Ask question

Ask question

All categories

3 years ago

9

Please help ASAP (a lot of points ) show your work please

1 answer:

allsm [11]3 years ago

8 0

Answer :-

1. value of x is 18

You might be interested in

<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

2 years ago

Which expression is equivalent to i 233?<br> a)1<br> b)–1<br> c)i<br> d)–i

Aneli [31]

We have to find the value of the expression $i^{233}$

We know that the below values.

$i^2=-1\\i^4=1$

Hence, in order to find the value of the given expression, we can first rewrite it in terms of $i^4$

$i^{233}=(i^4)^{58}\cdot i$

Now, we know that $i^4=1$

Hence, we have

$i^{233}=(1)^{58}\cdot i$

$i^{233}=1\cdot i$

$i^{233}=i$

C is the correct option.

5 0

3 years ago

Read 2 more answers

What is the value of p?

vfiekz [6]

Answer:

B

Step-by-step explanation:

8 0

3 years ago

Read 2 more answers

I really need help for this question <br>

katrin [286]

The answer is equal the lengths change when a shape is dilated but the ratio of it does not

7 0

3 years ago

Please help, thank you

irina1246 [14]

Answer:

It's kinda hard to see can you type out the question?

Step-by-step explanation:

4 0

3 years ago