Amanufacturer wants to make a ball bearing that is made of a mixture of zinc, iron, and copper and has come down to a choice of two alloys. alloy a has a density of 7.5 grams per cubic centimeter and alloy b has a density of 8.5 grams per cubic centimeter.
use the formula for the volume of a sphere, v=43πr3 , and the formula for density, d=mv , to write an equation for m as a function of r for each alloy.

Alloy A: m = 10πr³ . . . . . . . . . . . . mass in grams; radius in cmAlloy B: m = (34π/3)r³

Step-by-step explanation:

Solving the density equation for mass, we get ...

  D = m/V

  m = DV . . . . . multiply by volume

Substituting the volume formula gives ...

  m = D(4/3π)r³

Alloy A

Substituting D = 7.5 gives ...

  m = 7.5(4/3)πr³

  m = 10πr³ . . . . . simplify

__

Alloy B

Substituting D = 8.5 gives ...

  m = 8.5(4/3π)r³

  m = (34π/3)r³ . . . . . simplify

Answercounterclockwise rotation about the origin by 180 degrees followed by reflection about the y-axisexplanationthe given figure has verticesrecall that for counterclockwise rotation about the origin, when we rotate figure pqrs counterclockwise through an angle of 180° about the origin, the coordinates will becomenext, we reflect in the y-axis by negating the x-coordinates of the resulting figure to obtain,therefore the correct answer is c