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.
Answer: 182.075
Step-by-step explanation: 145.66 divided by 0.8 =182.0.75
Answer:
A straight line is equivalent to 180 degrees with that in mind,
(2.4x)+(9.6x)=180
2.4x+9.6x=180
12x=180
12x/12=180/12
x=15
Now to find the measurement of the larger angle,
9.6*15=144
Just in case you need it
180-144=36
Which is your smaller measurement.
Since you know it's a square, you also know that all the sides are 3 2/3. So to find area you multiply, so 3 2/3 x 3 2/3. An easy way to do this is convert it to a mixed number (11/3) and then multiply:
11/3 x 11/3 = 121/9
Answer:
1. 4x = 15
2. 4(n - 3) = 24
3. 2n + 5 = 13
4. (3/4)n = 9
5. 6x - 4 = 8
Step-by-step explanation:
this should be correct. hope this helps!
