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Y_Kistochka [10]
2 years ago
11

Given the function () = $

Mathematics
1 answer:
elena-s [515]2 years ago
6 0

The inverse of the function f(x) = 1/3x^2 - 3x + 5 is  f-1(x) = 9/2 + √[3(x + 7/4)], the sum of the arithmetic series is 1078 and the common ratio of the sequence is 2

<h3>The inverse of the function?</h3>

The function is given as:

f(x) = 1/3x^2 - 3x + 5

Next, we rewrite the function as in vertex form

Using a graphing calculator, the vertex form of the function f(x) = 1/3x^2 - 3x + 5 is

f(x) = 1/3(x - 9/2)^2 - 7/4

Express f(x) as y

y = 1/3(x - 9/2)^2 - 7/4


Swap x and y

x = 1/3(y - 9/2)^2 - 7/4

Add 7/4 to both sides

1/3(y - 9/2)^2 = x + 7/4

Multiply through  by 3

(y - 9/2)^2 = 3(x + 7/4)

Take the square root of both sides

y - 9/2 = √[3(x + 7/4)]

Add 9/2 to both sides

y = 9/2 + √[3(x + 7/4)]

Rewrite as an inverse function

f-1(x) = 9/2 + √[3(x + 7/4)]

<h3>Sum of arithmetic series</h3>

Here, we have:

5 + 18 + 31 + 44 + ... 161

Calculate the number of terms using:

L = a + (n -1)d

So, we have:

161 = 5 + (n - 1) * 13

This gives

(n - 1) * 13 = 156

Divide by 13

n - 1 = 12

Add 1

n = 13

The sum is then calculated as:

Sn = n/2 * [a + L]

This gives

Sn =13/2 * (5 + 161)

Evaluate

Sn = 1078

Hence, the sum of the arithmetic series is 1078

<h3>The common ratio of the sequence</h3>

Here, we have:

T11  = 32 * T6

The nth term of a geometric sequence is

Tn = ar^(n-1)

This gives

ar^10 = 32 * ar^5

Divide by ar^5

r^5 = 32

Take the fifth root

r = 2

Hence, the common ratio of the sequence is 2


Read more about sequence at:

brainly.com/question/7882626

#SPJ1

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Hey. Let me help you on this one.

As the question says, the area of the floor surface is 17 feet by 9 feet. Each floor tile is 1 foot in length, and 1 foot in width. We know that the area of one tile is 1^{2}ft squared if we substitute numbers into the square area formula and solve it.

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We understand that each tile costs a different amount of money, so that's why we need to set up an equation we can later solve. For this; however, we will need to know the complete area of the floor since this is going to be our total.

In order for us to solve for the total area, we have to use the same area formula we used a step ago.

Length of the floor is 17 feet, while the width is 8 feet. Let's multiply them together.

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Awesome! We know the complete area of the floor as the whole, which is 136 feet squared, and area of the individual tile is 1 foot squared.

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One half of 136 is 68, meaning that 68 tiles will cost 58 cents each, and that other 68 tiles will cost 49 cents each. Let's form the solution which we can then solve.

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Answer: 7276 cents, or $72.76 is the price of the floor.


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