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sashaice [31]
3 years ago
7

What is the sum of the first 20 terms of the arithmetic sequence shown? \displaystyle \frac{1}{3} 3 1 ​ , \displaystyle \frac{2}

{3} 3 2 ​ , 1, \displaystyle \frac{4}{3} 3 4 ​ , \displaystyle \frac{5}{3} 3 5 ​ , ...
Mathematics
1 answer:
Murrr4er [49]3 years ago
5 0

Answer:

70

Step-by-step explanation:

a_1 = First term = \dfrac{1}{3}

d = Common difference = \dfrac{2}{3}-\dfrac{1}{3}=\dfrac{1}{3}

n = Number of terms = 20

Sum of arithmetic progression is given by

S=\dfrac{n}{2}[2a_1+(n-1)d]\\\Rightarrow S=\dfrac{20}{2}\times (2\times \dfrac{1}{3}+(20-1)\dfrac{1}{3})\\\Rightarrow S=70

The sum of the first 20 terms of the arithmetic sequence is 70.

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How do you calculate tan^-1 (10/53)
frez [133]

Answer:

Use you calculator.

Step-by-step explanation:

There will be a way on your calculator to do tan^-1. It may be called arctan. They are the same thing.

5 0
3 years ago
Find the mass of the solid paraboloid Dequals=​{(r,thetaθ​,z): 0less than or equals≤zless than or equals≤8181minus−r2​, 0less th
Lubov Fominskaja [6]

Answer:

M = 5742π  

Step-by-step explanation:

Given:-

- Find the mass of a solid with the density ( ρ ):

                             ρ ( r, θ , z ) = 1 + z / 81

- The solid is bounded by the planes:

                             0 ≤ z ≤ 81 - r^2

                             0 ≤ r ≤ 9

Find:-

Find the mass of the solid paraboloid

Solution:-

- The mass (M) of any solid body is given by the following triple integral formulation:

                           M = \int \int \int {p ( r ,theta, z)} \, dV\\\\

- We can write the above expression in cylindrical coordinates:

                           M = \int\limits\int\limits_r\int\limits_z {r*p(r,theta,z)} \, dz.dr.dtheta \\\\M = \int\limits\int\limits_r\int\limits_z {r*[ 1 + \frac{z}{81}] } \, dz.dr.dtheta\\\\

- Perform integration:

                           M = \int\limits\int\limits_r{r*[ z + \frac{z^2}{162}] } \,|_0^8^1^-^r^2 dr.dtheta\\\\M = \int\limits\int\limits_r{r*[ 81-r^2 + \frac{(81-r^2)^2}{162}] } \, dr.dtheta\\\\M = \int\limits\int\limits_r{r*[ 81-r^2 + \frac{6561 -162r + r^2}{162}] } \, dr.dtheta\\\\M = \int\limits\int\limits_r{r*[ 81-r^2 + 40.5 -r +\frac{r^2}{162} ] } \, dr.dtheta\\\\M = \int\limits\int\limits_r{[ 121.5r-r^2 -\frac{161r^3}{162} ] } \, dr.dtheta\\\\

                           M = 2*\int\limits_0^\pi {[ 121.5r^2-r^3 -\frac{161r^4}{162} ] } |_0^6 \, dtheta\\\\M = 2*\int\limits_0^\pi {[ 121.5(6)^2-(6)^3 -\frac{161(6)^4}{162} ] }  \, dtheta\\\\M = 2*\int\limits_0^\pi {[ 4375-216 -1288] }  \, dtheta\\\\M = 2*\int\limits_0^\pi {[ 2871] }  \, dtheta\\\\M = 5742\pi  kg              

- The mass evaluated is M = 5742π                      

8 0
3 years ago
Completely factorize (2x+3)^-2 + 2x(2x+3)^-3
Alexxx [7]
Hello,

\dfrac{1}{(2x+3)^2} + \dfrac{2x}{(2x+3)^3} \\

= \dfrac{(2x+3)+2x}{(2x+3)^3}\\

= \dfrac{4x+3}{(2x+3)^3}
4 0
3 years ago
In a chest there are some gold coins. Captain takes half the coins. Sally takes a quarter of the coins. There are 3 coins left.
amid [387]

Answer:

<u>There were 12 gold coins in the chest at the start.</u>

Step-by-step explanation:

1. Let's review the information given to us to answer the question correctly:

x = Number of gold coins in a chest

1/2x = Number of gold coins taken by the captain

1/4x = Number of gold coins taken by Sally

3 = Number of gold coins left

2. How many coins were in the chest at the start?

Let's write the following equation to solve for x:

1/2x + 1/4x + 3 = x

2x + x + 12 = 4x (Lowest Common Denominator is 4)

4x - 2x - x = 12 (Like terms)

x = 12

<u>There were 12 gold coins in the chest at the start.</u>

3 0
3 years ago
Brandon buys a radio for $45.45 in a state where the sales tax is 7%.
svlad2 [7]
Given : Brandon buys a radio for $45.99 .sales tax rate is 7%.sales tax is a consumption tax imposed by the government on the sale of goods and services.
Let the price of Radio before the sales tax be $x. Sales tax on $x is 7% x.
Price before sales tax + Amount of sales tax= Cost of Radio.
x+7%x =45.99
Or x+0.07x=45.99
1.07x=45.99
Dividing both sides by 1.07.
x= 41.11
Cost of Radio before tax = $41.11
Sales tax paid = 43.99-41.11= 2.88
Tax paid = $2.90 (To nearest cent)
3 0
3 years ago
Read 2 more answers
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