According to the Rational Root Theorem, what are all the potential rational roots of f(x) = 15x11-6x8+x3-4x+3

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7 0

According to the Rational Root Theorem, what are all the potential rational roots of f(x) = 15x11 - 6x8 + x3 - 4x + 3? ... According to the Rational Root Theorem, the following are potential roots of f(x) = 60x² - 57x - 18.

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Prove that one of every three consecutive positive integer is divisible by 3

Inessa05 [86]

Hello :
all n in N ; n(n+1)(n+2) = 3a a in N or : ≡ 0 (mod 3)
1 ) n ≡ 0 ( mod 3)...(1)

n+1 ≡ 1 ( mod 3)...(2)
 n+2 ≡ 2 ( mod 3)...(3)
by (1), (2), (3) : n(n+1)(n+2) ≡ 0×1×2 ( mod 3) : ≡ 0 (mod 3)
2) n ≡ 1 ( mod 3)...(1)

n+1 ≡ 2 ( mod 3)...(2)
 n+2 ≡ 3 ( mod 3)...(3)
by (1), (2), (3) : n(n+1)(n+2) ≡ 1×2 × 3 ( mod 3) : ≡ 0 (mod 3) , 6≡ 0 (mod)
3) n ≡ 2 ( mod 3)...(1)

n+1 ≡ 3 ( mod 3)...(2)
 n+2 ≡ 4 ( mod 3)...(3)
by (1), (2), (3) : n(n+1)(n+2) ≡ 2×3 × 4 ( mod 3) : ≡ 0 (mod 3) , 24≡ 0 (mod3)

5 0

3 years ago

For questions 3 – 5, an airplane is heading south at an airspeed of 540 km/hr, but there is a wind blowing from the northeast at

GuDViN [60]

First, let's calculate the horizontal and vertical components of the wind speed (W) and the airplane speed (A), knowing that south is a bearing of 270° and northeast is a bearing of 45°:

$\begin{gathered} W_x=W\cos45°\\ \\ W_x=50\cdot0.707\\ \\ W_x=35.35\\ \\ \\ \\ W_y=W\sin45°\\ \\ W_y=50\cdot0.707\\ \\ W_y=35.35 \end{gathered}$ $\begin{gathered} A_x=A\cos270°\\ \\ A_x=540\cdot0\\ \\ A_x=0\\ \\ \\ \\ A_y=A\sin270°\\ \\ A_y=540\cdot(-1)\\ \\ A_y=-540 \end{gathered}$

Now, let's add the components of the same direction: