Answer:
A). 2(2n+7)+3n
B). 2(2(8)+7)+3(8)
2(16+7)+ 24
2(23)+24
46+24
70
Answer:<u> 9.42 inches</u>, 3π in terms of pi
Step-by-step explanation:
A full circle is 360 degrees, so if the segment has an arc of 120 degrees, it is 1/3 of a regular circle.
To find the area of a circle, we use the equation A = πr^2. In this case, we will divide the equation by 3 because we are only finding 1/ of a circle. So, our equation will be A = (πr^2)/3.
Using 3.14 for π:
A = (πr^2)/3.
A = (π3^2)/3
A = (π9)/3
A = 3π
A = 9.42
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: C. 30/7
Step-by-step explanation: To make an improper fraction out of a mixed one we have to multiply the denominator by the whole number (in this case is 4) and then add the numerator. So 7 x 4 = 28 + 2 = 30, so 30/7 would be the correct answer choice.
Hope this helps!
Answer: 40.8cm
Step-by-step explanation:
A hexagon is a polygon that is made up of 6 sides. The perimeter of a regular hexagon is calculated by multiplying the side given by 6
Since the length of a side of a regular hexagon is 6.8 cm, the perimeter will be:
= 6 × 6.8
= 40.8cm