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Anettt [7]
3 years ago
9

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

quared Over 4 EndFraction right parenthesis plus left parenthesis StartFraction y squared Over 9 EndFraction right parenthesis equals 1 x2 4 y2 9

Mathematics
1 answer:
Mashcka [7]3 years ago
7 0

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)

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Illusion [34]

Answer:

Option d. PQ = YZ

Step-by-step explanation:

<u><em>The question in English is</em></u>

Choose the most appropriate answer. The PQR triangle and the XYZ triangle are two congruent triangles. The angle P = the angle Y and PR = YX. Side pairs of the same length are ... a. PQ = XZ b. QR = YZ c. QR = XY d. PQ = YZ

we know that

If two triangles are congruent, then its corresponding sides and its corresponding angles are congruent

Corresponding sides are named using pairs of letters in the same position on either side of the congruence statement

so

we have that

m\angle P=m\angle Y

PR=YX

so

Triangle PQR is congruent with Triangle YZX

That means

<em><u>Corresponding angles</u></em>

m\angle P=m\angle Y

m\angle Q=m\angle Z

m\angle R=m\angle X

<u><em>Corresponding sides</em></u>

PQ=YZ\\QR=ZX\\PR=YX

8 0
3 years ago
If Sandy's cookie recipe calls for 1/3 cup of brown sugar and she increases it to 2/9, how much brown sugar does she use?
expeople1 [14]
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6 0
3 years ago
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If two of these shapes are randomly chosen, one after the other without replacement, what is the probability that the first will
aleksandrvk [35]

Answer:

P(T\ n\ S) = \frac{1}{14}

Step-by-step explanation:

*Missing Part of the Question*

4 stars

5 triangles

3 circles

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Total = 4 + 5 + 3 + 3

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P(T\ n\ S) = P(T) * P(S)

Solving for P(T)

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Solving for P(S)

The question implies a probability without replacement;

Hence Total has now been reduced by 1

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Recall that

P(T\ n\ S) = P(T) * P(S)

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P(T\ n\ S) = \frac{15}{15 * 14}

P(T\ n\ S) = \frac{1}{14}

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P(T\ n\ S) = \frac{1}{14}

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Answer:

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