Question

The energy of an object is dependent on its mass and can be described by the following equation: = 2m2 − 12m, where stands for energy and m stands for mass. if the energy of the object is 14 units, what is the mass of the object?

Answer 1

To find the mass of the object when the energy is 14 units, we solve the quadratic equation 14 = 2m^2 - 12m. After factoring, we find two possible mass values, -1 and 7, but since mass cannot be negative, the mass of the object is 7 units.

Step-by-step explanation:

The question involves solving a quadratic equation where the energy E of an object depends on its mass m and is given by the equation E = 2m2 - 12m. To find the mass when the energy is 14 units, we substitute E with 14 and solve for m:

14 = 2m2 - 12m

This is a quadratic equation in the form of am2 + bm + c = 0, where a = 2, b = -12, and c = -14. The solutions for m can be found using the quadratic formula or by factoring, if possible. Let's try factoring:

14 = 2m2 - 12m

0 = 2m2 - 12m - 14

By factoring, we have:

0 = (2m + 2)(m - 7)

Setting each factor equal to zero gives us two possible mass values:

2m + 2 = 0 or m - 7 = 0

For the first equation, m = -1 (which we discard as mass can't be negative), and for the second, m = 7. Therefore, the mass of the object is 7 units.