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LiRa [457]
3 years ago
6

Find the inverse of f(x)=5x-2

Mathematics
1 answer:
kompoz [17]3 years ago
5 0

Answer:

f^{-1}(x) = \frac{x+2}{5}

Step-by-step explanation:

Let y = f(x) and rearrange making x the subject

y = 5x - 2 ( add 2 to both sides )

y + 2 = 5x ( divide both sides by 5 )

\frac{y+2}{5} = x

Change y back into terms of x

f^{-1} (x) = \frac{x+2}{5}

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A ball slides up a frictionless ramp. It is then rolled without slipping and with the same initial velocity up another frictionl
KATRIN_1 [288]

Answer:

Rolling case achieves greater height than sliding case

Step-by-step explanation:

For sliding ball:

- When balls slides up the ramp the kinetic energy is converted to gravitational potential energy.

- We have frictionless ramp, hence no loss due to friction.So the entire kinetic energy is converted into potential energy.

- The ball slides it only has translational kinetic energy as follows:

                                   ΔK.E = ΔP.E

                                   0.5*m*v^2 = m*g*h

                                    h = 0.5v^2 / g

For rolling ball:

- Its the same as the previous case but only difference is that there are two forms of kinetic energy translational and rotational. Thus the energy balance is:

                                  ΔK.E = ΔP.E

                                  0.5*m*v^2 + 0.5*I*w^2 = m*g*h

- Where I: moment of inertia of spherical ball = 2/5 *m*r^2

             w: Angular speed = v / r

                               0.5*m*v^2 + 0.2*m*v^2 = m*g*h

                               0.7v^2 = g*h

                               h = 0.7v^2 / g

- From both results we see that 0.7v^2/g for rolling case is greater than 0.5v^2/g sliding case.

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3 years ago
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