Calculus

He got that scar 3 years before the 23rd World Tournament from training.

vector

26.3333

(1/3)*(pi)*(radius^2)*(height of cone)

Because simple math, combined with complex equations are needed later in life to figure out answers to common questions where specific amounts are used.

x^2+8x=20

x^2+8x-20=0

(x+10)(x-2)=0

x=-10 and x=2 are the roots (intercepts)

(-10,0) and (2,0) are the x-intercepts.

Using the formula for the solution of a quadratic equation ax2+bx+c=0:

x = (-b +- sqrt(b2-4ac)) / 2a

(There are two roots, one is found by addition of the square root, the other by subtraction of it).

Which for the given equation 8x2+5x+6=0 means a=8, b=5, c=6, giving:

x = (-5 +- sqrt(52-4x8x6)) / (2x8)

x = (-5 +- sqrt(25-192)) / 16

x = (-5 +- sqrt(-167)) / 16

which has no solution

Unless you know about complex numbers and the use of i = sqrt(-1), in which case, the solutions are:

x = -5/16 + 12.9i and x = -5/16 - 12.9i

See

http://www.wolframalpha.com/input/?i=integrate+2exp(-x2)+over+3+to+7

18360 WHAT a dumb question you could have did it your self . On a calulator

sIGNing by: Back pack

4x+4y=16

y=5

4x+ 20=16

4x=-4

x=-1

0.5(x)+3=9

First you subtract 3 from the problem on the left side. +3 and -3 cancel out. Whatever you do to one side you do to the other so you subtract 3 from the right side to. 9-3=6.

Then bring everything else down.

0.5(x)=6

Since you still want to isolate the (x), you have to divide by 0.5 underneath the multiply by 0.5. This cancels it out. Whatever you do to one side, you do to the other. 6/.5=12

x=12

To check your answer you do the 3 (or more) step check. This check will be 4 steps.

1. Rewrite (rewrite the problem): 0.5(x)+3=9

2. Replace (plug in your answer for x) 0.5(12)+3=9

3. Solve (solve the problem (may take more than one step)): Multiply 0.5 * 12

Bring down: 6+3=9

4. Compare (compare what you got on the left with what if on the right): 9=9

Yes! 9 equals 9! We got it right! The answer is 12.

No.

No.

No.

No.

5.2

The integral of a single term of a polynomial, in the form of AxN is (A/N+1) x (N+1).

The first integral of 2x is x2 + C.

The second integral of 2x is the first integral of x2 + C, which is 1/3x3 + Cx + C.

I firmly believe that most brilliant ideas come from people just playing with things.

"Hmmm... what happens if I assume that the solution is in this form..."

5y2 : the only factors are 5y and y

Similarly the only factors of 5 are 5 and 1

these figures must be arranged so that their indiviual multiples total 26y:

This can only be (5y + 1)(y + 5)

So x = -1/5 or -5

Calculate 10^2 - 4*(-16)*(-20)

2+2=4

4+1=5

∫ f'(x)g(x) dx = f(x)g(x) - ∫ f(x)g/(x) dx

This is known as integration by parts.

No. The sum of (x) and (x+6) is (2x + 6), not 6.

What you want is (x) and (6 - x). The sum of those two is always 6, no matter what 'x' is.

The question was posted several years ago so Raja was not absent from the class yesterday. He no longer goes to school!

What is the value of what. You didnt specify. And this equations dont make sense. 100millimeters can equal 11.70 nothing and 150millimeters can equal 34.20 when 100mm equals 11.70. And what is the random 40mm for

Finding volumes. Engineering problems. General science problems.

4x + 2.5

-3x + 7y = -1 -2x + 5y = 0

What I would do is split the equation into two and label them:

[A] -3x + 7y = 0

[B] -1 -2x +5y = 0

Now change [B] so that the number term is on the other side (not essential, but it makes it a bit cleaner)

[B'] -2x + 5y = 1

Now you can use elimination to get rid of either x or y. I'm going to do it for x, but first you need to make the numbers on the x's the same. So we multiply all of [A] by 3 and [B'] by 2:

[A'] -6x + 14y = 0

[B''] -6x + 15y = 3

Now you can subtract one from the other and since the x terms are the same, they will cancel out. I'm going to subtract [A'] from [B''].

-6x - (-6x) + 15y - 14y = 3 - 0

so

y = 3

Then you put y back into one of the equations, for example [A]:

-3x + 7y = 0

-3x + 7(3) = 0

-3x + 21 = 0

-3x = -21

3x = 21

x = 7

hence

x = 7, y = 3