The table below shows the energy of a 10kg as a function of velocity. How much energy will the ball have at 10 m/s?0/0 2/12 3/27 6/108 10/?

600 J

Explanation:

Energy is proportional to the square of the velocity of a body.

From the table, when the velocity is 2 m/s, then the energy is 24 J.

If we take the square of the velocity,we get . So, we need to multiply 4 to 6 to get the energy equal to 24 as . Similar formula can be observed for the next value also.

For velocity equal to 3 m/s, the energy is given as:

Therefore, the general formula to find the energy is given as:

Now, for velocity equal to 10 m/s, energy is given as:

Therefore, the ball will have 600 J of energy at 10 m/s.

answer:

c. the third graph

simplifying

5(x + -6) = 2(x + 3)

reorder the terms:

5(-6 + x) = 2(x + 3)

(-6 * 5 + x * 5) = 2(x + 3)

(-30 + 5x) = 2(x + 3)

reorder the terms:

-30 + 5x = 2(3 + x)

-30 + 5x = (3 * 2 + x * 2)

-30 + 5x = (6 + 2x)

solving

-30 + 5x = 6 + 2x

solving for variable 'x'.

move all terms containing x to the left, all other terms to the right.

add '-2x' to each side of the equation.

-30 + 5x + -2x = 6 + 2x + -2x

combine like terms: 5x + -2x = 3x

-30 + 3x = 6 + 2x + -2x

combine like terms: 2x + -2x = 0

-30 + 3x = 6 + 0

-30 + 3x = 6

add '30' to each side of the equation.

-30 + 30 + 3x = 6 + 30

combine like terms: -30 + 30 = 0

0 + 3x = 6 + 30

3x = 6 + 30

combine like terms: 6 + 30 = 36

3x = 36

divide each side by '3'.

x = 12

simplifying

x = 12

this should .