"you have a flat piece of plastic of uniform density ρ in the shape of a right triangle. the legs of the triangle are given as a and b. where is the center of mass of this triangle? using the coordinate system given, enter the coordinates of the center of mass in terms of a and b."

Since the piece of plastic with uniform density is a Right angled triangle ;

For a right angled triangle the centroid and the center of mass is the same. the center of mass can be determined by taking the average value of the three legs of the right angled triangle.

Therefore to actually determine the  location of the center of mass in the triangle, look for  the point of intersection between 1/3 height and 1/3 base length of the triangle.

Hence we can conclude that The center of mass of the triangle is located at the point where ; 1/3 base length and 1/3 height of the triangle intersects and The coordinates of the center of mass  is ; ( a/3 , b/3 ).

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find the surface area of the sphere to the nearest square unit. use a calculator.

a. 254 in.2

b. 64 in.2

c. 127 in.2

d. 1,018 in.2

the design of a ski jumping suit involves a trade-off between giving the skiers lift to get higher jumps and ensuring the skier does not face a lot of drag before the jump itself. an expansive suit may to lift the skier higher, but at the same time, it will also increase the air resistance. higher air resistance as the skier goes down the slope limits the speed of the jump. a big suit also increases the risk of losing balance or control, especially if there's a strong gust of wind. while technologically enhanced suits a lot, clothing is not the only factor in a ski jumper’s success. gathering speed while skiing down the slope, ensuring good speed on the ramp, and maintaining good body posture and form in the air all contribute to a ski jumper's success.