The elements that are visible include A, B, and C.
Answer:
Step-by-step explanation:
Delivery charge = $7.50
Cost per pizza = $14
Budgeted total = $60
7.50 + 14p < 60
First, subtract 7.50 from both sides
14p < 60 - 7.50
14p < 52.50
Now divide both sides by 14
p < 52.50 / 14
p < 3.75
Each pizza consists of 8 slices
Therefore, the total number of slices she can buy = 3.75 × 8
= 30 slices
Past due amount = $87.50
Late fee equals 15% of $87.50, which is 0.15 × 87.50 = $13.125
New charges are $75.00
Total due now = 87.50 + 13.125 + 75 = $175.625
Final total: $175.63
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
