What angle values, in radians, give positive values for tangent functions?
Tangent functions can be written as (sine/cosine), therefore the angles where both sine and cosine have positive values and the angles where they both have negative values are where the tangent function would have a positive value. So the angles are (0,pi/2) U (pi, (3*pi)/2).
What is the derivative of the function x^3 + (x^2)/2 - 12*x ?
To take the derivative of a polynomial you can take the derivatives of each individual term and sum them afterwards. Using the chain rule, we know that to take the derivative of a function raised to a power you will multiply the function by the exponent and subtract one from from the exponent, and then multiply the entire new function by the derivative of what was being raised by a power. For example for x^3 we would multiply the 3 to x^(3-1) which is 3*x^2. The derivative of the inside function would (dx/dx) which gives simply one. Applying this logic to each term we get 3*x^(2) + x - 12.
The physics quantity "Work" can be calculated by considering what ? A) how quickly a moving object changes in position B) how much force is applied to an object, and how much time that Force is applied C) how much an object accelerates, divided by its mass D) how much Force is applied to an object, and how much displacement that Force is applied over E) how quickly a moving object changes it acceleration
The correct answer is "D". The definition of "Work" done on an object is found through the formula "Work = Force * displacement " or " W = F*d" The physics definition of work is very different from how we use the word work in the english language. For example saying " I'm doing work on the chair" means something specific to a physics student opposed to saying " I have a lot of work to do tonight." Also when looking at work, you are only interested in knowing how much force you are putting on an object and what direction the force is going, and looking at if the direction of your force and the direction of your displacement are the same.