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2) x = -1, y = 3 (Real solutions)

    x = -1+(2 i π c_2)/(log(3)) and y = (log(64)+2 i π c_1)/(log(4)) and c_1 element Z and c_2 element Z(Complex solutions).

1) MAX: THIS WILL MAKE YOUR HEAD SPIN!!!.

Expand the following:
(1/x-1/y)/((π x-π y) (x^2+(π x y)^(1/9)+8 π y^2))

(x^2+8 π y^2+π^(1/9) (x y)^(1/9)) (π x-π y) = π x (x^2+8 π y^2+π^(1/9) (x y)^(1/9))-π y (x^2+8 π y^2+π^(1/9) (x y)^(1/9)):
(1/x-1/y)/(π x (x^2+8 π y^2+π^(1/9) (x y)^(1/9))-π y (x^2+8 π y^2+π^(1/9) (x y)^(1/9)))

(1/x-1/y)/(π x (x^2+8 π y^2+π^(1/9) (x y)^(1/9))-π y (x^2+8 π y^2+π^(1/9) (x y)^(1/9))) = 1/((π x (x^2+8 π y^2+π^(1/9) (x y)^(1/9))-π y (x^2+8 π y^2+π^(1/9) (x y)^(1/9))) x)-(1)/(y (π x (x^2+8 π y^2+π^(1/9) (x y)^(1/9))-π y (x^2+8 π y^2+π^(1/9) (x y)^(1/9)))):
1/(x (π x (x^2+8 π y^2+π^(1/9) (x y)^(1/9))-π y (x^2+8 π y^2+π^(1/9) (x y)^(1/9))))-1/(y (π x (x^2+8 π y^2+π^(1/9) (x y)^(1/9))-π y (x^2+8 π y^2+π^(1/9) (x y)^(1/9))))

x (π x (x^2+8 π y^2+π^(1/9) (x y)^(1/9))-π y (x^2+8 π y^2+π^(1/9) (x y)^(1/9))) = x π x (x^2+8 π y^2+π^(1/9) (x y)^(1/9))+x (-π y (x^2+8 π y^2+π^(1/9) (x y)^(1/9))):
1/π x x (x^2+8 π y^2+π^(1/9) (x y)^(1/9))-π x y (x^2+8 π y^2+π^(1/9) (x y)^(1/9))-1/(y (π x (x^2+8 π y^2+π^(1/9) (x y)^(1/9))-π y (x^2+8 π y^2+π^(1/9) (x y)^(1/9))))

x π x (x^2+8 π y^2+π^(1/9) (x y)^(1/9)) = x^2 π (x^2+8 π y^2+π^(1/9) (x y)^(1/9)):
1/(π x^2 (x^2+8 π y^2+π^(1/9) (x y)^(1/9))-π x y (x^2+8 π y^2+π^(1/9) (x y)^(1/9)))-1/(y (π x (x^2+8 π y^2+π^(1/9) (x y)^(1/9))-π y (x^2+8 π y^2+π^(1/9) (x y)^(1/9))))

π x^2 (x^2+8 π y^2+π^(1/9) (x y)^(1/9)) = π x^2 x^2+π x^2×8 π y^2+π x^2 π^(1/9) (x y)^(1/9):
1/(π x^2 x^2+π×8 π x^2 y^2+π π^(1/9) x^2 (x y)^(1/9)-π x y (x^2+8 π y^2+π^(1/9) (x y)^(1/9)))-1/(y (π x (x^2+8 π y^2+π^(1/9) (x y)^(1/9))-π y (x^2+8 π y^2+π^(1/9) (x y)^(1/9))))

π x^2 x^2 = π x^4:
1/(π x^4+π×8 π x^2 y^2+π π^(1/9) x^2 (x y)^(1/9)-π x y (x^2+8 π y^2+π^(1/9) (x y)^(1/9)))-1/(y (π x (x^2+8 π y^2+π^(1/9) (x y)^(1/9))-π y (x^2+8 π y^2+π^(1/9) (x y)^(1/9))))

π x^2×8 π y^2 = π^2 x^2×8 y^2:
1/(π x^4+π^2×8 x^2 y^2+π π^(1/9) x^2 (x y)^(1/9)-π x y (x^2+8 π y^2+π^(1/9) (x y)^(1/9)))-1/(y (π x (x^2+8 π y^2+π^(1/9) (x y)^(1/9))-π y (x^2+8 π y^2+π^(1/9) (x y)^(1/9))))

π x^2 π^(1/9) (x y)^(1/9) = π^(1+1/9) x^2 (x y)^(1/9):
1/(π x^4+π^2×8 x^2 y^2+π^(1+1/9) x^2 (x y)^(1/9)-π x y (x^2+8 π y^2+π^(1/9) (x y)^(1/9)))-1/(y (π x (x^2+8 π y^2+π^(1/9) (x y)^(1/9))-π y (x^2+8 π y^2+π^(1/9) (x y)^(1/9))))

1+1/9 = 10/9:
1/(π x^4+π^2×8 x^2 y^2+π^10/9 x^2 (x y)^(1/9)-π x y (x^2+8 π y^2+π^(1/9) (x y)^(1/9)))-1/(y (π x (x^2+8 π y^2+π^(1/9) (x y)^(1/9))-π y (x^2+8 π y^2+π^(1/9) (x y)^(1/9))))

-π x y (x^2+8 π y^2+π^(1/9) (x y)^(1/9)) = -(π x y x^2)-π x y×8 π y^2-π x y π^(1/9) (x y)^(1/9):
1/(π x^4+π^2×8 x^2 y^2+π^(10/9) x^2 (x y)^(1/9)+-(π x y x^2)-π×8 π x y y^2-π π^(1/9) x y (x y)^(1/9))-1/(y (π x (x^2+8 π y^2+π^(1/9) (x y)^(1/9))-π y (x^2+8 π y^2+π^(1/9) (x y)^(1/9))))

-π x y x^2 = -π x^(1+2) y:
1/(π x^4+π^2×8 x^2 y^2+π^(10/9) x^2 (x y)^(1/9)+-(π x^(1+2) y)-π×8 π x y y^2-π π^(1/9) x y (x y)^(1/9))-1/(y (π x (x^2+8 π y^2+π^(1/9) (x y)^(1/9))-π y (x^2+8 π y^2+π^(1/9) (x y)^(1/9))))

1+2 = 3:
1/(π x^4+π^2×8 x^2 y^2+π^(10/9) x^2 (x y)^(1/9)-π x^3 y-π×8 π x y y^2-π π^(1/9) x y (x y)^(1/9))-1/(y (π x (x^2+8 π y^2+π^(1/9) (x y)^(1/9))-π y (x^2+8 π y^2+π^(1/9) (x y)^(1/9))))

-π x y×8 π y^2 = -π^2 x y^(1+2)×8:
1/(π x^4+π^2×8 x^2 y^2+π^(10/9) x^2 (x y)^(1/9)-π x^3 y+-(π^2×8 x y^(1+2))-π π^(1/9) x y (x y)^(1/9))-1/(y (π x (x^2+8 π y^2+π^(1/9) (x y)^(1/9))-π y (x^2+8 π y^2+π^(1/9) (x y)^(1/9))))

1+2 = 3:
1/(π x^4+π^2×8 x^2 y^2+π^(10/9) x^2 (x y)^(1/9)-π x^3 y-π^2×8 x y^3-π π^(1/9) x y (x y)^(1/9))-1/(y (π x (x^2+8 π y^2+π^(1/9) (x y)^(1/9))-π y (x^2+8 π y^2+π^(1/9) (x y)^(1/9))))

-π x y π^(1/9) (x y)^(1/9) = -π^(1+1/9) x y (x y)^(1/9):
1/(π x^4+π^2×8 x^2 y^2+π^(10/9) x^2 (x y)^(1/9)-π x^3 y-π^2×8 x y^3+-(π^(1+1/9) x y (x y)^(1/9)))-1/(y (π x (x^2+8 π y^2+π^(1/9) (x y)^(1/9))-π y (x^2+8 π y^2+π^(1/9) (x y)^(1/9))))

1+1/9 = 10/9:
Answer: | 1/(π x^4+π^2×8 x^2 y^2+π^(10/9) x^2 (x y)^(1/9)-π x^3 y-π^2×8 x y^3-π^10/9 x y (x y)^(1/9))-1/(y (π x (x^2+8 π y^2+π^(1/9) (x y)^(1/9))-π y (x^2+8 π y^2+π^(1/9) (x y)^(1/9))))

\(\frac{2}{3}*n=10\)
\(n= \frac{10*3}{2}\)

\(n=15\)

sqrt(2, 8) = 1.0905077326652577

Use the calculator  \(\sqrt[y]{x}\)

–7 ≥ 13 – 5x   |+5x

5x-7>13          |-7

   5x>6            |:5

     x>\(\frac{6}{5}=1\frac{1}{5}\)

negative 96 = -96.

That's a derivative problem..... Not a usual volume problem.

-3(x-1)^2 + 27

= -3(x^2 - 2x + 1) + 27

= -3x^2 + 6x - 3 + 27

= -3x^2 + 6x + 24

= -3(x^2 - 2x - 8)

= -3(x-4)(x+2)

First question: (-1) x 1 = -1.

Second question: -2 x 2 = -4 = -2^2 not 2^2.

You mean \(\dfrac{1}{\frac{1}{10}}+\dfrac{\frac{1}{10}}{\frac{1}{10}}\)?

The first part of this (before the plus sign) is 10.

1/(1/a)= a

The remaining part is 1.

a/a = 1

Then we add them up and the answer is 11.

Do you think that "Radio" and " Radius" mean the same thing??!!

Omi67 have got the exact value! :D

The only obvious answer is B.......

A is not corrected to 2 dp there are 3 digits after the decimal point so that it's not A.

That's not a good way to get points :(

The answer is 59.765675341338 degrees though. 

Use the calculator here, it is super useful that it can do big numbers like 2^100.

\(\sqrt{\dfrac{64}{9}}\\ =\dfrac{\sqrt {64}}{\sqrt 9}\\ =\dfrac{8}{3}\)

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|                |

|                | b

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      a

Perimeter = 2 times (a + b).

It doesn't matter what unit you use, whether you use centimeters, meters, inches,..... etc. it's the same equation.

21) a = -2, b = 5, c = -4, and d = 6; a^2 + 2ad + d^2

a^2 + 2ad + d^2 = (a + d)^2 = (-2 + 6)^2 = 4^2 = 16.

22) x = -2.34, y = -3.14, and z = 4.12; to the nearest tenth; y - 2z

y - 2z = -3.14 - 2(4.12) = -3.14 - 8.24 = -11.38 approx -11.4

23) x = -2.34, y = -3.14, and z = 4.12; to the nearest tenth; x^2 + y^2

x^2 + y^2 = (-2.34)^2 + (-3.14)^2 = 15.3352(using calc.) approx 15.3

16) a = -2, b = 5, c = -4, and d = 6; d^3 - b^3

d^3 - b^3 = (6)^3 - (5)^3 = 216 - 125 = 91.

17) a = -2, b = 5, c = -4, and d = 6; (d - b)^3

(d - b)^3 = (6 - 5)^3 = 1^3 = 1.

18) a = -2, b = 5, c = -4, and d = 6; (d - b)(d^2 + db + b^2)

Same answer as 16). ANS: 91.

19) a = -2, b = 5, c = -4, and d = 6; b^2 + a^2

b^2 + a^2 = 5^2 + (-2)^2 = 25 + 4 = 29.

20) a = -2, b = 5, c = -4, and d = 6; (b + a)^2 

(b + a)^2 = (5 - 2)^2 = 3^2 = 9.

11) a = -2, b = 5, c = -4, and d = 6; 3d + (2c/b)

3d + (2c/b) = 3(6) + 2(-4/5) = 18 - 8/5 = 16 2/5 OR 16.4

12) a = -2, b = 5, c = -4, and d = 6; (3d - 2b)/(5a + d)

(3d - 2b)/(5a + d) = (3(6) - 2(5))/(5(-2) + 6) = (18-10)/(-10 + 6) = 8/(-4) = -2.

13) a = -2, b = 5, c = -4, and d = 6; d^2-b^2

d^2 - b^2 = (d+b)(d-b) = (6 + 5)(6 - 5) = 6 + 5 = 11.

14) a = -2, b = 5, c = -4, and d = 6; (d - b)^2

(d - b)^2 = (6 - 5)^2 = 1^2 = 1.

15) a = -2, b = 5, c = -4, and d = 6; (d - b)(d + b)

Same answer as 13). ANS: 11.

6) a = -2, b = 5, c = -4, and d = 6; 2a^2+3b^2

2a^2 + 3b^2 = 2(-2)^2 + 3(5)^2 = 2(4) + 3(25) = 8 + 75 = 83.

7) a = -2, b = 5, c = -4, and d = 6; 2(a+b)

2(a + b) = 2(-2 + 5) = 2(3) = 6.

8) a = -2, b = 5, c = -4, and d = 6; 4(2a - d)

4(2a - d) = 4(2(-2) - 6) = 4(-4 - 6) = 4(-10) = -40.

9) a = -2, b = 5, c = -4, and d = 6; a(b + 3c)

a(b + 3c) = -2(5 + 3(-4)) = -2(5 - 12) = 2(12 - 5) = 2(7) = 14.

Note the 3rd step: -2(5 - 12) = 2(12 - 5): \(\boxed{\color{red}-(a-b)=b-a}\)

10) a = -2, b = 5, c = -4, and d = 6; (8b) / (5c)

(8b) / (5c) = (8/5)(b/c) = (8/5)(-5/4) = -2.

1) a = -2, b = 5, c = -4, and d = 6; 3c - 2b.

3c - 2b = 3(-4) - 2(5) = -12 - 10 = -22.

2) a = -2, b = 5, c = -4, and d = 6; 8b + 2c.

8b + 2c = 8(5) + 2(-4) = 40 - 8 = 32.

3) a = -2, b = 5, c = -4, and d = 6; -b^2 + b

-b^2 + b = -(5)^2 + 5 = -25 + 5 = -20.

4) a = -2, b = 5, c = -4, and d = 6; 3a^2

3a^2 = 3(-2)^2 = 3(4) = 12.

5) a = -2, b = 5, c = -4, and d = 6; c^2 - 2d

(-4)^2 - 2(6) = 16 - 12 = 4.

2 x 2 = 2 + 2 = 4.

2 x 2 = 2 + ...... + 2 with 2 times in this case which is 2 + 2.

Just post it here!! :D

Give n and k numerical value, which might be easier to visualize: i. e. n=11, k=3

(11 -1)C(3 - 1)=45 + (11 - 2)C(3 - 1)=36+ (11 - 3)C(3 - 1)=28+(11 - 4)C(3-1)=21........=11C3=165

       45                   +         36                   +         28                 +       21........+15+ 10+6+3+1  =165

I answered this question a day or two ago.

Go find the origial question and answer!