Calculus

The "root" of a function is also called the "zero" of a function. This is where the function equals zero.

The function y=4-x2 has roots at x=2 and x=-2

The function y=4-x2 has zeroes at x=2 and x=-2

Those are equivalent statements.

Yes.

y= 3x - 4

y= -2x + 1

Since both equations are equal to y, it is possible to set both equations equal to each other: 3x - 4 = -2x + 1

Now, move the x variables to one side and the numbers to the other.

Add 2x to both sides:

5x - 4 = 1

Add 4 to both sides:

5x = 5

Divide both sides by 5:

x = 1

it is the only way to compare. if you want to know something then say you want to know... X The worldwide known symbol for variable i.e. some number

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It is NOT equal. Try calculating tan x, and tan 6x, for a few values of "x", on your scientific calculator. Perhaps you are supposed to solve an equation, and see FOR WHAT values of "x" the two are equal?

The simplest answer would be that it is simple the way it is. A linear change in distance and gravity just doesn't match up with reality. So a better answer is that this is way it must be. Nothing else really describes what is happening.

His family was mostly German and also he was born in Germany.

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No. That function describes a parabola who's vertex is at the point (0, -4).

4

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Circle.

24

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Y=m*x+b

Y = Y coordinate

M = slope

X = X coordinate

B = Y intercept

To get a coordinate just put a number into X and see what Y comes out as.

example:

Y = 2x - 1

coordinates:

(X,Y)

(-3,-7)

(-2,-5)

(-1,-3)

(0,-1)

(1,1)

(2,3)

(3,5)

x = -1/5 and y = 14/5

Solved by forming a simultaneous equation and eliminating y.

4

x3 - 3x2 - 9x + 27

= x2(x - 3) - 9(x - 3)

= (x - 3)(x2 - 9)

= (x - 3)(x - 3)(x + 3)

Those aren't functions. If you mean f(x) = x + 1 and f(x) = 3x - 2, the domain is the the set of all real numbers, R. I, of course, am assuming you haven't been introduced to the complex number plane, so I'm ignoring those.

You can only solve the equation if both sides are shown. Assuming that the expression is made equal to 0, then x can be found by factorising:

x2 + 3x - 4 = 0

(x+4)(x-1) = 0

either x+4 = 0, therefore x=-4

or x-1 = 0, therefore x = 1

he invented calculus but was accused of taking credit from Newton

They are both parallel because the slope or gradient is the same but the y intercept is different.

164 metres x 100 cm = 16400 cm

1 inch = 2.54 cm

16400 divided by 2.54 = 6456.6929 inchres

√(5a) + 2√(80a) - 7√(125a)

first square the whole equation

[√(5a)]2 + [2√(80a)]2 - [7√(125a)]2

when you square a sqrt the sqrt goes away

5a + 4 * 80a - 49 * 125a

dont forget to square the numbers outside the sqrts

5a + 320a - 6125a

just add and subtract

-5800a is your answer