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Sum of series 1 +1/3 +1/3².... is?​

Answers

Answer 1
Answer:

Answer:

The sum of the series is 3/2

Step-by-step explanation:

Given

1 + 1/3 + 1/3^2 + ....

Required

The sum of the series

This implies that we calculate the sum to infinity.

We have:

a = 1 -- The first term

First, calculate the common ratio (r)

r = (1)/(3^2) / (1)/(3)

Change to product

r = (1)/(3^2) * (3)/(1)

Solve

r = (1)/(3)

The sum of the series is then calculated as:

S_(\infty) = (a)/(1 - r)

S_(\infty) = (1)/(1 - 1/3)

Solve the denominator

S_(\infty) = (1)/(2/3)

Express as product

S_(\infty) = 1 * (3)/(2)

S_(\infty) = (3)/(2)

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Lydia and Adam are buildng a display of soup cans at the market where they work. the display is in the form of a square pyramid, with a base of 81 cans. They will continue making smaller layers until there is one can at the top. Adam is going to the stockroom to get the can they will need. a. How many layers will be in the display?

b. How many canse will Lydia and Adam use total?

Answers

Answer:

(a). 9 layers

(b). 285

Step-by-step explanation:

In the question,

The Square Pyramid is needed to be made from the cans.

The base of the pyramid has = 81 cans

So,

Side of the Square = s

So,

s^(2)=81\ns = 9

Therefore, the number of cans on one side of the square base = 9 cans

So,

The number of cans will be reducing by 1 in each layer upto the point we are left with only 1 can in the top.

So,

1st layer = 9 cans

2nd layer = 8 cans

3rd layer = 7 cans

4th layer = 6 cans

5th layer = 5 cans

6th layer = 4 cans

7th layer = 3 cans

8th layer = 2 cans

9th layer = 1 can

Number of layers are = 9

(b).

Total number of cans used by Lydia and Adam will be,

Sum of number of cans in all the layers.

Number\,of\,cans=9^(2)+8^(2)+7^(2)+6^(2)+5^(2)+4^(2)+3^(2)+2^(2)+1^(2)\nNumber\,of\,cans=81+64+49+36+25+16+9+4+1\nNumber\,of\,cans=285

Therefore, the number of cans = 285

suppose a ladder 20 feet long is placed against a vertical wall 20 feet high. How far would the top of the ladder move down the wall by pulling out the bottom of the ladder by 5 feet?

Answers

the ladder would now be 15 feet long

Let f be the linear function (in blue) and let g be the parabolic function (in red) below. I have already tried 0,2,-1 and none of them work for the g o g(2) one and I'm soo confused. Please help!

Answers

Based on the graph of the linear function (in blue) and parabolic function (in red), the corresponding output values include the following;

(f∘g)(2) = -1.

(g∘f)(2) = 1.

(f∘f)(2) = 0.

(g∘g)(2)= 4.

(f + g)(4) = 7.

(f/g)(2) = DNE.

What is a function?

In Mathematics and Geometry, a function composition is an operation (∘) that combines two functions f(x) and g(x), in order to produce a composite function h(x) = (g∘f)(x), such that h(x) = g.

In this exercise, we would determine the corresponding output values for each of the composite functions by using the substitution method as follows;

(f∘g)(2) = f(g(2))

f(g(2)) = f(0)

f(0) = -1.

Part 2.

(g∘f)(2) = g(f(2))

g(f(2)) = g(1)

g(1) = 1.

Part 3.

(f∘f)(2) = f(f(2))

f(f(2)) = f(1)

f(1) = 0.

Part 4.

(g∘g)(2) = g(g(2))

g(g(2)) = g(0)

g(0) = 4.

Part 5.

(f + g)(4) = f(4) + g(4)

f(4) + g(4) = 3 + 4

f(4) + g(4) = 7.

Part 6.

(f/g)(2) = f(2)/g(2)

f(2)/g(2) = 1/0

f(2)/g(2) = DNE.

Read more on composite function here: brainly.com/question/30660139

#SPJ2

Step-by-step explanation:

g(g(2))

= g(0)

= 4

Does anyone wanna help

Answers

Answer:

b

Step-by-step explanation: you have to multiply the number your starting with and you will get the answer 2x=3p
i think the answer might be b

I need help ASAP because this has to be turned in tomorrow

Answers

Answer:

You should look for this assignment quizlet. quizlet has pretty much every assignment!

Step-by-step explanation:

Go online, go to the search bar, type quizlet.com, look for assignment. boom. answers.

30. What is the degree of the polynomial?31. Which polynomial is in descending order in terms of x?

Picture attached

Answers

Answer:

Step-by-step explanation:

30). 5^(th) degree ( 4 + 1 = 5 ; 1 + 1 = 2 and 2 + 2 = 4 )

31) D) Choice D

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