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Ksivusya [100]
3 years ago
8

Find the 7th term of the geometric sequence whose common ratio is 1/3 and whose first term is 5.

Mathematics
1 answer:
wolverine [178]3 years ago
8 0

Answer:

t_7 =\frac{5}{729}

Step-by-step explanation:

We are given that:

First term (a) = 5

common ratio (r) =\frac{1}{3}

The nth term of a geometric sequence is given as:

t_n =ar^{n-1} \\\therefore t_7 =5\times \bigg(\frac{1}{3}\bigg) ^{7-1} \\\therefore t_7 =5\times \bigg(\frac{1}{3}\bigg) ^{6} \\\therefore t_7 =5\times \bigg(\frac{1}{3}\bigg) ^{6} \\\therefore t_7 =5\times \frac{1}{729}\\\\\huge\red{\boxed{\therefore t_7 =\frac{5}{729} }}

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Drag the expressions to the correct functions. Not all expressions will be used.
postnew [5]

The function composition exists an operation " ∘ " that brings two functions f and g, and has a function h = g ∘ f such that h(x) = g(f(x)).

Let the functions be f(x) = 4x² + 1 and g(x) = x² - 3

The correct answer is (f o g)(x) = 4x⁴ - 96x + 37 and

(g o f)(x) = 16x⁴ + 8x² - 2.

<h3>What is composition function?</h3>

The function composition exists an operation " ∘ " that brings two functions f and g, and has a function h = g ∘ f such that h(x) = g(f(x)). In this operation, the function g exists used for the outcome of applying the function f to x.

Given:

f(x) = 4x² + 1 and g(x) = x² - 3

a) (f o g)(x) = f[g(x)]

f[g(x)] = 4(x² - 3)² + 1

substitute the value of g(x) in the above equation, and we get

    = 4(x⁴ - 24x + 9) + 1

simplifying the above equation

    = 4x⁴ - 96x + 36 + 1

    = 4x⁴ - 96x + 37

(f o g)(x) = 4x⁴ - 96x + 37

b) (g o f)(x) = g[f(x)]

substitute the value of g(x) in the above equation, and we get

g[f(x)] = (4x² + 1)²- 3

      = 16x⁴ + 8x² + 1 - 3

simplifying the above equation

      = 16x⁴ + 8x² - 2

(g o f)(x) = 16x⁴ + 8x² - 2.

Therefore, the correct answer is (f o g)(x) = 4x⁴ - 96x + 37 and

(g o f)(x) = 16x⁴ + 8x² - 2.

To learn more about the function refer to:

brainly.com/question/26709985

#SPJ9

7 0
1 year ago
What two number multiply to 24 and add to -11
enot [183]

Answer:

8 and 3

Step-by-step explanation:

Brainliest Please

4 0
2 years ago
Read 2 more answers
Use the commutative property for addition to rearrange the algebraic expression 5x-7y-8x+y
BartSMP [9]

You want to use the addition property, so you need to ADD each term. Just change the minuses to pluses, making sure you keep the negative with the number


5x-8x-7y+y =

5x + -8x + -7y +y

5 0
3 years ago
NEED HELP PLEASE!
USPshnik [31]

Answer:

(x + (3+5i))^2 = x^2 + 6x + (10x+30)i - 16

Step-by-step explanation:

Complex numbers identity:

The complex numbers identity is:

i^2 = -1

Square of the sum:

(x + y)^2 = x^2 + 2xy + y^2

In this question:

(x + (3+5i))^2

x^2 + 2x(3+5i) + (3+5i)^2

x^2 + 6x + 10xi + 9 + 30i + 25i^2

x^2 + 6x + 9 + (10x+30)i - 25

x^2 + 6x + (10x+30)i - 16

So

(x + (3+5i))^2 = x^2 + 6x + (10x+30)i - 16

5 0
2 years ago
What’s the answer no links.
lisabon 2012 [21]

Answer:

12÷2?

I guess I dunno :/ lel

4 0
3 years ago
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