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:
3.4 yards cubed
Step-by-step explanation:
Volume is length x width x height
Length 2 4/5, Width 2, Height 3/5 so 2 4/5 x 2 x 3/5
It looks like they want the answer in decimal form, so you can convert the fractions into decimals.
For the length 2 4/5, you divide the 4 by 5 to get a decimal of .8 so now it's 2.8
For the height of 3/5, you divide the 3/5 & get .6
Now it's 2.8 x 2 x .6 = 3.36 yards cubed which could get rounded up to 3.4 yards cubed
100 cm = 1m
To find 60 000cm, multiply by 600 :
60 000 cm = 600m
To convert from m to km, divide by 1000 :
600m ÷ 1000 = 0.6km
Answer:
b 24/25
Step-by-step explanation:
SOHCAHTOA
tan is Opposite over Adjacent sides of the triangle from the perspective of angle A
so the opposite side was 24 and the adjacent side was 25
so the answer is 24/25 aka B
Answer:
Approximately 6 buses
Step-by-step explanation:
If you are wanting know how many vans they are going to need:
26 + 32 -This helps you know how many total kids there are
= 58
58 / 10 -This solves how many buses you'll need
= 5.8 - Round up, and say you need 6 buses.
