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3 years ago

8

Write standard form twenty-five thousand, four hundred eight

1 answer:

hoa [83]3 years ago

8 0

In standard form it is 25,408

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<img src="https://tex.z-dn.net/?f=%20%5Csqrt%7Bx%20%5Csqrt%7Bx%20%5Csqrt%7Bx%20%5Csqrt%7Bx....%7D%20%7D%20%7D%20%7D%20%20%3D%20%

andrey2020 [161]

First observe that if $a+b>0$ ,

$(a + b)^2 = a^2 + 2ab + b^2 \\\\ \implies a + b = \sqrt{a^2 + 2ab + b^2} = \sqrt{a^2 + ab + b(a + b)} \\\\ \implies a + b = \sqrt{a^2 + ab + b \sqrt{a^2 + ab + b(a+b)}} \\\\ \implies a + b = \sqrt{a^2 + ab + b \sqrt{a^2 + ab + b \sqrt{a^2 + ab + b(a+b)}}} \\\\ \implies a + b = \sqrt{a^2 + ab + b \sqrt{a^2 + ab + b \sqrt{a^2 + ab + b \sqrt{\cdots}}}}$

Let $a=0$ and $b=x$ . It follows that

$a+b = x = \sqrt{x \sqrt{x \sqrt{x \sqrt{\cdots}}}}$

Now let $b=1$ , so $a^2+a=4x$ . Solving for $a$ ,

$a^2 + a - 4x = 0 \implies a = \dfrac{-1 + \sqrt{1+16x}}2$

which means

$a+b = \dfrac{1 + \sqrt{1+16x}}2 = \sqrt{4x + \sqrt{4x + \sqrt{4x + \sqrt{\cdots}}}}$

Now solve for $x$ .

$x = \dfrac{1 + \sqrt{1 + 16x}}2 \\\\ 2x = 1 + \sqrt{1 + 16x} \\\\ 2x - 1 = \sqrt{1 + 16x} \\\\ (2x-1)^2 = \left(\sqrt{1 + 16x}\right)^2$

(note that we assume $2x-1\ge0$ )

$4x^2 - 4x + 1 = 1 + 16x \\\\ 4x^2 - 20x = 0 \\\\ 4x (x - 5) = 0 \\\\ 4x = 0 \text{ or } x - 5 = 0 \\\\ \implies x = 0 \text{ or } \boxed{x = 5}$

(we omit $x=0$ since $2\cdot0-1=-1\ge0$ is not true)

3 0

1 year ago

The train from Geneva, Switzerland, to Milan, Italy, travels at 100 miles per hour, and the two cities are 200 miles apart. How

Hatshy [7]

Answer:

Step-by-step explanation:

Three customers have accounts owing money. The table shows the account balances.

Which customer owes the least amount of money?

Customer Balance

M. Palmer –$56.72

B. Leftwich –$74.19

R. Jordan –$54.31

does anybody know

8 0

3 years ago

Determine the effective annual yield for each investment.

Lyrx [107]

I think it’s B but don’t at me

3 0

3 years ago

Simon, 35, works for a company which offers a 4% match to his 401(k) plan. He previously invested $25,000 into an IRA. What woul

Paha777 [63]

Answer: answer

Step-by-step explanation:

4 0

3 years ago

The product if the following numbers is evenly divided by what numbers 737×74

IceJOKER [234]

737 X 74 = 54,538
Evenly divided by: 2, 11, and 22

6 0

3 years ago