Response: 87%
Solution:
87 correct answers out of 100 = 87/100 = 0.87 = (convert to percentage by shifting the decimal place two positions to the right) 87%
Answer:
53
Step-by-step explanation:
When I entered 53 into PLATO, it appears to be the correct answer.
(a) x= 0,1,2..........10 (b) p=0.02 (c) standard deviation = 0.44 (d) p=0.18. A comprehensive explanation of the answer is available in the attached file.
Answer:
Refer to the detailed explanation below
Step-by-step explanation:
* Let’s organize the procedure to bisect angle ABC
- Angle ABC has vertex at point B and rays BA and BC
# Step 1:
- Center the compass at point B and draw an arc that crosses rays BA and BC ⇒ fifth step
# Step 2:
- Mark point D where the arc intersects ray BA and point E where it meets ray BC ⇒ third step
# Step 3:
- With the compass on point D, create an arc inside the angle ⇒ sixth step
# Step 4:
- Using the same compass width, set it on point E and draw an arc inside the angle ⇒ second step
# Step 5:
- Let point F be the intersection of the arcs from points D and E ⇒ fourth step
# Step 6:
- Draw a ray from point B through point F ⇒ first step
* This ray divides angle ABC into two equal parts
Assuming arcs are measured in degrees, let S represent the following sum:
S = sin 1° + sin 2° + sin 3° +... + sin 359° + sin 360°
By rearranging, S can be reformulated as
S = [sin 1° + sin 359°] + [sin 2° + sin 358°] +... + [sin 179° + sin 181°] + sin 180° +
+ sin 360°
S = [sin 1° + sin(360° – 1°)] + [sin 2° + sin(360° – 2°)] +... + [sin 179° + sin(360° – 179)°]
+ sin 180° + sin 360° (i)
However, for any real k,
sin(360° – k) = – sin k
Thus,
S = [sin 1° – sin 1°] + [sin 2° – sin 2°] +... + [sin 179° – sin 179°] + sin 180° + sin 360°
S results in 0 + 0 +... + 0 + 0 + 0 (... since sine of 180° and 360° are both equal to 0)
Therefore, S equals 0.
Each pair within the brackets negates itself, leading the sum to total zero.
∴ sin 1° + sin 2° + sin 3° +... + sin 359° + sin 360° equals 0. ✔
I hope this clarifies things. =)
Tags: sum summatory trigonometric trig function sine sin trigonometry
