Help I got this question on a math test, I feel like it has no answer!

[Youbetternot]

How would it be 1 that would mean the area is less the circumference because(unless that's possible) since pi*2*1(substituted for r) is 2pi and the area pi*r^1 is 1pi. 

[Youbetternot]

@Youbetternot here's why it doesnt work

 

 

 

it's not 0 btw, its 1 mb lol

I see what you did, I think this problem is impossible.

[Youbetternot]

It equals pi because neither the circumference nor the area of a circle will ever be a whole number and just number sense will tell you that the area of the circle can't be x squared so we can figure out that the answer is pi no math required

Math is all about those little loop holes

Hmm not sure because this is a state standard test their must be a expression used to solve it if possible

[piplupgao]

Hmm not sure because this is a state standard test their must be a expression used to solve it if possible

If I weren't on an iPad I would type a 2 page rant on the American education system

[Canoas]

The area of a circle is πr² and the circunference is 2πr, so

x² = πr²

x = 2πr

 

sqrt(πr²) = 2πr

πr² = (2πr)²

πr² = 4π²r²

r² = 4πr²

1 = 4π

 

r must be 0 for this to be true, it's not possible to have such a circle and all those answers are wrong.

[Stonep11]

Typed it up in Excel, none of these answers worked.  Also, e. is X wtf?

 

Tried running a Solver to figure out what would, zero is all you could use.

[Youbetternot]

The area of a circle is πr² and the circunference is 2πr, so

x² = πr²

x = 2πr

 

sqrt(πr²) = 2πr

πr² = (2πr)²

πr² = 4π²r²

r² = 4πr²

1 = 4π

 

r must be 0 for this to be true, it's not possible to have such a circle and all those answers were wrong.

Yea it seems as it is either impossible or a piece of information has not been given or a typo in the answer key

[Youbetternot]

Typed it up in Excel, none of these answers worked.  Also, e. is X wtf?

Who knows X can brian fuck some people, they want that

[Youbetternot]

 

 

sqrt

Just to make sure is sqrt square root?

[FloRolf]

The area of a circle is πr² and the circunference is 2πr, so

x² = πr²

x = 2πr

 

sqrt(πr²) = 2πr

πr² = (2πr)²

πr² = 4π²r²

r² = 4πr²

1 = 4π

 

r must be 0 for this to be true, it's not possible to have such a circle and all those answers are wrong.

(2pir)^2 =/= 4pi^2r^2

You have to multiply everything.

2*2+2*pi+2*r+pi*2+pi*pi+....

But even then it makes no sense because (as i stated earlier) you cant have a circle with an area as big as the circumference squared.

@op: your problem is bad and you should feel bad!

[Youbetternot]

(2pir)^2 =/= 4pi^2r^2

You have to multiply everything.

2*2+2*pi+2*r+pi*2+pi*pi+....

But even then it makes no sense because (as i stated earlier) you cant have a circle with an area as big as the circumference squared.

@op: your problem is bad and you should feel bad!

How should I feel bad the State gave me this problem on the test which alot of people in my school got stuck on

[piplupgao]

How should I feel bad the State gave me this problem on the test which alot of people in my school got stuck on

*insert American education system rant here*

[FloRolf]

How should I feel bad the State gave me this problem on the test which alot of people in my school got stuck on

Chill dude it was a joke.

But why do they give you these problems with only wrong answers?

What grade are u in btw?

[TheMissxu]

They are trying to say, "The area of a circle is x [units] squared, the circumference of the same circle is x [units long]." Thinking in terms of meters: x meters squared (m²⁾ and x meters long (m).

 

Thus,

x = πr²
x = 2πr

πr² = 2πr (Divide both sides by πr.)
r = 2

 

That means needmorewood was right, the answer is B; 2.

[Sundanc3]

So by the statement  The area of a circle is x squared we get x^2 = Pir^2. If we solve this equation x=sqrt(pi)*r. Then if we substitute this is in for the stated equation of circumference, C = x. We see that the Circumference of a circle is clearly not equal to the sort(pi)*r. So the question is still completely wrong

[ionbasa]

It's 2, tried it with WoolframAlpha and MATLAB, Solution:

 

Solve for r over the real numbers:
2 pi r = pi r^2
Move everything to the left hand side.
Subtract pi r^2 from both sides:
2 pi r-pi r^2 = 0
Factor the left hand side.
Factor r and constant terms from the left hand side:
-(pi r (r-2)) = 0
Divide both sides by a constant to simplify the equation.
Divide both sides by -pi:
r (r-2) = 0
Solve each term in the product separately.
Split into two equations:
r-2 = 0 or r = 0
Look at the first equation: Solve for r.
Add 2 to both sides:
Answer: |
| r = 2 or r = 0

 

 

Note: r=0 is an extraneous answer.

 

I showed it with factoring, you can also complete the square.

[Giggitygoebbels]

Pi r ^2= (2 Pi r)^2

Pi r^2=4 Pi ^2 r^2

r^2= 4Pi r^2

I am confused...

R=0?

Forgive me i failed maths

Wait i think it is option e,because X can be Zero.So the circle is essentially a dot.

[Giggitygoebbels]

Lets sub each number and see what happens:

Option 1:1

(2*pi*1)^2=Pi*1^2

4Pi^2=Pi

Wrong.

Option 2:2

(2*pi*2)^2=Pi*2^2

16Pi^2=4Pi

Wrong.

Option 3:4

(2*pi*4)^2=Pi*4^2

64Pi^2=16Pi

Wrong.

Option 4:Pi

(2*pi^2)^2=Pi^3

4Pi^4=Pi^3

Wrong.

Option 5:X

(2Pi*X)^2=X^2 * Pi

4Pi^2*X^2= X^2 * Pi

Since X can be 0,this option makes most sense to me.You cannot cancel X^2 because it might be 0.

[Scottonpc]

There is the two simultaneous equations x^2= pi*r^2 and x= 2*pi*r

Substituting x=2*pi*r into x^2 = pi*r^2 gives (2*pi*r)^2 = pi*r^2

Expanding the squared bracket u get 4*p^2*r^2 = pi*r^2

Moving everything to one side u get 4*pi^2*r^2 - pi*r^2 = 0

Factorising by r^2 gives r^2(4*pi^2 - pi) = 0

Dividing both sides by (4*pi^2 - pi) gives r^2 = 0

Therefore r = 0

[Canoas]

(2pir)^2 =/= 4pi^2r^2

You have to multiply everything.

2*2+2*pi+2*r+pi*2+pi*pi+....

huh?

(2πr)² = 2πr * 2πr = 2*2*π*π*r*r = 4π²r²

 

Maybe you're confusing it with (2 + π + r)²? But it's a completely different thing..

[FloRolf]

huh?

(2πr)² = 2πr * 2πr = 2*2*π*π*r*r = 4π²r²

 

Maybe you're confusing it with (2 + π + r)²? But it's a completely different thing..

Yeah sorry. It was late and my brain hurt, you are totally right

Either way, theres no correct answer in the given ones.

[Canoas]

It's 2, tried it with WoolframAlpha and MATLAB, Solution:

 

Solve for r over the real numbers:

2 pi r = pi r^2

Move everything to the left hand side.

Subtract pi r^2 from both sides:

2 pi r-pi r^2 = 0

Factor the left hand side.

Factor r and constant terms from the left hand side:

-(pi r (r-2)) = 0

Divide both sides by a constant to simplify the equation.

Divide both sides by -pi:

r (r-2) = 0

Solve each term in the product separately.

Split into two equations:

r-2 = 0 or r = 0

Look at the first equation: Solve for r.

Add 2 to both sides:

Answer: |

| r = 2 or r = 0

 

 

Note: r=0 is an extraneous answer.

 

I showed it with factoring, you can also complete the square.

 

"The area of a circle is x squared"

"the circumference of the same circle is x"

 

You're saying that the area of the circle is x when the question says it's x^2, so it's not 2 pi r = pi r^2, it's sqrt(2 pi r) = pi r^2, to which there is no possible answer but 0

[ionbasa]

"The area of a circle is x squared"

"the circumference of the same circle is x"

 

You're saying that the area of the circle is x when the question says it's x^2, so it's not 2 pi r = pi r^2, it's sqrt(2 pi r) = pi r^2, to which there is no possible answer but 0

Ahh, misread what the question was, sorry. In that case the only possible answer is 0.

[TheMissxu]

"The area of a circle is x squared"

"the circumference of the same circle is x"

 

You're saying that the area of the circle is x when the question says it's x^2, so it's not 2 pi r = pi r^2, it's sqrt(2 pi r) = pi r^2, to which there is no possible answer but 0

Obviously you are wrong... There is no option for the answer to be 0. They must have simply excluded the word "units."

 

When r=2, x=4π and in the case of area, A=4π squared units not A=(4π)² units.

 

Read them out loud, they are the same, but mean two different things.

x = πr²

x = 2πr

πr² = 2πr (Divide both sides by πr.)

r = 2

[Canoas]

Obviously you are wrong... There is no option for the answer to be 0. They must have simply excluded the word "units."

 

When r=2, x=4π and in the case of area, A=4π squared units not A=(4π)² units.

 

Read them out loud, they are the same, but mean two different things.

That is not how things work, if the word units is omitted then the meaning of the sentence changes. x squared = x²