)\) leaving your answer in surd form...
The equation of a circle is \(x^{2} + y^{2} - 8x + 9y + 15 = 0\). Find its radius....
Express \(\frac{2}{3 - \sqrt{7}} \text{ in the form} a + \sqrt{b}\), where a and b are integers....
Evaluate \(\cos 75°\), leaving the answer in surd form....
If \(f(x) = mx^{2} - 6x - 3\) and \(f'(1) = 12\), find the value of the constant m....