Question
The owner of a convenience store installs two security cameras, represented by points C1
and C2. Both cameras point towards the centre of the store’s cash register, represented by
the point R.
The following diagram shows this information on a cross-section of the store.
The cameras are positioned at a height of 3.1m, and the horizontal distance between the
cameras is 6.4m. The cash register is sitting on a counter so that its centre, R, is 1.0m
above the floor.
The distance from Camera 1 to the centre of the cash register is 2.8m.
(a) Determine the angle of depression from Camera 1 to the centre of the cash register.
Give your answer in degrees.
(b) Calculate the distance from Camera 2 to the centre of the cash register.
(c) Without further calculation, determine which camera has the largest angle of
depression to the centre of the cash register. Justify your response.
Answer/Explanation
Ans:
(a) sin \(\theta = \frac{2.1}{2.8}\) OR tan \(\theta = \frac{2.1}{1.85202…}\)
\((\theta=) 48.6^0 (48.5903…^0)\)
(b) METHOD 1
\(\sqrt{2.8^2 – 2.1^2}\) OR 2.8 cos (48.5903…) OR \(\frac{2.1}{tan (48.5903…)}\)
1.85 (m) (1.85202…)
(6.4 – 1.85202…)
4.55 m (4.54797…)
\(\sqrt{(4.54797…)^2 + 2.1^2}\)
5.01 m (5.00939…m)
METHOD 2
attempt to use cosine rule
\((c^2=) 2.8^2 + 6.4^2 – 2(2.8)(6.4) cos (48.5903…)\)
\((c=) 5.01 m (5.00939…m)
(c) camera 1 is closer ot the cash register (than camera 2 and both cameras are at the same height on the wall )
teh larger angel of depression is from camera 1
Question
A polygraph test is used to determine whether people are telling the truth or not, but it is not completely accurate. When a person tells the truth, they have a 20% chance of failing the test. Each test outcome is independent of any previous test outcome. 10 people take a polygraph test and all 10 tell the truth.
(a) Calculate the expected number of people who will pass this polygraph test.
(b) Calculate the probability that exactly 4 people will fail this polygraph test.
(c) Determine the probability that fewer than 7 people will pass this polygraph test.
Answer/Explanation
Ans:
(a) (E(X)=) \(10 \times 0.8\)
8 (people)
(b) recognition of binomial probability
0.0881 (0.0880803…)
(c) 0.8 and 6 seen OR 0.2 and 3 seen
attempt to use binomial probability
0.121 (0.120873…)