Answer:
180
Step-by-step explanation:
2 times 30 equals 60 which is an hour so 6 times 30 equals 180.
Starting from what I know (the difference between ribbons), I decided to go from the bottom and work my way up. I then noticed a pattern (each sum was three more of the previous one), and decided to keep my pattern of the three numbers but not have to do any major mental work and instead add three to the previous sum until I got to 38.
The trapezoidal approximation will be the average of the left- and right-endpoint approximations.
Let's consider a simple example of estimating the value of a general definite integral,

Split up the interval
![[a,b]](https://tex.z-dn.net/?f=%5Ba%2Cb%5D)
into

equal subintervals,
![[x_0,x_1]\cup[x_1,x_2]\cup\cdots\cup[x_{n-2},x_{n-1}]\cup[x_{n-1},x_n]](https://tex.z-dn.net/?f=%5Bx_0%2Cx_1%5D%5Ccup%5Bx_1%2Cx_2%5D%5Ccup%5Ccdots%5Ccup%5Bx_%7Bn-2%7D%2Cx_%7Bn-1%7D%5D%5Ccup%5Bx_%7Bn-1%7D%2Cx_n%5D)
where

and

. Each subinterval has measure (width)

.
Now denote the left- and right-endpoint approximations by

and

, respectively. The left-endpoint approximation consists of rectangles whose heights are determined by the left-endpoints of each subinterval. These are

. Meanwhile, the right-endpoint approximation involves rectangles with heights determined by the right endpoints,

.
So, you have


Now let

denote the trapezoidal approximation. The area of each trapezoidal subdivision is given by the product of each subinterval's width and the average of the heights given by the endpoints of each subinterval. That is,

Factoring out

and regrouping the terms, you have

which is equivalent to

and is the average of

and

.
So the trapezoidal approximation for your problem should be
Answer:
=−0.888168
Step-by-step explanation:
sin(5(3.1415933))
=sin((5)(31.006277))
=sin(155.031383)
=−0.888168
:)