Answer:
Dy/Dx=x
(
2
ln
(
x
)
−
1
)/
ln
^2
(
x)
Step-by-step explanation:
We have this function and let's derive it in terms of x.
y =x^2/In x
Dy/Dx=(x^2/In x)'=2/lnx *(x^2)'-(x^2/In x)'=> 2
x
*ln
(
x
)
−
x
*ln
^2
(
x
)
=x
(
2
ln
(
x
)
−
1
)/
ln
^2
(
x)
Answer:
29037.036 miles
Step-by-step explanation
There are two possible ways to solve this problem.
The first option starts with the $2800 dollars for the years. You first want to divide this by $2.70, because it will give you the amount of gallons of gas you can buy with that money.
2800/2.70 = 1037.037
This means you can buy 1037.037 gallons of gas in the year. Now you need to convert this to miles by multiplying by the amount of miles per gallon.
1037.037 x 28 = 29037.036 gallons
The second way to look at this is dimensional analysis. If you have learned this, then continue on reading this, but if you haven't I might only confuse you. I only suggest this because it can make it a little easier.
For the dimensional analysis, you need to start with what you are given and move to what you need to know, so you will start with the $2800 dollars and move to gallons. $2.70 per gallon and 28 miles per gallon are your conversion factors.
Set it up like this:
This allows the equation to be more organized, and you can check your work by canceling the units.
Hope this helps.
Answer:
f(x) = x
Step-by-step explanation:
f(x) = |x| will give you V graph
f(x) = x will give you line graph (linear)
f(x) = x² will give you a curve graph
Answer:
The answer to your questions is: 25 new teachers
Step-by-step explanation:
Data
# of students = 2000
ratio = 3:80 teachers to students
New teachers = ?
Process
I suggest to use rule of three to solve this problem
3 teachers ---------------- 80 students
x ---------------- 2000 students
x = (2000 x 3) / 80 = 75 teachers
Number of initial teachers = 75
The ratio change to 1:20
1 teacher ------------------- 20 students
x ------------------- 2000 students
x = (2000 x 1) / 20
x = 100 teachers
Number of new teachers = 100 - 75 = 25