Monica needs to increase her savings by 20%. If she has $85 already in her savings account, how much does she need to add?

<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

Which of the following hypotheses/theories suggests that investors regard a change in dividend payments as a signal that the fir

lutik1710 [3]

Answer:

C

Step-by-step explanation:

Dividend policy (hypothesis) of firms as stated by Musa (2009) is a cultural phenomenon that changes continuously according to environment and time, hence it is necessary to continuously modify dividend behavioural models to capture those factors that are peculiar to a particular period and environment, as well as changes in tax.

Hope this helps

7 0

3 years ago

Write 5.641 in word form

WINSTONCH [101]

Answer:

Five and Six hundred Forty one thousandths

Step-by-step explanation:

5.641 in words can be written as

the first number is considered same, decimal is considered as and and digits after decimal are considered as regular number.

So, 5.641 in word form is:

Five and Six hundred Forty one thousandths

5 0

3 years ago

Read 2 more answers

Joey made 300 greeting cards. He sold 40% of the cards, gave 85% of the remaining cards to him friends, and kept the rest of the

Sedbober [7]

I believe he kept 18 cards.

4 0

2 years ago

A blacksmith blends one alloy of silver that is 35% silver and another that is 95% silver. To the nearest ton, how much of the a

hammer [34]

Answer:

Let x be the unknown quantity of 50% silver.

Look at the silver concentrations... This will be 0.5x of actual silver,

Added to 5% silver in 500g or 0.05(500)g of actual silver

Totaling to (500+x)g of 20% silver which will have 0.2(500+x)g of silver

Your equation is:

0.5x + 0.05(500) = 0.2(500+x)

Solve for x to find the grams of 50% silver used

Step-by-step explanation:

sana maka tulong po sorry po kung mali

5 0

3 years ago