Find the exact area of the shaded region

Marina86 [1]

17 Answer: 205

Step-by-step explanation:

$\{1\dfrac{2}{3}+1\dfrac{5}{6}+2+...+8\dfrac{1}{3}\}\implies a_1=1\dfrac{2}{3},\ d=\dfrac{1}{6}\\\\\\a_n=a_1+d(n-1)\qquad solve\ for\ n\\\\8\dfrac{1}{3}=1\dfrac{2}{3}+\dfrac{1}{6}(n-1)\\\\\\\dfrac{25}{3}=\dfrac{5}{3}+\dfrac{1}{6}n-\dfrac{1}{6}\\\\\\\dfrac{50}{6}=\dfrac{10}{6}+\dfrac{1}{6}n-\dfrac{1}{6}\\\\\\\dfrac{41}{6}=\dfrac{1}{6}n\\\\\\\dfrac{41}{6}\cdot 6=n\\\\41=n$

$\text{Now use the sum formula:}\\\\S_n=\dfrac{a_1+a_n}{2}\cdot n\\\\\\S_{41}=\dfrac{1\dfrac{2}{3}+8\dfrac{1}{3}}{2}\cdot 41\\\\\\.\quad =\dfrac{10}{2}\cdot 41\\\\\\.\quad =5\cdot 41\\\\.\quad =\large\boxed{205}$

18 Answer: 1968

Step-by-step explanation:

$a_1=-6,\ d=2,\ n=48, \quad \text{solve for }a_{48}\\\\a_{n}=a_1+d(n-1)\\\\a_{48}=-6+2(48-1)\\\\.\quad =-6+2(47)\\\\.\quad =-6+94\\\\.\quad =88$

$\text{Now use the sum formula:}\\\\S_n=\dfrac{a_1+a_n}{2}\cdot n\\\\\\S_{48}=\dfrac{-6+88}{2}\cdot 48\\\\\\.\quad =\dfrac{82}{2}\cdot 48\\\\\\.\quad =41\cdot 48\\\\.\quad =\large\boxed{1968}$

19 Answer: -116

Step-by-step explanation:

$\{3, -2, -7, ...\}\\a_1=3,\ d=-5,\ n=8, \quad \text{solve for }a_{8}\\\\a_{n}=a_1+d(n-1)\\\\a_{8}=3-5(8-1)\\\\.\quad =3-5(7)\\\\.\quad =3-35\\\\.\quad =-32\\\\\text{Now use the sum formula:}\\\\S_8=\dfrac{a_1+a_8}{2}\cdot 8\\\\\\S_{8}=\dfrac{3-32}{2}\cdot 8\\\\\\.\quad =\dfrac{-29}{2}\cdot 8\\\\\\.\quad =-29\cdot 4\\\\.\quad =\large\boxed{-116}$

6 0

2 years ago

• Trey attended a New Year's Eve event and watched a ball drop at midnight. Prior

jekas [21]

Answer:

x=60.9°

Step-by-step explanation:

Given that the height of ball from the ground is 150ft

The base of the pole with the ball is 80 ft from where Trey is standing

Trey's horizontal line of sight is 6 feet above ground, then;

The height of ball from Trey's horizontal line of sight is;

150ft-6ft = 144ft

To find the angle x, assume a triangle with a base of 80 ft , a height of 144 ft and a slant height that represent the line of sight at an angle x

To get angle x , you apply the tangent of an angle formula where;

tan Ф°= length of opposite site of the angle/length of the adjacent side of the angle

tan x°= 144/80

tan x°= 1.8

x°= tan⁻(1.8)

x°=60.9°

7 0

3 years ago

What is the least common denominator (LCD)

Romashka [77]

The least common denominator is 15. The equivalent fractions would be 10/15 and 12/15.

3 0

2 years ago

Please help whats the answer !!

STALIN [3.7K]

Yes, they are proportional. if you divide the second fraction down to simplest form, you get 7/12, which is equal to the first fraction.

3 0

3 years ago

Please help me with these 2 questions!!

IceJOKER [234]

Answer: 53. B similar

Step-by-step explanation:

8 0

2 years ago

Read 2 more answers