4 years ago

0 = x3 + 4x² - 9x-36 Rational roots?

Mathematics

1 answer:

Alex4 years ago

7 0

Answer:

Roots are x=-4,-3, and 3

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$M_x = 2, M_y = 3$

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Step-by-step explanation:

Given a set of objects $m_1, \dots, m_k$ located at the points $P_1(x_1, y_1), \dots, P_k(x_k,y_k)$ The moments Mx and My are calculated as follows.

$M_x = \sum_{n=1}^k m_n\cdot y_n, M_y = \sum_{n=1}^k m_n\cdot x_n$

and the Center of mass is given at the coordinates $(\frac{My}{M}, \frac{Mx}{M})$ where M is the total mass of the system.

We have that m1=3, m2=4 and m3=3, so M = 3+4+3 = 10.

We have that m1 is at point P1(2,-6), m2 at point P2(-3,2) and m3 at point P3 (3,4), then

$M_x = \sum_{n=1}^k m_n\cdot y_n = 3\cdot(-6)+4\cdot(2)+3\cdot(4)=2$

$M_y = \sum_{n=1}^k m_n\cdot x_n = 3\cdot(2)+4\cdot(-3)+3\cdot(3)= 3$

Then, the center of Mass is at $(\frac{3}{10},\frac{2}{10})$

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