Please help with these?

<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

P=2a+2b, solve for b

Serggg [28]

Answer:

answer in in the photo with a explanation

8 0

2 years ago

a manufacturer uses a mold to make a part in the shape of a triangular prism. The dimensions of this part are shown below. Whic

VMariaS [17]

To estimate the volume of Thai triangular prism you will use the formula for finding the volume.

V=Bh, where B is the area of the base and h is the height of the prism.

V = (1/2 x 12.6 x 1.6) x 10.75
V = 108.36 cubic mm

You answer is approximately 108 cubic millimeters.

8 0

3 years ago

Read 2 more answers

The measures of two supplementary angles total 180 degrees. The measure of angle y is 65 degrees less than the measure of angle

iVinArrow [24]

The measures of the angles are given to be x and y. Since y is 65 degrees less than the measure of angle x then, it can also be expressed as x - 65. The sum of the angles x and y should be 180 degrees as they are supplementary angles,
x + y = 180
x + (x - 65) = 180
The value of x is 122.5 and that of y is 57.5. Therefore, the measures of the angles are 122.5 and 57.5.

3 0

2 years ago

It's time for another financial calculator problem. A UCF student (who has not taken FIN 2100) decides that he really needs a la

AysviL [449]

Answer:

interest rate is 38.68 %

Step-by-step explanation:

Given data

installment = $60

time = 36 months = 36/12 = 3 years

principal = $1000

to find out

interest rate

Solution

we know student pay $60 for 36 months

so he pay total = 60 × 36 = 2160

total amount pay by student = $ 2160

so we can find interest rate by given formula

rate = (1/time)(amount/Principal - 1)

put the value time amount and principal here

rate = (1/3)(2160/1000 - 1)

rate = 0.386667

interest rate is 38.68 %

5 0

2 years ago