Suppose the dimensions of the rectangle is x by y and let the side enclosed by a house be one of the sides measuring x, then the sides that is to be enclosed are two sides measuring y and one side measuring x.
Thus, the length of fencing needed is given by
P = x + 2y
The area of the rectangle is given by xy,
i.e.
Substituting for y into the equation for the length of fencing needed, we have
For the amount of fencing to be minimum, then
Now, recall that
Thus, the length of fencing needed is given by
P = x + 2y = 24 + 2(12) = 24 + 24 = 48.
Therefore, 48 feets of fencing is needed to enclose the garden.
3/10
As you know the answer already I don't think you need any further explanation :)
First of all, let's make the following observations:
15 is an integer, so in particular it is rational. The sum of two rational is rational. This means that is irrational if and only if is irrational.
Similarly, since 17 is rational and the multiplication of two rationals is rational, we have that is irrational if and only if is irrational.
The proof that is irrational is the following: suppose by contradiction that we could write
where a and b are two integers with no common factors.
Squaring both sides, we have
So, is a multiple of 3. This happens if and only if a itself is a multiple of 3. So, we can write and the expression becomes
So, is a multiple of 3 as well, and this happens if and only if b is itself a multiple of 3.
So, we started with the assumption that we could write as a reduced fraction, but this assumption led to a contradiction.
We deduce that is irrational, and so are and
The derivitive of sec(x) is sec(x)tan(x)
find the slope at pi/3
sec(pi/3)=2
tan(pi/3)=√3
sec(x)tan(x) at x=pi/3 is 2√3
for slope=m and a point is (x1,y1)
the equation is
y-y1=m(x-x1)
slope=2√3
point=(pi/3,2)
equation is
y-2=2√3(x-pi/3)
Answer: 15
Step-by-step explanation:
Given: The present ratio of students to teachers at a certain school is to . If the student enrollment were to increase by students and the number of teachers were to increase by , the ratio of students to teachers would then be to .
To Find: What is the present number of teachers.
Solution:
let the number of teachers in schools are
As the current ratio of students to teachers is to
Number of students in school are
Now,
If number of student enrollment and teachers were to increase by and respectively.
New number of students in school would be
New number of teacher in school would be
new ratio of students to teachers is
Hence the number of teachers in school is