Determine the work done by force f=[1,4] in newtons for an object moving along the vector d =[6,3]
Okay i found the vector equation and then the parametric and now i have no clue what do please help :)
One more thing there a question that say given the graph f(x) sketch a graph the represents rate of change....Does anyone know how i would do this
To determine the work done by force f = [1,4] in newtons for an object moving along the vector d = [6,3], you can use the formula for work:
Work = f · d
where · denotes the dot product.
To calculate the dot product, multiply the corresponding components of the two vectors and then sum them up:
f · d = (1 * 6) + (4 * 3) = 6 + 12 = 18
Therefore, the work done by force f in newtons is 18.
Regarding your second question about sketching a graph that represents the rate of change of a given function f(x), here is what you can do:
1. Write down the function f(x) given in the question.
2. Determine the first derivative of f(x) (denoted as f'(x)), which represents the rate of change of the function.
3. Plot the graph of f'(x) with the x-axis representing the input values (x) and the y-axis representing the corresponding rate of change values (f'(x)).
4. Look for key points on the graph such as where f'(x) crosses the x-axis (indicating stationary points or points of zero rate of change) or where f'(x) changes sign (indicating increasing or decreasing rate of change).
5. Connect these points with smooth curves to sketch the graph that represents the rate of change of f(x).
Remember, the process may vary depending on the specific function f(x) given, so it's important to apply the appropriate mathematical techniques to find the rate of change.