The answer is 10. Between 10 and 35, there are 7 prime numbers: 11, 13, 17, 19, 23, 29, and 31. Multiplying 11 by any of the others yields a product smaller than 350, resulting in 6 products. The product of 13 with anything below 26 will also be less than 350, adding 3 more products. Similarly, the product of 17 with anything below 20 yields 1 additional product. Therefore, the total count of different products under 350 amounts to 10.
Answer:
m = - 3
Step-by-step explanation:
a³ + 27 can be recognized as a sum of cubes, which factors generally as
a³ + b³ = (a + b)(a² - ab + b²). Therefore:
a³ + 27
= a³ + 3³
= (a + 3)(a² - 3a + 9).
By comparing a² - 3a + 9 to a² + ma + 9, we find that
m = - 3.
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
<span>The volume of a rectangular prism is
V = l · w · h
V = 252 cm3
h = 3 cm
l = 5 + W
Let W = x, therefore l = 5 + x
V = (5 + x) * x * 3 = 252
3x</span><span>^2 + 15x = 252 cm3
</span><span>
This equation models the volume of the tray based on its width, x, in centimeters.</span>
3x^2 + 15x = 252 cm3<span>
</span>
for a width of 7.5 cm
3x^2
+ 15x = 3*(7.5)^2 + 15*7.5 = 281.25 cm3
<span>281.25 > 252 </span><span> </span>
<span>Thus, a width of 7.5 cm is not possible.</span>
