Calculus

10 millimetres = 1 centimetre

so 17.5 mm = 1.75 cm

The answer depends on 12 WHAT!

The golden ratio is not a ratio of two whole numbers but an irrational number. It is 0.5*(1+sqrt(5)). Because it is irrational you cannot find two whole numbers such that their ratio equals the golden ratio. All you can do is get closer and closer to it.

62/38 = 1.6315789

618/382 = 1.6178010 and so on.

directrix

We have two equations.
6x-y=-9 and -y=7x+4.

We substitue 7x+4 into the first equation and we have

6x+7x+4=-9 or 13x=-13 so x=-13/13 of -1
Now plug that into either equation and we have
-y=-7+4 or -y=-3 so y=3.
The solution is (-1,3)

29.......just add

No - because it can be represented as a ratio :

5.2 = 520/100 = 52/10 = 26/5 etc.

Any number that can be represented as a ratio of 2 integers is classified as a rational number (other than that you can't use 0 for the denominator)

Given y=ln(1/x)

y'=(1/(1/x))(-x-2)=(1/(1/x))(1/x2)=x/x2=1/x

Use the chain rule. The derivative of ln(x) is 1/x. Instead of just "x" inside the natural log function, it's "1/x". Since the inside of the function is not x, the derivative must be multiplied by the derivative of the inside of the function.

So it's

1/(1/x) [the derivative of the outside function, natural log]

times

-x-2=1/x2 [the derivative of the inside of the function, 1/x]

This all simplifies to 1/x

So the derivative of ln(1/x) is 1/x

825

-5x+7y-6z

12x2 + 20x - 25 IS a polynomial that factors into (2x + 5)(6x - 5)

4

No, duh, he's just faking his death.

In a problem where you are given two letters to add, subtract, multiply, divide, ect, you can put in any number you want for the letters. The only rule is that the two numbers must equal the number given.

For Example:

X=4 Y=5

X=3 Y=6

X=2 Y=7

X=1 Y=8

X=9 Y=0

X=10 Y=-1

x2 - (-b/a)x + (c/a) = 0 or

x2 - (sum of the roots)x + (product of the roots) = 0

Let the roots be r1 and r2. So we have:

r1 + r2 = 5

(r1)2 + (r2)2 = 15

r1 = 5 - r2 (express r1 in term of r2)

(5 - r2)2 + (r2)2 = 15

25 - 10r2 + (r2)2 + (r2)2 = 15

2(r2)2 - 10r + 25 = 15 (subtract 15 to both sides)

2(r2)2 - 10r + 10 = 0 (divide by 2 to both sides)

(r2)2 - 5r + 5 = 0 (use the quadratic formula)

r2 = [-b + &- sq root of (b - 4ac)]/2a

r2 = {-(-5) + &- sq root of [(-5)2 - 4(1)(5)]}/2(1) = [5 + &- sq root of (25 - 20)]/2 = (5 + &- sq root of 5)/2

r1 = 5 - r2

r1 = 5 - (5 + &- sq root of 5)/2

Thus, when r2 = (5 + sq.root of 5)/2, r1 = (5 - sq.root of 5)/2 or vice versa.

Since the given equation is x2 + bx + c = 0, a = 1, then c equals to the product of roots.

So that,

c = (r1)(r2) = [(5 - sq.root of 5)/2][(5 + sq.root of 5)/2] = [52 - (sq.root of 5)2]/4 = 5

15

Inverse: as x increases so y diminishes and vice-versa.

8 x 106 = 848

x= (-1/2)y-2.5

7

10x - 78 = 1, 10x = 79, x = 7.9

Yes.

A={(6,5),(5,6)} And The probability P(A) equals1/8

That's going to depend on the value of 'x', and it'll change every time 'x' changes.

Whatever number 'x' happens to be at the moment, 'y' equals 6 more than

triple the negative of that number.

x+4=2

x=2-4 (taking 4 to other side )

x=-2

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substituting x=-2

x+4=2

-2+4=2

2=2