All Answers 356097 Answers

I have no idea what you are talking about!

To correct an earlier error  :

(x + 1) ^2   +  ( y + 2)^2  =  4

Simplify the following:
4+3×5-6^4/(4+2)^3 2

6^4 = (6^2)^2:
4+3×5-(6^2)^2/(4+2)^3 2

6^2 = 36:
4+3×5-36^2/(4+2)^3 2
4+3×5-1296/(4+2)^3 2

4+2 = 6:
4+3×5-1296/6^3×2

6^3 = 6×6^2:
4+3×5-1296/6×6^2×2

6^2 = 36:
4+3×5-1296/(6×36)×2

6×36  =  216:
4+3×5-1296/216×2

The gcd of 1296 and 216 is 216, so 1296/216 = (216×6)/(216×1) = 216/216×6 = 6:
4+3×5-6×2

3×5  =  15:
4+15-6×2

-6×2  =  -12:
4+15+-12

4+15 = 19:
19-12
Answer: |  7

Jesus Christ! where is Nauseated?

The dumbest of athletes would probably know the first one is a better deal. If for no other reason they could afford a financial advisor to inform them.

Lately, these Batshit-Stupid answers have become so numerous, it's causing a major out-break of Contagious Dumbness Disease.

Nauseated, where in Hades's shadow are you?!

Solve for x:
4 x^3 = 24

Divide both sides by 4:
x^3 = 6

Taking cube roots gives 6^(1/3) times the third roots of unity:
Answer: |  x = -(-6)^(1/3)    or    x = 6^(1/3)    or    x = (-1)^(2/3) 6^(1/3)

Here is the "Real" solution:

Solve for x over the real numbers:
x^5 = 243

Take 5^th roots of both sides:
Answer: |  x = 3

Here are the "complex solutions.

Solve for x:
x^5 = 243

Taking 5^th roots gives 3 times the 5^th roots of unity:
Answer: |  x = 3    or    x = -3 (-1)^(1/5)    or    x = 3 (-1)^(2/5)    or    x = -3 (-1)^(3/5)    or    x = 3 (-1)^(4/5)

I meant \(x^2\times x^3=243\).  Sorry about that.

Here are the 3 solutions in approximated forms in answer #1 above.

1) x=~  5.9241 (Real)

2) x=~ -3.4620-5.3882 i

3) x=~ -3.4620+5.3882 i

P. S. It has ONLY 3 roots, since 3 the highest power of x. One "real" and two "complex". It is highly involved and was generated by computer.

Solve for x:
x^3+x^2 = 243

Subtract 243 from both sides:
x^3+x^2-243 = 0

Eliminate the quadratic term by substituting y = x+1/3:
-243+(y-1/3)^2+(y-1/3)^3 = 0

Expand out terms of the left hand side:
y^3-y/3-6559/27 = 0

If y = z+lambda/z then z = 1/2 (y+sqrt(y^2-4 lambda)) which will be used during back substitution:
-6559/27+1/3 (-z-lambda/z)+(z+lambda/z)^3 = 0

Multiply both sides by z^3 and collect in terms of z:
-(6559 z^3)/27+z^6+lambda^3+z^4 (3 lambda-1/3)+z^2 (3 lambda^2-lambda/3) = 0

Substitute lambda = 1/9 and then u = z^3, yielding a quadratic equation in the variable u:
u^2-(6559 u)/27+1/729 = 0

Find the positive solution to the quadratic equation:
u = 1/54 (6559+81 sqrt(6557))

Substitute back for u = z^3:
z^3 = 1/54 (6559+81 sqrt(6557))

Taking cube roots gives (6559+81 sqrt(6557))^(1/3)/(3 2^(1/3)) times the third roots of unity:
z = 1/3 (1/2 (6559+81 sqrt(6557)))^(1/3) or z = -1/3 (1/2 (-6559-81 sqrt(6557)))^(1/3) or z = 1/3 (-1)^(2/3) (1/2 (6559+81 sqrt(6557)))^(1/3)

Substitute back for z = y/2+1/2 sqrt(y^2-(4)/9):
y/2+1/2 sqrt(y^2-(4)/9) = 1/3 (1/2 (6559+81 sqrt(6557)))^(1/3) or z = -1/3 (1/2 (-6559-81 sqrt(6557)))^(1/3) or z = 1/3 (-1)^(2/3) (1/2 (6559+81 sqrt(6557)))^(1/3)

Rewrite the left hand side by combining fractions. y/2+1/2 sqrt(y^2-(4)/9)  =  1/6 (3 y+sqrt(9 y^2-4)):
1/6 (3 y+sqrt(9 y^2-4)) = 1/3 (1/2 (6559+81 sqrt(6557)))^(1/3) or z = -1/3 (1/2 (-6559-81 sqrt(6557)))^(1/3) or z = 1/3 (-1)^(2/3) (1/2 (6559+81 sqrt(6557)))^(1/3)

Multiply both sides by 6:
3 y+sqrt(9 y^2-4) = 2^(2/3) (6559+81 sqrt(6557))^(1/3) or z = -1/3 (1/2 (-6559-81 sqrt(6557)))^(1/3) or z = 1/3 (-1)^(2/3) (1/2 (6559+81 sqrt(6557)))^(1/3)

Subtract 3 y from both sides:
sqrt(9 y^2-4) = 2^(2/3) (6559+81 sqrt(6557))^(1/3)-3 y or z = -1/3 (1/2 (-6559-81 sqrt(6557)))^(1/3) or z = 1/3 (-1)^(2/3) (1/2 (6559+81 sqrt(6557)))^(1/3)

Raise both sides to the power of two:
9 y^2-4 = (2^(2/3) (6559+81 sqrt(6557))^(1/3)-3 y)^2 or z = -1/3 (1/2 (-6559-81 sqrt(6557)))^(1/3) or z = 1/3 (-1)^(2/3) (1/2 (6559+81 sqrt(6557)))^(1/3)

Expand out terms of the right hand side:
9 y^2-4 = 9 y^2-6 2^(2/3) (6559+81 sqrt(6557))^(1/3) y+2 2^(1/3) (6559+81 sqrt(6557))^(2/3) or z = -1/3 (1/2 (-6559-81 sqrt(6557)))^(1/3) or z = 1/3 (-1)^(2/3) (1/2 (6559+81 sqrt(6557)))^(1/3)

Subtract 9 y^2-6 2^(2/3) (6559+81 sqrt(6557))^(1/3) y+2 2^(1/3) (6559+81 sqrt(6557))^(2/3) from both sides:
6 2^(2/3) (6559+81 sqrt(6557))^(1/3) y-4-2 2^(1/3) (6559+81 sqrt(6557))^(2/3) = 0 or z = -1/3 (1/2 (-6559-81 sqrt(6557)))^(1/3) or z = 1/3 (-1)^(2/3) (1/2 (6559+81 sqrt(6557)))^(1/3)

Factor constant terms from the left hand side:
2 (3 2^(2/3) (6559+81 sqrt(6557))^(1/3) y-2-2^(1/3) (6559+81 sqrt(6557))^(2/3)) = 0 or z = -1/3 (1/2 (-6559-81 sqrt(6557)))^(1/3) or z = 1/3 (-1)^(2/3) (1/2 (6559+81 sqrt(6557)))^(1/3)

Divide both sides by 2:
3 2^(2/3) (6559+81 sqrt(6557))^(1/3) y-2-2^(1/3) (6559+81 sqrt(6557))^(2/3) = 0 or z = -1/3 (1/2 (-6559-81 sqrt(6557)))^(1/3) or z = 1/3 (-1)^(2/3) (1/2 (6559+81 sqrt(6557)))^(1/3)

Add 2+2^(1/3) (6559+81 sqrt(6557))^(2/3) to both sides:
3 2^(2/3) (6559+81 sqrt(6557))^(1/3) y = 2+2^(1/3) (6559+81 sqrt(6557))^(2/3) or z = -1/3 (1/2 (-6559-81 sqrt(6557)))^(1/3) or z = 1/3 (-1)^(2/3) (1/2 (6559+81 sqrt(6557)))^(1/3)

Divide both sides by 3 2^(2/3) (6559+81 sqrt(6557))^(1/3):
y = (2+2^(1/3) (6559+81 sqrt(6557))^(2/3))/(3 2^(2/3) (6559+81 sqrt(6557))^(1/3)) or z = -1/3 (1/2 (-6559-81 sqrt(6557)))^(1/3) or z = 1/3 (-1)^(2/3) (1/2 (6559+81 sqrt(6557)))^(1/3)

Substitute back for y = x+1/3:
x+1/3 = (2+2^(1/3) (6559+81 sqrt(6557))^(2/3))/(3 2^(2/3) (6559+81 sqrt(6557))^(1/3)) or z = -1/3 (1/2 (-6559-81 sqrt(6557)))^(1/3) or z = 1/3 (-1)^(2/3) (1/2 (6559+81 sqrt(6557)))^(1/3)

Subtract 1/3 from both sides:
x = (2+2^(1/3) (6559+81 sqrt(6557))^(2/3))/(3 2^(2/3) (6559+81 sqrt(6557))^(1/3))-1/3 or z = -1/3 (1/2 (-6559-81 sqrt(6557)))^(1/3) or z = 1/3 (-1)^(2/3) (1/2 (6559+81 sqrt(6557)))^(1/3)

Substitute back for z = y/2+1/2 sqrt(y^2-(4)/9):
x = (2+2^(1/3) (6559+81 sqrt(6557))^(2/3))/(3 2^(2/3) (6559+81 sqrt(6557))^(1/3))-1/3 or y/2+1/2 sqrt(y^2-(4)/9) = -1/3 (1/2 (-6559-81 sqrt(6557)))^(1/3) or z = 1/3 (-1)^(2/3) (1/2 (6559+81 sqrt(6557)))^(1/3)

Rewrite the left hand side by combining fractions. y/2+1/2 sqrt(y^2-(4)/9)  =  1/6 (3 y+sqrt(9 y^2-4)):
x = (2+2^(1/3) (6559+81 sqrt(6557))^(2/3))/(3 2^(2/3) (6559+81 sqrt(6557))^(1/3))-1/3 or 1/6 (3 y+sqrt(9 y^2-4)) = -1/3 (1/2 (-6559-81 sqrt(6557)))^(1/3) or z = 1/3 (-1)^(2/3) (1/2 (6559+81 sqrt(6557)))^(1/3)

Multiply both sides by 6:
x = (2+2^(1/3) (6559+81 sqrt(6557))^(2/3))/(3 2^(2/3) (6559+81 sqrt(6557))^(1/3))-1/3 or 3 y+sqrt(9 y^2-4) = -2^(2/3) (-6559-81 sqrt(6557))^(1/3) or z = 1/3 (-1)^(2/3) (1/2 (6559+81 sqrt(6557)))^(1/3)

Subtract 3 y from both sides:
x = (2+2^(1/3) (6559+81 sqrt(6557))^(2/3))/(3 2^(2/3) (6559+81 sqrt(6557))^(1/3))-1/3 or sqrt(9 y^2-4) = -2^(2/3) (-6559-81 sqrt(6557))^(1/3)-3 y or z = 1/3 (-1)^(2/3) (1/2 (6559+81 sqrt(6557)))^(1/3)

Raise both sides to the power of two:
x = (2+2^(1/3) (6559+81 sqrt(6557))^(2/3))/(3 2^(2/3) (6559+81 sqrt(6557))^(1/3))-1/3 or 9 y^2-4 = (-2^(2/3) (-6559-81 sqrt(6557))^(1/3)-3 y)^2 or z = 1/3 (-1)^(2/3) (1/2 (6559+81 sqrt(6557)))^(1/3)

Expand out terms of the right hand side:
x = (2+2^(1/3) (6559+81 sqrt(6557))^(2/3))/(3 2^(2/3) (6559+81 sqrt(6557))^(1/3))-1/3 or 9 y^2-4 = 9 y^2+6 2^(2/3) (-6559-81 sqrt(6557))^(1/3) y+2 2^(1/3) (-6559-81 sqrt(6557))^(2/3) or z = 1/3 (-1)^(2/3) (1/2 (6559+81 sqrt(6557)))^(1/3)

Subtract 9 y^2+6 2^(2/3) (-6559-81 sqrt(6557))^(1/3) y+2 2^(1/3) (-6559-81 sqrt(6557))^(2/3) from both sides:
x = (2+2^(1/3) (6559+81 sqrt(6557))^(2/3))/(3 2^(2/3) (6559+81 sqrt(6557))^(1/3))-1/3 or -6 2^(2/3) (-6559-81 sqrt(6557))^(1/3) y-4-2 2^(1/3) (-6559-81 sqrt(6557))^(2/3) = 0 or z = 1/3 (-1)^(2/3) (1/2 (6559+81 sqrt(6557)))^(1/3)

Factor constant terms from the left hand side:
x = (2+2^(1/3) (6559+81 sqrt(6557))^(2/3))/(3 2^(2/3) (6559+81 sqrt(6557))^(1/3))-1/3 or -2 (3 2^(2/3) (-6559-81 sqrt(6557))^(1/3) y+2+2^(1/3) (-6559-81 sqrt(6557))^(2/3)) = 0 or z = 1/3 (-1)^(2/3) (1/2 (6559+81 sqrt(6557)))^(1/3)

Divide both sides by -2:
x = (2+2^(1/3) (6559+81 sqrt(6557))^(2/3))/(3 2^(2/3) (6559+81 sqrt(6557))^(1/3))-1/3 or 3 2^(2/3) (-6559-81 sqrt(6557))^(1/3) y+2+2^(1/3) (-6559-81 sqrt(6557))^(2/3) = 0 or z = 1/3 (-1)^(2/3) (1/2 (6559+81 sqrt(6557)))^(1/3)

Subtract 2+2^(1/3) (-6559-81 sqrt(6557))^(2/3) from both sides:
x = (2+2^(1/3) (6559+81 sqrt(6557))^(2/3))/(3 2^(2/3) (6559+81 sqrt(6557))^(1/3))-1/3 or 3 2^(2/3) (-6559-81 sqrt(6557))^(1/3) y = -2-2^(1/3) (-6559-81 sqrt(6557))^(2/3) or z = 1/3 (-1)^(2/3) (1/2 (6559+81 sqrt(6557)))^(1/3)

Divide both sides by 3 2^(2/3) (-6559-81 sqrt(6557))^(1/3):
x = (2+2^(1/3) (6559+81 sqrt(6557))^(2/3))/(3 2^(2/3) (6559+81 sqrt(6557))^(1/3))-1/3 or y = -((-1)^(2/3) (-2-2^(1/3) (-6559-81 sqrt(6557))^(2/3)))/(3 2^(2/3) (6559+81 sqrt(6557))^(1/3)) or z = 1/3 (-1)^(2/3) (1/2 (6559+81 sqrt(6557)))^(1/3)

Substitute back for y = x+1/3:
x = (2+2^(1/3) (6559+81 sqrt(6557))^(2/3))/(3 2^(2/3) (6559+81 sqrt(6557))^(1/3))-1/3 or x+1/3 = -((-1)^(2/3) (-2-2^(1/3) (-6559-81 sqrt(6557))^(2/3)))/(3 2^(2/3) (6559+81 sqrt(6557))^(1/3)) or z = 1/3 (-1)^(2/3) (1/2 (6559+81 sqrt(6557)))^(1/3)

Subtract 1/3 from both sides:
x = (2+2^(1/3) (6559+81 sqrt(6557))^(2/3))/(3 2^(2/3) (6559+81 sqrt(6557))^(1/3))-1/3 or x = -1/3-((-1)^(2/3) (-2-2^(1/3) (-6559-81 sqrt(6557))^(2/3)))/(3 2^(2/3) (6559+81 sqrt(6557))^(1/3)) or z = 1/3 (-1)^(2/3) (1/2 (6559+81 sqrt(6557)))^(1/3)

Substitute back for z = y/2+1/2 sqrt(y^2-(4)/9):
x = (2+2^(1/3) (6559+81 sqrt(6557))^(2/3))/(3 2^(2/3) (6559+81 sqrt(6557))^(1/3))-1/3 or x = -1/3-((-1)^(2/3) (-2-2^(1/3) (-6559-81 sqrt(6557))^(2/3)))/(3 2^(2/3) (6559+81 sqrt(6557))^(1/3)) or y/2+1/2 sqrt(y^2-(4)/9) = 1/3 (-1)^(2/3) (1/2 (6559+81 sqrt(6557)))^(1/3)

Rewrite the left hand side by combining fractions. y/2+1/2 sqrt(y^2-(4)/9)  =  1/6 (3 y+sqrt(9 y^2-4)):
x = (2+2^(1/3) (6559+81 sqrt(6557))^(2/3))/(3 2^(2/3) (6559+81 sqrt(6557))^(1/3))-1/3 or x = -1/3-((-1)^(2/3) (-2-2^(1/3) (-6559-81 sqrt(6557))^(2/3)))/(3 2^(2/3) (6559+81 sqrt(6557))^(1/3)) or 1/6 (3 y+sqrt(9 y^2-4)) = 1/3 (-1)^(2/3) (1/2 (6559+81 sqrt(6557)))^(1/3)

Multiply both sides by 6:
x = (2+2^(1/3) (6559+81 sqrt(6557))^(2/3))/(3 2^(2/3) (6559+81 sqrt(6557))^(1/3))-1/3 or x = -1/3-((-1)^(2/3) (-2-2^(1/3) (-6559-81 sqrt(6557))^(2/3)))/(3 2^(2/3) (6559+81 sqrt(6557))^(1/3)) or 3 y+sqrt(9 y^2-4) = (-2)^(2/3) (6559+81 sqrt(6557))^(1/3)

Subtract 3 y from both sides:
x = (2+2^(1/3) (6559+81 sqrt(6557))^(2/3))/(3 2^(2/3) (6559+81 sqrt(6557))^(1/3))-1/3 or x = -1/3-((-1)^(2/3) (-2-2^(1/3) (-6559-81 sqrt(6557))^(2/3)))/(3 2^(2/3) (6559+81 sqrt(6557))^(1/3)) or sqrt(9 y^2-4) = (-2)^(2/3) (6559+81 sqrt(6557))^(1/3)-3 y

Raise both sides to the power of two:
x = (2+2^(1/3) (6559+81 sqrt(6557))^(2/3))/(3 2^(2/3) (6559+81 sqrt(6557))^(1/3))-1/3 or x = -1/3-((-1)^(2/3) (-2-2^(1/3) (-6559-81 sqrt(6557))^(2/3)))/(3 2^(2/3) (6559+81 sqrt(6557))^(1/3)) or 9 y^2-4 = ((-2)^(2/3) (6559+81 sqrt(6557))^(1/3)-3 y)^2

Expand out terms of the right hand side:
x = (2+2^(1/3) (6559+81 sqrt(6557))^(2/3))/(3 2^(2/3) (6559+81 sqrt(6557))^(1/3))-1/3 or x = -1/3-((-1)^(2/3) (-2-2^(1/3) (-6559-81 sqrt(6557))^(2/3)))/(3 2^(2/3) (6559+81 sqrt(6557))^(1/3)) or 9 y^2-4 = 9 y^2-6 (-2)^(2/3) (6559+81 sqrt(6557))^(1/3) y-2 (-2)^(1/3) (6559+81 sqrt(6557))^(2/3)

Subtract 9 y^2-6 (-2)^(2/3) (6559+81 sqrt(6557))^(1/3) y-2 (-2)^(1/3) (6559+81 sqrt(6557))^(2/3) from both sides:
x = (2+2^(1/3) (6559+81 sqrt(6557))^(2/3))/(3 2^(2/3) (6559+81 sqrt(6557))^(1/3))-1/3 or x = -1/3-((-1)^(2/3) (-2-2^(1/3) (-6559-81 sqrt(6557))^(2/3)))/(3 2^(2/3) (6559+81 sqrt(6557))^(1/3)) or 6 (-2)^(2/3) (6559+81 sqrt(6557))^(1/3) y-4+2 (-2)^(1/3) (6559+81 sqrt(6557))^(2/3) = 0

Factor constant terms from the left hand side:
x = (2+2^(1/3) (6559+81 sqrt(6557))^(2/3))/(3 2^(2/3) (6559+81 sqrt(6557))^(1/3))-1/3 or x = -1/3-((-1)^(2/3) (-2-2^(1/3) (-6559-81 sqrt(6557))^(2/3)))/(3 2^(2/3) (6559+81 sqrt(6557))^(1/3)) or 2 (3 (-2)^(2/3) (6559+81 sqrt(6557))^(1/3) y-2+(-2)^(1/3) (6559+81 sqrt(6557))^(2/3)) = 0

Divide both sides by 2:
x = (2+2^(1/3) (6559+81 sqrt(6557))^(2/3))/(3 2^(2/3) (6559+81 sqrt(6557))^(1/3))-1/3 or x = -1/3-((-1)^(2/3) (-2-2^(1/3) (-6559-81 sqrt(6557))^(2/3)))/(3 2^(2/3) (6559+81 sqrt(6557))^(1/3)) or 3 (-2)^(2/3) (6559+81 sqrt(6557))^(1/3) y-2+(-2)^(1/3) (6559+81 sqrt(6557))^(2/3) = 0

Subtract (-2)^(1/3) (6559+81 sqrt(6557))^(2/3)-2 from both sides:
x = (2+2^(1/3) (6559+81 sqrt(6557))^(2/3))/(3 2^(2/3) (6559+81 sqrt(6557))^(1/3))-1/3 or x = -1/3-((-1)^(2/3) (-2-2^(1/3) (-6559-81 sqrt(6557))^(2/3)))/(3 2^(2/3) (6559+81 sqrt(6557))^(1/3)) or 3 (-2)^(2/3) (6559+81 sqrt(6557))^(1/3) y = 2-(-2)^(1/3) (6559+81 sqrt(6557))^(2/3)

Divide both sides by 3 (-2)^(2/3) (6559+81 sqrt(6557))^(1/3):
x = (2+2^(1/3) (6559+81 sqrt(6557))^(2/3))/(3 2^(2/3) (6559+81 sqrt(6557))^(1/3))-1/3 or x = -1/3-((-1)^(2/3) (-2-2^(1/3) (-6559-81 sqrt(6557))^(2/3)))/(3 2^(2/3) (6559+81 sqrt(6557))^(1/3)) or y = 1/3 (-1)^(2/3) ((6559+81 sqrt(6557))/(2))^(1/3)-1/3 ((-2)/(6559+81 sqrt(6557)))^(1/3)

Substitute back for y = x+1/3:
x = (2+2^(1/3) (6559+81 sqrt(6557))^(2/3))/(3 2^(2/3) (6559+81 sqrt(6557))^(1/3))-1/3 or x = -1/3-((-1)^(2/3) (-2-2^(1/3) (-6559-81 sqrt(6557))^(2/3)))/(3 2^(2/3) (6559+81 sqrt(6557))^(1/3)) or x+1/3 = 1/3 (-1)^(2/3) ((6559+81 sqrt(6557))/(2))^(1/3)-1/3 ((-2)/(6559+81 sqrt(6557)))^(1/3)

Subtract 1/3 from both sides:
Answer: |  x = (2+2^(1/3) (6559+81 sqrt(6557))^(2/3))/(3 2^(2/3) (6559+81 sqrt(6557))^(1/3))-1/3    or    x = -1/3-((-1)^(2/3) (-2-2^(1/3) (-6559-81 sqrt(6557))^(2/3)))/(3 2^(2/3) (6559+81 sqrt(6557))^(1/3))    or    x = 1/3 (-1)^(2/3) ((6559+81 sqrt(6557))/(2))^(1/3)+(-1/3-1/3 (-2/(6559+81 sqrt(6557)))^(1/3))

Infinity

Since it was not specifically specified, I will solve for x first and then solve for y second.

Solve for x.

\(\sqrt{(x-1)^2+(y-2)^2}+\sqrt{(x-2)^2+(y-2)^2}=4\)

\(2\sqrt{(x-1)^2+(y-2)^2}=4\)

\((2\sqrt{(x-1)^2+(y-2)^2})^2=4^2\)

\(4((x-1)^2+(y-2)^2)=16\)

\(\frac{4((x-1)^2+(y-2)^2)}{4}=\frac{16}{4}\)

\((x-1)^2+(y-2)^2=4\)

\((x-1)^2+(y-2)^2-(y-2)^2=4-(y-2)^2\)

\((x-1)^2=4-(y-2)^2\)

\(\sqrt{(x-1)^2}=±\sqrt{4-(y-2)^2}\)

\(x-1=±\sqrt{4-(y-2)^2}\)

\(x-1=±\sqrt{4-(y^2-4y+4)}\)

\(x-1=±\sqrt{4-y^2+4y-4}\)

\(x-1=±\sqrt{-y^2+4y}\)

\(x-1=±\sqrt{y(-y+4)}\)

\(x-1=±\sqrt{y(4-y)}\)

\(x-1+1=±\sqrt{y(4-y)}+1\)

\(x-=±\sqrt{y(4-y)}+1\)

\(x=\sqrt{y(4-y)}+1,\) \(x=-\sqrt{y(4-y)}+1\)

Solve for y

\(\sqrt{(x-1)^2+(y-2)^2}+\sqrt{(x-2)^2+(y-2)^2}=4\)

\(2\sqrt{(x-1)^2+(y-2)^2}=4\)

\((2\sqrt{(x-1)^2+(y-2)^2})^2=4^2\)

\(4((x-1)^2+(y-2)^2)=16\)

\(\frac{4((x-1)^2+(y-2)^2)}{4}=\frac{16}{4}\)

\((x-1)^2+(y-2)^2=4\)

\((x-1)^2+(y-2)^2-(x-1)^2=4-(x-1)^2\)

\((y-2)^2=4-(x-1)^2\)

\(\sqrt{(y-2)^2}=±\sqrt{4-(x-1)^2}\)

\(y-2=±\sqrt{4-(x-1)^2}\)

\(y-2=±\sqrt{4-(x^2-2x+1)}\)

\(y-2=±\sqrt{4-x^2+2x-1}\)

\(y-2=±\sqrt{3-x^2+2x}\)

\(y-2=±\sqrt{-x^2+2x+3}\)

\(y-2=±\sqrt{(-x+3)(x+1)}\)

\(y-2+2=±\sqrt{(-x+3)(x+1)}+2\)

\(y=±\sqrt{(-x+3)(x+1)}+2\)

\(y=\sqrt{(-x+3)(x+1)}+2,\) \(y=-\sqrt{(-x+3)(x+1)}+2\)

Isn't obvious to you which one has a better contract?

1) The first athlete simply gets 1/10 of $100 million, or $10 million per year for ten years.

2) The second athlete will begin with $10 million the 1st year, $10.5 million the 2nd year, $11.025 million the 3rd year and so on for a total of $125,778,925.36 over the ten-year period.

But the best comparison between their two contracts is to find the PV, or present value, of their contracts as of today. Using that method:

1) The PV of the first athlete discounted at 5% compounded annually=$77,217,349.29 as of today's money.

2) The PV of the second athlete is of course =$100,000,000 as of today's money.

3) The difference between them being=$100,000,000 - $77,217,349.29 =$22,782,650.71

\((\frac{x}{2})-(\frac{x}{3})>5\)

\(\frac{x}{2}-\frac{x}{3}>5\)

\(\frac{x}{2}\times6-\frac{x}{3}\times6>5\times6\)

\(\frac{6x}{2}-\frac{6x}{3}>30\)

\(\frac{3x}{1}-\frac{2x}{1}>30\)

\(3x-2x>30\)

\(x>30\)

\(\frac{16}{100}+\frac{17}{10}\)

\(\frac{16}{100}+\frac{170}{100}\)

\(\frac{186}{100}\)

\(\frac{93}{50}\)

\(1.86\)

(x/2)-(x/3)>5 The LCD of 2 and 3 is 6,

(3x/6) - (2x/6) > 5

x/6 > 5, or

x > 30

use division button and the two numbers

idk

Just enter the fraction as you would by hand: 1/4 + 3/8 =5/8. Try it and see what you get.

What is 313221112223333444428 factorial?

10^(10^21.79821565360993), it begins with:196720569083480711890882359...

42! =14 0500611775 2879898543 1426062445 1156993638 4000000000

  (3.2 x 10^1)(5 x 10^6)=160,000,000 standard notation=1.6 x 10^8 scientific notation.

What is the passing grade? 50%, 60%........etc.  And what is the maximum grade that you can get?

thanks

a neclace costs $45 it is on sale for 30% what is it's sale price

$45 x .70(70%) =$31.50 New sales price, or:

$45 x .30(30%) =$13.50 this is discount due to 30% sale,

$45 - $13.50 =$31.50 Sales price due to 30% discount.