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FrozenT [24]
2 years ago
6

Please help very urgent

Mathematics
2 answers:
elena-14-01-66 [18.8K]2 years ago
6 0

Answer:  answers are( 2,4,8,16)

Step-by-step explanation:

if a/1=32    that means that the only possible number that has to be multiplied by 32 to get 32 is 1

 formulae guess and test method : use a variable

if so, then 32 and 1 are our key numbers in the sequence

solution:: make your own sequence

which consists of factors of 32

32,16,8,4,2,1  whereby 1x2 is 2 2x4 is 8 e.t.c

therefore 2,4,8,16,is the answer to this arithmetic

Alik [6]2 years ago
3 0

Answer:

32, <u>16</u>, <u>8</u>, <u>4</u>, <u>2</u>, 1

Explanation:

The geometric mean can be represented by \sqrt[n]{x_{1} • x_{2} • x_{3} • .. x_{n}}.

Which is the mean of the product of n numbers, used to find the average of a geometric progression.

Don't get confused by geometric mean, it is only asking you about the next numbers in the geometric sequence given the first and sixth term.

The explicit rule for a geometric sequence can be modeled by:

a_{n} = a_{1} • r^{n-1}

Where a_{n} is the nth term, a_{1} is the first term in the sequence, n is the term number, and r is the common ratio.

Since we already know the first term, a_{1} will simply be 32.

Since we know it's geometric, there will be an exponential relationship, which means that we will use the geometric mean to find the common ratio.

There are 6 total terms, r is raised to the n – 1 so 6 – 1 = 5, and that will be the degree of this root.

\sqrt[5]{\frac{a_{6}}{a_{1}}} =

\sqrt[5]{\frac{1}{32}} =

\frac{1}{2}.

Therefore: r = \frac{1}{2}.

Using all the information we have, we can find the explicit rule:

a_{n} = a_{1} • r^{n-1}

  • a_{1} = 32
  • r = \frac{1}{2}

a_{n} = a_{1} • r^{n-1} →

\boxed{a_{n} = 32 • (\frac{1}{2})^{n-1}}

________________________________

We can test that this works by substituting the number location of the term you want to find.

For instance:

a_{1} = 32 • (\frac{1}{2})^{1-1}

a_{1} = 32 • (\frac{1}{2})^{0}

a_{1} = 32 • 1

a_{1} = 32

a_{6} = 32 • (\frac{1}{2})^{6-1}

a_{6} = 32 • (\frac{1}{2})^{5}

a_{6} = 32 • \frac{1}{32}

a_{6} = 1

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5 0
2 years ago
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3 years ago
The length of a rectangle is 3 cm more than twice the width. The area of the rectangle is 65 square centimeters. Find the dimens
polet [3.4K]

Answer:

5 cm and 13 cm

Step-by-step explanation:

Let b be the width of the rectangle.

Length = 3+2b

The area of the rectangle is 65 cm²

We need to find the dimensions of the rectangle. The area of a rectangle is given by :

A = lb

65=(3+2b)b\\\\65=3b+2b^2\\\\3b+2b^2-65=0\\\\b=5\ cm,-6.5\ cm

Neglecting the negative value, the width of the rectangle is 5 cm.

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6 0
3 years ago
Use the number line above to correctly compare the following numbers.
tatyana61 [14]

Answer:

C

Step-by-step explanation:

9/4= 2.25

PIE=3.14

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3 0
3 years ago
Use the properties of exponents to simplify the expression: 2532
Vlad1618 [11]

Question

Use the properties of exponents to simplify the expression: 25^{\frac{3}{2}}

Answer:

25^{\frac{3}{2}} = 125\

Step-by-step explanation:

Given

25^{\frac{3}{2}}

Required

Simplify

25^{\frac{3}{2}}

Apply the following law of indices

a^{\frac{m}{n}} = (a^m)^{\frac{1}{n}}

So, the expression becomes

25^{\frac{3}{2}} = (25^3)^{\frac{1}{2}}

Express 25^3 as 15625

25^{\frac{3}{2}} = (15625)^{\frac{1}{2}}

In indices: a^{\frac{1}{2}} = \sqrt a

So, we have:

25^{\frac{3}{2}} = \sqrt{15625

25^{\frac{3}{2}} = 125

6 0
3 years ago
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