Use the drawing tools to form the correct answer on the graph.

Mathematics

2 answers:

Scorpion4ik [409]3 years ago

7 0

Answer:

Solution = (-8,-28)

Step-by-step explanation:

IgorC [24]3 years ago

5 0

^^ he is correct that is the answer

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Find the centroid of the region that is bounded below by the x-axis and above by the ellipse left parenthesis StartFraction x s

Mashcka [7]

Answer with explanation:

The equation of the ellipse is ,whose centroid we have to find is

$\rightarrow \frac{x^2}{4}+\frac{y^2}{9}=1$

The curve cuts the x axis at (2,0) and (-2,0) and y axis at (0,3) and (0,-3).

We have to find centroid of the Ellipse on the right of y axis.

Center of gravity will lie on x axis.

$\bar{x}=\frac{\int \int {x} \, dx dy}{\int \int dxdy}\\\\\bar{y}=\frac{\int \int {y} \, dx dy}{\int \int dxdy}\\\\ \bar{x}=\frac{\int\limits^2_0 {x} \, dx \int\limits^3_{-3} {1} \, dy}{\int\limits^2_0 {1} \, dx \int\limits^3_{-3} {1} \, dy}\\\\\bar{y}=0\\\\\bar{x}=\frac{(\frac{x^2}{2})\left \{ {{x=2} \atop {x=0}} \right \times (y)\left \{ {{y=3} \atop {y=-3}} \right.}{(x) \left \{ {{x=2} \atop {x=0}} \right \times (y)\left \{ {{y=3} \atop {y=-3}}}$

$\bar{x}=\frac{\frac{2^2}{2} \times [3-(-3)]}{2*3}\\\\ \bar{x}=\frac{6}{6}\\\\ \bar{x}=1\\\\ \bar{y}=0\\\\ \text{Center of gravity}=(\bar{x},\bar{y})=(1,0)$