Calculus

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

412 < x < infinity

A wire 24cm long is cut into two, and one part is bent into the shape of a circle, and the other into the shape of a square. How should it be cut if the sum of the areas of the circle and the square is to be a minimum? I know the answer is (24pi)/(4+pi)cm for the circle and (96)/(4+pi)cm for the square but how to solve for it?

-5, 5

The answer to this equation is the number 99. This is taught in high school math.

W. Y. Fullerton has written:

'Thomas Spurgeon'

4

7x1/2 = 7/2 = 3.5

Probably not much; of course you'll learn new things (just as you did in algebra), but they will be introduced gradually (just as they were in algebra).

1

Fox Entertainment Group is named after William Fox, born Wilhelm Fried, who created the original Fox Film Corporation.

It depends on f(x).

f(x) may be smaller, the same or bigger or even undefined.

No. 3x means 3 times x. Subtracting three from it would become 3x - 3.

To convert mg to gm divide by 1,000

550,000 milligrams = 550 grams