generis wrote:

Bunuel wrote:

The figure shown above consists of three identical circles that are tangent to each other. If the area of the shaded region is \(64\sqrt{3}-32\pi\), what is the radius of each circle?

(A) 4

(B) 8

(C) 16

(D) 24

(E) 32

dave13 wrote:

JeffTargetTestPrep wrote:

We can let each radius = r, and so the side of each triangle = 2r.

Notice that the area of the equilateral triangle consists of the central shaded region and three identical circular sectors, each of which is a 60-degree sector from its circle. Using this information, we can create the following equation:

(Area of equilateral triangle) - (3 x area of 1/6 of each circle) = area of shaded region

(2r)^2√3/4 - 3(1/6 x π r^2) = 64√3 − 32π

[(4r^2)√3]/4 - (πr^2)/2 = 64√3 − 32π

(r^2)√3 - (πr^2)/2 = 64√3 − 32π

Multiplying both sides by 2, we have:

2(r^2)√3 - πr^2 = 128√3 − 64π

r^2(2√3 - π) = 128√3 − 64π

Dividing both sides by (2√3 - π), we have:

r^2 = 64

r = 8

Answer: B

hi

generis its been raining here... so after the rain i feel like solving algebra

regarding this "\(r^2(2√3 - π) = 128√3 − 64π\) divide both sides by (2√3 - π) "

\(r^2= \frac{128√3 − 64π}{(2√3 - π)}\) after this step i am getting confused (when i dvide numerator by denominator)

so this is what i get in numerator first i smplify numerator 128√3 − 64π ( i subtract 128 - 64 = 64) --->

\(r^2=\frac{64√3-π}{2√3 - π}\) now when i divide numerator by denominator i divide 64 by 2

\(r^2= 32\) and get this

why

have a great sunny weekend

La France va gagner la coupe du monde

3:1

Hi

dave13 - et le score final était de 4-2! Es-tu heureux que la France a remporté la coupe? (Can't remember; do I need "de"??)

So close! One mistake.

**Quote:**

first i smplify numerator

128√3 − 64π

(i subtract 128 - 64 = 64) --->

\(r^2=\frac{64√3-π}{2√3 - π}\)

This numerator is not correct:

\(64√3-π\)

\((128√3 − 64π)=\)

\(64(2√3 -π)\)

Put the terms \(128√3\) and \(64π\) in factors to make

dividing 64 out easier ("factorize" the terms)

In the numerator, we have

\((128*√3)-(64*π)=\)

\((64*2*√3)-(64*π)\)

Factor out \(64\), thus \(64(2√3)-64(π)\)

Remove the common factor again. UNlike terms go together in parentheses with the minus sign: \(64(2√3-π)\)

That's your numerator.

So now we have \(r^2=\frac{64(2√3-π)}{(2√3-π)}\)

You should see it now. Hope that helps!

generisSalut! non, je dirais que je suis ni heureux ni malheureux

, mais je croyais fortement que l`equipe francaise remporterait la coupe du monde

D`ailleurs, le score final 3-1 etait ma prognostique

je l`ai ecrit avant le debut du match

je suis heureux de voir ta solution fantastique

merci beaucoup

What if i would not factor it, how should we solve this ? i like to choose the hard way , the most sinuous ways

i tried to solve it myself but something went wrong

\(r^2= \frac{128√3 − 64π}{(2√3 - π)}\) = \(r^2= \frac{128√3 − 64π}{(2√3 - π)} * \frac{(2√3 + π)}{(2√3 + π)}\) = \(\frac{256√3 +128n√3 -128n√3+64n^2}{4√9+2n√3-2n√3-n^2}\) = so here i will cancel out +/- 128n√3 in numerator and +/-2n√3 in denominator = i get \(\frac{256*3+64n^2}{27-n}\) so from here i get wrong answer

i followed the rule / pattern in the last example here

https://www.cliffsnotes.com/study-guide ... xpressions P.S.

And no need to use "de' in your sentence

The French Partitive Articles

When you are talking about a portion of an item (food), or something that cannot be quantified (e.g. qualities, like patience), use a partitive article:

du (+ masculine word)

de la (+ feminine word),

de l’ (followed by a vowel),

des (+ plural word).

FYI:

https://www.frenchtoday.com/blog/french ... e-articles Also you cant say " Es-tu heureux que la France

a remporté la coupe? " you need to use here Passe du subjonctive since action took place in the past "Es-tu heureux que la France

ait remporté la coupe" is correct version

After verbs expressing feelings such as etre heureux, etre contente que, regretter que, avoir envie de, avoir hate de, etre sur, etc you need to use either present du Subjonctif or passe du Subjonctif. if action takes place in the past use "passe du Subjonctif" if action takes place in the present use present du Subjonctif

Example: Je suis content (présent de l’indicatif) en ce moment qu'elle soit (présent du subjonctif) ici aujourd'hui.

i am glad now that she is today here.

Example :

Je suis triste (présent de l’indicatif) maintenant qu’elle soit partie (passé du subjonctif) hier.

i am sad now that she left yesterday

belle journee

_________________

In English I speak with a dictionary, and with people I am shy.