Split up the interval [0, 3] into 6 subintervals,
[0, 1/2], [1/2, 1], [1, 3/2], [3/2, 2], [2, 5/2], [5/2, 3]
The right endpoints are given by the arithmetic sequence,

with
.
We approximate the integral of
on the interval [0, 3] by the Riemann sum,




Recall the formulas,


Then the value of the integral is approximately

Compare to the exact value of the integral, -9.
Answer:
Option A is correct
3.33 ft wide should the metal piece be.
Step-by-step explanation:
Area of rectangle(A) is given by:
.....[1]
l is the length and w is the width of the rectangle respectively.
As per the statement:
One more rectangular-shaped piece of metal siding needs to be cut to cover the exterior of a pole barn. The area of the piece is 30 ft²
⇒A = 30 ft²
It is also given that the length is 1 less than 3 times the width
⇒
ft
Substitute the given values in [1] we have;

Using distributive property: 
then;

We can write this as:

Factorize this equation:
Split the middle term we have;

⇒
⇒
By zero product property we have;
and w+3 = 0
Since, w cannot be negative;
so,
ft
Therefore, to the nearest hundredth of a foot, 3.33 ft wide should the metal piece be.
The perimeter of a triangle is:
P = a + b + c
We are given that:
b = a + 3
c = 2 a – 3
Therefore:
68 = a + a + 3 + 2 a – 3
68 = 4 a
a = 17
and,
b = a + 3 = 20
<span>c = 2a – 3 = 31</span>
Answer:

Step-by-step explanation:
Given

Required
Find 

In trigonometry:
If sin(A) = cos(B), then

So, we have:

Collect Like Terms



Answer:
216 Books
Step-by-step explanation:
If she reads 36 books every year, you multiply the amount of books by the number of years. Which, in this case, would be 6 years. So 6×36 is 216 books