Photo AI

1.1 Determine the gradient of DE - NSC Technical Mathematics - Question 1 - 2023 - Paper 2

Question icon

Question 1

1.1-Determine-the-gradient-of-DE-NSC Technical Mathematics-Question 1-2023-Paper 2.png

1.1 Determine the gradient of DE. 1.2.1 Calculate the angle $eta$, given that $ an \beta = m = 1$. Thus, $eta = 45^{\circ}$. 1.2.2 Let y = x + 6 OR OF y - x = 6... show full transcript

Worked Solution & Example Answer:1.1 Determine the gradient of DE - NSC Technical Mathematics - Question 1 - 2023 - Paper 2

Step 1

Determine the gradient of DE.

96%

114 rated

Answer

To find the gradient, use the formula for the gradient of a line which is given by:

m=y2−y1x2−x1m = \frac{y_2 - y_1}{x_2 - x_1}

For the points D(-4; 8) and E(4; -4), we have:

m=−4−84−(−4)=−128=−32m = \frac{-4 - 8}{4 - (-4)} = \frac{-12}{8} = -\frac{3}{2}

Thus, the gradient of DE is ( m = -\frac{3}{2} ).

Step 2

Calculate the angle \( \beta \), given that \( \tan \beta = m = 1 \).

99%

104 rated

Answer

Using the relationship between tangent and angle,

tan⁡β=m\tan \beta = m

Given ( m = 1 ), we find:

β=arctan⁡(1)=45∘.\beta = \arctan(1) = 45^{\circ}.

Step 3

Let y = x + 6 OR OF y - x = 6.

96%

101 rated

Answer

From the equations, if we solve for d:

  1. From ( y = x + 6 ):

    For the point M(-10; -4):

    −4=−10+6⇒−4=−4 (True)-4 = -10 + 6 \Rightarrow -4 = -4 \text{ (True)}

  2. From ( y - x = 6 ):

    −4−(−10)=6⇒6=6 (True)-4 - (-10) = 6 \Rightarrow 6 = 6 \text{ (True)}

Thus, d can be resolved as ( d = -2 ).

Join the NSC students using SimpleStudy...

97% of Students

Report Improved Results

98% of Students

Recommend to friends

100,000+

Students Supported

1 Million+

Questions answered

;