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## Sagot :

[tex]\[ W = F \cdot d \cdot \cos(\theta) \][/tex]

where:

- [tex]\( W \)[/tex] is the work done,

- [tex]\( F \)[/tex] is the force applied (20 newtons in this case),

- [tex]\( d \)[/tex] is the distance moved (40 meters in this case),

- [tex]\( \theta \)[/tex] is the angle between the force and the direction of movement ([tex]\( 45.0^\circ \)[/tex] in this case),

- [tex]\(\cos\)[/tex] is the cosine function.

Let's walk through the steps:

1.

**Convert the angle from degrees to radians**, because trigonometric functions in physical equations typically use radians. The conversion from degrees to radians is given by:

[tex]\[ \theta_{\text{radians}} = \theta_{\text{degrees}} \times \frac{\pi}{180} \][/tex]

For [tex]\( \theta = 45.0^\circ \)[/tex]:

[tex]\[ \theta_{\text{radians}} = 45.0 \times \frac{\pi}{180} = 0.7853981633974483 \text{ radians} \][/tex]

2.

**Calculate the cosine of the angle**:

[tex]\[ \cos(0.7853981633974483) = 0.7071067811865476 \][/tex]

3.

**Substitute the values into the work formula**:

[tex]\[ W = 20 \, \text{N} \times 40 \, \text{m} \times 0.7071067811865476 \][/tex]

4.

**Compute the total work done**:

[tex]\[ W = 20 \times 40 \times 0.7071067811865476 = 565.685424949238 \text{ joules} \][/tex]

Rounding this to one decimal place, we get approximately [tex]\( 565.7 \)[/tex] joules. Now, converting this to scientific notation, we have:

[tex]\[ W = 5.7 \times 10^2 \text{ joules} \][/tex]

Given the available options in the multiple-choice question:

A. [tex]\( 8.0 \times 10^2 \)[/tex] joules

B. [tex]\( 9.0 \times 10^2 \)[/tex] joules

C. [tex]\( 5.6 \times 10^2 \)[/tex] joules

D. [tex]\( 3.6 \times 10^2 \)[/tex] joules

The closest and correct answer to our calculation is [tex]\( 5.6 \times 10^2 \)[/tex] joules.

Therefore, the correct answer is:

**C. [tex]\( 5.6 \times 10^2\)[/tex] joules**.