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2 years ago

Of the 1000 students in a local college ,

Mathematics

1 answer:

dimaraw [331]2 years ago

5 0

Can you please explain? Or maybe continue your question please?

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<img src="https://tex.z-dn.net/?f=The%20%5C%3A%20%20value%20%20%5C%3A%20of%20%20%5C%3A%20%20%5Csqrt%7B6%20%2B%20%20%5Csqrt%7B6%2

saul85 [17]

$\large\underline{\sf{Solution-}}$

Let us assume that:

$\sf \longmapsto x = \sqrt{6 + \sqrt{6 + \sqrt{6 + ... \infty } } }$

We can also write it as:

$\sf \longmapsto x = \sqrt{6 + x }$

Squaring both sides, we get:

$\sf \longmapsto {x}^{2} =6 + x$

$\sf \longmapsto {x}^{2} - x - 6 =0$

By splitting the middle term:

$\sf \longmapsto {x}^{2} - 3x + 2x - 6 =0$

$\sf \longmapsto x(x - 3) + 2(x - 3 ) =0$

$\sf \longmapsto (x+ 2)(x - 3 ) =0$

Therefore:

$\longmapsto\begin{cases} \sf (x+ 2) =0 \\ \sf (x - 3) = 0 \end{cases}$

$\sf \longmapsto x = - 2,3$

But x cannot be negative. 

$\sf \longmapsto x = 3$

Therefore, the value of the expression is 3.

$\large\underline{\sf{Verification-}}$

Given:

$\sf\longmapsto x=3$

We can also write it as:

$\sf\longmapsto x = \sqrt{9}$

$\sf\longmapsto x = \sqrt{6+3}$

$\sf\longmapsto x = \sqrt{6 + \sqrt{9}}$

$\sf\longmapsto x = \sqrt{6 + \sqrt{6+3}}$

$\sf\longmapsto x = \sqrt{6 + \sqrt{6+\sqrt{9}}}$

$\sf\longmapsto x = \sqrt{6 + \sqrt{6+\sqrt{6+3}}}$

This pattern will continue.

$\sf\longmapsto x = \sqrt{6 + \sqrt{6+\sqrt{6+...\infty}}}$

7 0

2 years ago

The price of a man's shirt went from $15 to $20. What was the percent of increase of the price of the shirt? A. 25% A. , 25%, B.

dexar [7]

Answer: 33 1/3%

Step-by-step explanation:

Percentage increase of the shirt will be calculated as:

= Price Increase / Old price × 100%

Price Increase = $20 - $15 = $5

Old price = $15

Percent increase = Price Increase / Old price × 100%

= 5/15 × 100

= 1/3 × 100

= 33 1/3%

4 0

2 years ago

Read 2 more answers

BRAINLIEST if right! Which of the flowing graphs is increasing only when x<0?

prohojiy [21]

I believe it would be Z

6 0

3 years ago

Read 2 more answers

Solve for b.

AlekseyPX

Answer:

$b=+-5\sqrt{C}$

Step-by-step explanation:

$C=b^2/25$

$25C=b^2$

$\sqrt{b^2}=+-\sqrt{25C}$

$b=+-5\sqrt{C}$

8 0

3 years ago

Read 2 more answers

6 - 3x = 5x - 10x + 8

Jet001 [13]

Answer:

x=1

Step-by-step explanation:

6-3x=5x-10x+8=

move all terms to the left:

6-3x-(5x-10x+8)=0

add all the numbers together, and all the variables

-3x-(-5x+8)+6=0

get rid of parentheses

-3x+5x-8+6=0

add all the numbers together, and all the variables

2x-2=0

move all terms containing x to the left, all other terms to the right

2x=2

x=2/2

x=1

3 0

3 years ago