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To find the inverse function ( f^{-1}(x) ) for the function ( f(x) = 3x - 1 ), we start by setting ( y = f(x) ), which gives us ( y = 3x - 1 ). We then solve for ( x ) in terms of ( y ):
- Add 1 to both sides: ( y + 1 = 3x ).
- Divide by 3: ( x = \frac{y + 1}{3} ).
Thus, the inverse function is ( f^{-1}(x) = \frac{x + 1}{3} ).
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What happens when two forces act on an object in the same direction?
the forces cancel each other out Huh? The forces simply add. F1x + F2x = F3x
What is the magnitude of the sum of 3 newton and 5 newton acts at an angle of sixty degrees?
Answer 7 Newtons at an angle of 38.2 degrees to the direction of the 3N force.Explanation The easier way is to draw the forces in scale, form a parallelogram of forces, and measure the resultant.But if you need a precise answer, you would need to add them as vectors.Construct a coordinate system, and place the force F1 = 5N on X-axis. Place the force F2 = 3N at 600 angle from the X-axis. The forces should converge in (0,0).To add the forces, we need to break them down to components parallel to the axes. As we placed F1 directly on an axis, we already know:F1x = 5NF1y = 0For F2, we get the components through trigonometry:F2x = 5N * cos(600) = 2.5 NF2y = 5N * sin(600) = 4.33 NNow the components of the resultant force Fr are:Frx = F1x + F2x = 5N + 2.5N = 7.5 NFry = F1y + F2y = 0 + 4.33N = 4.33 NThe magnitude of Fr is calculated with Pythagoras' Theorem:|Fr| = square_root( 7.5N + 4.33N) = 8.66 NThe angle of Fr is calculated from tangent.tan(angle) = Fry/Frxangle = 300
