Final answer:
The x component of the force exerted by the dog on the pillow is approximately 7.2 N, which can be calculated using the cosine function and the given force and angle. None of the provided options exactly match the calculated value.
Step-by-step explanation:
To find the x component of the force exerted by the dog on the pillow, which is angled at 31° above the horizontal, you use the cosine function in trigonometry. The x component (Fx) can be calculated using the formula:
Fx = F * cos(θ)
Where F is the total force and θ is the angle with respect to the horizontal plane. In this case, F = 8.4 N and θ = 31°, so the calculation will be:
Fx = 8.4 N * cos(31°)
Performing this calculation gives us the x component of the force:
Fx ≈ 8.4 N * 0.8572 (cosine of 31°) ≈ 7.2 N
Therefore, none of the provided options (a) 4.3 N, (b) 6.9 N, (c) 7.8 N, (d) 8.4 N exactly match the calculated value. The closest option to our calculated value of 7.2 N would typically be (c) 7.8 N, assuming a rounding or calculation error not accounted for in the provided options.