# How much work would it take to push a # 10 kg # weight up a # 7 m # plane that is at an incline of # pi / 6 #?

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To calculate the work required to push a 10 kg weight up a 7 m plane inclined at an angle of π/6 radians, you can use the formula:

Work = Force × Distance × Cosine(angle)

First, calculate the force required to overcome gravity along the incline:

Force = Mass × Gravity × Sin(angle)

Then, calculate the work:

Work = Force × Distance × Cosine(angle)

Substitute the given values:

Mass (m) = 10 kg Distance (d) = 7 m Angle (θ) = π/6 radians Gravity (g) = 9.8 m/s²

Calculate the force: Force = 10 kg × 9.8 m/s² × Sin(π/6) Force ≈ 10 kg × 9.8 m/s² × 0.5 Force ≈ 49 N

Now, calculate the work: Work = 49 N × 7 m × Cos(π/6) Work ≈ 49 N × 7 m × √3/2 Work ≈ 49 N × 7 m × 0.866 Work ≈ 299.7 Joules

So, it would take approximately 299.7 Joules of work to push a 10 kg weight up a 7 m plane inclined at an angle of π/6 radians.

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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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