Answer :
The resultant force: 45 pounds along the positive x-axis at approximately 33.77°.
To determine the resultant force of two given forces, we employ vector addition. The force of 40 pounds along the x-axis remains unchanged. For the 25-pound force at an 80° angle, we break it into x and y components through trigonometric functions.
x-component of 25-pound force: [tex]\(25 \times \cos(80°) \approx -4.93\)[/tex] pounds
y-component of 25-pound force: [tex]\(25 \times \sin(80°) \approx 24.01\)[/tex] pounds
Adding x-components: [tex]\(40 + (-4.93) \approx 35.07\)[/tex] pounds
The y-component remains: [tex]\(24.01\)[/tex] pounds
Using Pythagorean theorem: [tex]\(\sqrt{(35.07)^2 + (24.01)^2} \approx 45\)[/tex]pounds
Direction: [tex]\(\theta = \tan^{-1}\left(\frac{24.01}{35.07}\right) \approx 33.77°\)[/tex]
The resultant force: 45 pounds along the positive x-axis at approximately 33.77°.
The Mean Value Theorem, however, is not applicable here; trigonometric functions and vector addition are used.
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