Answer: Slope is the measure of the steepness of a line. It can be calculated with the equation rise/run or change in y/change in x.
Step-by-step explanation:
Answer:
John
Step-by-step explanation:
70 mi/(60 min) ≈ 1 1/6 mi/min.
1 1/6 miles is significantly farther than 50 ft, so John is driving (much) faster.
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:
<em>Student 2 is incorrect because he didn't use the formula properly</em>
Step-by-step explanation:
The exponential function is often used to model natural growing or decaying processes, where the change is proportional to the actual quantity.
An exponential decaying function is expressed as:
Where:
C(t) is the actual value of the function at time t
Co is the initial value of C at t=0
r is the decaying rate, expressed in decimal
The initial value of the item is Co=$1000, the rate of decay is r=40%=0.4, and the time is t=3 years.
Substituting into the formula:
C(3)=$216
Student 2 is incorrect because he didn't use the formula properly
Table 2 heheheheheehehehehheheheheehheheheheheheheehehehehhehehehehhehehehehehe
