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
Answer:
The total probability exceeds 100%, indicating a problem with the findings; moreover, the distribution shows excessive uniformity which disqualifies it as a normal distribution.
Detailed explanation:
The sum of probabilities should be exactly 100%. When you add the probabilities of this distribution:
22+24+21+26+28 = 46+21+26+28 = 67+26+28 = 93+28 = 121
This exceeds 100%, highlighting a significant error in the results.
A typical normal distribution possesses a bell curve. If we plot the probabilities for this distribution, we'd see bars at 22, 24, 21, 26, and 28.
The bars would fail to form a bell-shaped curve, confirming that this is not a normal distribution.
Let's start by calculating the cost of the first 10 boxes, which totals $75, and the next 10 boxes cost $55.
Together, these 20 boxes amount to $130 spent. With $18 remaining, you can purchase 4 more boxes since 18 divided by 4.5 equals 4.
Therefore, the maximum number of boxes you can buy with $148 is 24.
Respuesta: Los contratos de opciones pueden ser valuados empleando modelos matemáticos tales como el modelo de precios Black-Scholes o el modelo Binomial. El costo de una opción se divide principalmente en dos componentes: su valor intrínseco y su valor temporal.... El valor temporal depende de la volatilidad anticipada del activo subyacente y del tiempo restante hasta que la opción expire.
Explicación paso a paso: ¡espero que esto ayude!
Por cierto, ¡también hablo inglés!
surface area = 4 x pi x r^2
diameter is 1, thus radius = 1/2 = 0.5
4 x 3.14 x 0.5^2 = 3.14 square meters
