Mathematics, 20.07.2019 09:10 Ponypepper3499

An object is made from a uniform piece of sheet metal. the object has dimensions of a = 1.25 ft , where a is the diameter of the semi-circle, b = 3.17 ft , and c = 1.95 ft . a hole with diameter d = 0.750 ft is centered at (1.05,0.625). find x¯,y¯, the coordinates of the body's centroid.

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From the given figure, we can divide it into three separate shapes: a semicircle, a rectangle and a right triangle.

The centroid of the body is the arithmetic mean of the centroid of the individual shapes.

Centre of the diameter of the semicircle is located at $\left( \frac{1.25}{2} ,\ \frac{1.25}{2}\right)=(0.625,\ 0.625)$ and the centroid of the semicircle is located at $\left( \frac{0.625}{2} ,\ 0.625\right)=(0.3125,\ 0.625)$ .

The length of the base of the right triangle is obtained as follows:

$\sqrt{(1.95)^2-(1.25)^2} = \sqrt{3.8025-1.5625} = \sqrt{2.24} =1.4967ft$

The length of the base of the rectangle is given by

3.17-1.4967-0.625=1.0483ft

The centroid of the rectangle is given by

$\left( \frac{0.625+1.0483}{2} ,\ 0.625\right)=\left( \frac{1.6733}{2} ,\ 0.625\right)=(0.8367,\ 0.625)$

The centroid of the rectangle with the hole is given by

$\left( \frac{0.8367+1.05}{2} ,\ 0.625\right)=\left( \frac{1.8867}{2} ,\ 0.625\right)=(0.9434,\ 0.625)$

The midpoint of side c of the triangle is given by

$\left( \frac{0.625+1.0483+3.17}{2},\ 0.625\right)=\left( \frac{4.8433}{2},\ 0.625\right)=(2.4217,\ 0.625)$

The midpoint of the altitude of the right triangle is given by (0.625 + 1.0483, 0.625) = (1.6733, 0.625)

The equation of the line joining points (1.6733, 0) and (2.4217, 0.625) is given by y = 0.8351x - 1.3974

The equation of the line joining points (3.17, 0) and (1.6733, 0.625) is given by y = -0.4176x + 1.3238

The x-value of the point of intersection of line y = 0.8351x - 1.3974 and y = -0.4176x + 1.3238 is given by

0.8351x - 1.3974 = -0.4176x + 1.3238
1.2527x = 2.7212
x = 2.1723

The y-value of the point of intersection of line y = 0.8351x - 1.3974 and y = -0.4176x + 1.3238 is given by

y = 0.8351(2.1723) - 1.3974 = 1.8141 - 1.3974 = 0.4167

Thus, the centroid of the right triangle is given by (2.1723, 0.4167).

Therefore, the centroid of the object is given by:

$\left( \frac{0.3125+0.8367+2.1723}{3} ,\ \frac{0.625+0.625+0.4167}{3} \right) \\ \\ = \left(\frac{3.3215}{3} ,\ \frac{1.6667}{3}\right)=(1.1072,\ 0.5556)$

Answer from: Quest

to find the perimeter, you add up all the lengths of the sides. in this case you would have to add up 18+22+40+80 which equals 160.

Answer from: Quest

$17x-13$

step-by-step explanation:

consider the parallelogram shown in the attached image.

in the parallelogram hijk, the length of hk is given as,

$17x-13$

from the properties of parallelogram we know that the opposite sides of a parallelogram are parallel to each other and are equal in measure.

therefore, the length of the side ij must be equal to the length of the side hk and that is $17x-13$ .

hence, the expression $17x-13$ for the length of ij confirms that hijk is a parallelogram.

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An object is made from a uniform piece of sheet metal. the object has dimensions of a = 1.25 ft , wh...