Answer:
Step-by-step explanation:
Recall that the notion of the derivative of a function is the rate of change of it. So it kind of tells us how much the value of functioin changes as the independt variable increases or decreases. If it is positive, this means that the function will increase as the indepent variable increases, and if it is negative, that means that the function will decrease as the indepent variable increases.
a) Since f(x) is the number of units you can make out of x units of raw material, it is natural to think that the more material you have, the more units you can make, so we expect f'(x) to be positive.
b) The company buys each unit of raw material at the price w. So the product wx represents the total cost of the raw material used to produce f(x) units. Since each produced unit is sell at the price of p, then the product pf(x) represents the total income for selling all f(x) units.Recall that the profit is the difference between the total income and the total cost of production. Hence, the profit in this case is represented by the formula pf(x)-wx.
c) Recall that a function h(x) that is differentiable attains it's maximum when it's derivative is 0 and it's second derivative is negative.
In this case, we know that the derivative of the profit function, evaluated at x* must be 0, since it is a maximum. So, using the rules of derivation, we know that the derivative of the profit function is pf'(x)-w. Hence,
pf'(x*)-w =0. From where we know that f'(x*)=w/p.
I believe the answer is A
tax gets added to the price of the camera
so the equation is:
x + 0.07x = 45; x = $42.06
Answer:
.6601
Step-by-step explanation:
to find u, which we assume is an angle of course, we can take arctan of both sides. so arctan(-7.721) = -1.4420. this angle is in quadrant 4, but it is not in the range. In this instance you just go around the circle again, or add 2pi, which gets us 4.8412. You can check and you get the same answer if you take the tangent of either.
So now we have a number in the appropriate range in the appropriate quadrant. That means we have the correct angle. The question asks what is sine of that angle cut in half. so sin(4.8412/2), which gets you your answer. let em know if something didn't make sense.
