# How much work would it take to push a # 4 kg # weight up a # 5 m # plane that is at an incline of # pi / 4 #?

It takes

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To calculate the work done in pushing the weight up the inclined plane, you can use the formula:

Work = Force × Distance

The force exerted to push the weight up the inclined plane can be broken down into two components: the force parallel to the incline (F_parallel) and the force perpendicular to the incline (F_perpendicular).

The force parallel to the incline can be calculated using the formula: F_parallel = mg sin(θ), where m is the mass (4 kg), g is the acceleration due to gravity (9.8 m/s^2), and θ is the angle of inclination (π/4 radians).

The distance moved along the incline is the hypotenuse of the right triangle formed by the incline, which is given as 5 meters.

Now, calculate F_parallel: F_parallel = (4 kg) × (9.8 m/s^2) × sin(π/4 radians)

Then, calculate the work done: Work = F_parallel × Distance

Finally, substitute the values and compute the work.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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