Answer the whole of this question on a sheet of graph paper. Use a scale of 2cm to 1 unit on the x axis and…

Question

Answer the whole of this question on a sheet of graph paper. Use a scale of 2cm to 1 unit on the x axis and 2cm to 5 units on the y axis. The table below is for values of the function y = 6x − x2 - x3.

ScanSolve AI Tutor · Accepted Answer

Here's the solution for question 10(b):

b) (i)
The gradient of a slope is given by the tangent of its angle of inclination with the horizontal.
The slope AC is inclined to the horizontal ground AH at $15^\circ$ .

Identify the angle of inclination.
The angle of inclination is $\theta = 15^\circ$ .
Calculate the gradient using the tangent function.
$\text{Gradient} = \tan(\theta) = \tan(15^\circ)$ $\text{Gradient} \approx 0.267949...$
Round the answer to 2 decimal places.
$\text{Gradient} \approx \boxed{0.27}$
b) (ii)
We need to calculate $\angle APB$ .
The problem states that BP is a post standing on the sloping ground AC. In geometry, a post standing on the ground is typically assumed to be perpendicular to the ground unless stated otherwise. The diagram also shows a right-angle symbol at P, indicating that BP is perpendicular to AC.
Identify the relationship between BP and AC.
BP is perpendicular to AC.
Determine the angle $\angle APB$ .
Since BP is perpendicular to AC, the angle formed at their intersection P is $90^\circ$ .
$\angle APB = \boxed{90^\circ}$

Point	x	y
x-intercept	−3	0
Minimum	−1.79	−8.21
x-intercept	0	0
Maximum	1.12	4.06
x-intercept	2	0

Answer the whole of this question on a sheet of graph paper. Use a scale of 2cm to 1 unit on the x axis and 2cm to 5 units on the y axis. The table below is for values of the function y = 6x − x2 − x3.

Step-by-step solution

Identify the angle of inclination.

Calculate the gradient using the tangent function.

Round the answer to 2 decimal places.

Identify the relationship between BP and AC.

Determine the angle $\angle APB$ .

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