Quick Maths

[FlameChrome]

Basically you just solve the math problem the person before you gives, then you give a another problem!
Ex:
First person- 2+2
second person- A: 4
Q: 52/16
(incase you dont know, "/" means divide, specially since divide sign isnt on my keyboard)
Also If its not a regular multiply, add, subtract, or divide problem. Say what you are suppose to do!
Ex:
Simplify; (X+2)(X-3)(X+4)
Well thats all, Lets begin!

84/6

 

[NMLewis]

14

14 x 13

 

[FlameChrome]

182

Simplify:
X(X-2)(X+6)

 

[正真正銘]

x(x - 2)(x + 6)
x(x² + 6x - 2x -12)
x(x² - 4x -12)
x³ - 4x² - 12x

Solve for x:
x² - 9 = 0

 

[Dusk Mane Koopa]

x² = 9
x = 3

Factor completely: 4x² + 12x + 5

 

[正真正銘]

4x² + 12x + 5
x² +12x + 20
(x + 10)(x + 2)
(x + 10/4)(x + 2/4)
(x + 5/2)(x + 1/2)
(2x + 5)(2x + 1)

Calculate:
cos(90°)

 

[Dusk Mane Koopa]

cos(90) = 0

Calculate: i¹⁰

 

[正真正銘]

i¹⁰ = -1

Find dy/dx:
f(x) = 5x³ + 20e^2x

 

[Sawsbuck]

Wat

 

[正真正銘]

Wat

In other words, take the derivative of the given function.

Here's the solution:
Find dy/dx:
f(x) = 5x³ + 20e^2x
f'(x) = 15x² + 40e^2x

Here's another problem.
Solve for x:
x³ + 6x² + 8x = 0

 

[Dusk Mane Koopa]

x³ + 6x² + 8x = 0
x(x² + 6x + 8) = 0
x(x + 4)(x + 2) = 0
x = 0, -4 or -2

Divide:
(x³ + 12x² + 47x + 60) / (x + 4)

 

[正真正銘]

Divide:
(x³ + 12x² + 47x + 60) / (x + 4)

(Format is hard to adjust, thus the numbers don't line up as they should. In the editor, it looks alright.)
4 1 12 47 60
-4 -32 -60
_________________
1 8 15 0

x² + 8x + 15

Another problem:
Assume that a right triangle has sides a, b, and c. If a = 6 and b = 8, what is the length of c?

 

[strangerhypno]

Pythagorean theorem. square root of 36 + 64. = 10 = side c.

Solve the integral, ? ln (3x^2) dx

 

[正真正銘]

? ln (3x²) dx
This function can be rewritten as ln(3x²)(1)
?uv' = uv - ?u'vdx (Integration by Parts)
u = ln(3x²)
u' = (2/x)
v = x
v' = 1
? ln(3x²)(1) = xln(3x²) - ? (2/x)(x)dx
? ln(3x²)(1) = xln(3x²) - 2
? ln(3x²)(1) = x(2ln|x|+ ln(3) - 2) + C

I think that is correct.

Find (?²f/?x²)
f(x,y) = 10x³y + 7y + 4x - 9