Calculus

Parenthesis, exponents, multiplication, division, addition, subtraction. PEMDAS

For example, imagine a submarine is at a dangerous depth and we are interested in that fact. You might ask:

What is the temperature down there? In case they freeze down there.

What is the pressure on the hull? In case it is crushed.

What is the speed of the submarine? So they can get out of trouble quickly.

Now, the answers to the first two questions will satisfy your curiosity. They probably will freeze at -12 degrees but the hull can withstand a pressure of 12,000 megapascals, but told that the sub was going at 2 knots wouldn't help. You'd probably ask again, "Up, down, backwards or forwards?"

Pressure and temperature are NOT VECTORS in physics. They just need a quantity to show all about them. VECTORS on the other hand, like velocity, have quantity and also direction, and both of these are necessary to show them. Two knots down is very different from two knots up.

You might argue that the pressure on the top of the sub is down and the pressure on the bottom of the sub is up. This is true, but we know that information without anybody looking or telling us. It's not necessry to be told that. The direction a pressure acts is defined by the situation, but a velocity isn't given by the shape of the object or the direction it's facing.

Therefore, Vectors are qualities with quantity and direction.

For example, suppose you are in a car going at 60 mph due North and there is a cross-wind blowing at 20 mph from the west. What will be the speed and direction of the airflow over the car? If you do that, you're doing a Vector algebra sum.

First one:

f'(x) = 2x*lnx + x^2*(1/x) = 2x*lnx + x = x*(2*lnx + 1)

Second derivate:

f"(x) = D [x*(2*lnx + 1)] = 1*(2*lnx + 1) + x*(2/x)

= 2*lnx+1+2

= 2*lnx + 3

So, there is a minimum in this graph on point (1/e^(1/2)), -1/(2e)) = MIN(x, y)

Van Sanden David

Belgium

The domain of y=lnx is (0,∞) and the range is (-∞,∞).

u0/4

yo wats good my home dog skillet

None - except that some people are, unreasonably, uncomfortable with equations.

Those are different names for the same unit.

Delta represents a change. Therefore, "delta x" means "change in x."

No.

No. 12 is rational because it can be written as a fraction, 12/1, or 24/2, 120/10, and so on. Also, it terminates at the decimal place, and does not continue on forever without pattern. However, the square root of 12 is irrational.

the simplest form of function.

y = 3X - 1

y2-3y=0

y(y-3)

y=0,3

+6

x/3 + 5 = 11

Subtract 5 from both sides: x/3 = 6

Multiply both sides by 3: x = 18

12/24 = 1/2

The prefixes are "milli" (not milla) for 1/1000, and "centi" (not center) for 1/100. One centimeter = 10 mm, therefore, to convert from cm to mm, you simply multiply by 10.

When the ball hits the ground some energy is given up during the compression and decompression of the ball. The difference between bouncing it on concrete and sand. The sand almost stops the ball while the concrete bounces it back up fairly well. The sound it makes requires energy. Also gravity would rather have an object falling towards the larger mass than away.

NM equals 2x + 1, as stated in the question!

4*sqrt(2)

Rational multiples of irrational numbers are irrational.

sqrt(2) is about 1.414, and 5/4 = 1.25 < 1.414... < 1.75 = 7/4 so

4*sqrt(2) is between 5 and 7, and is irrational.

Yah, (80 + 10)... it's a polynomial

but after you add them up, (90) it's a monomial.

Hope I helped :)

That's called the commutative property.

That's called the commutative property.

That's called the commutative property.

That's called the commutative property.

3x + 6 = 5x - 20

Subtract 3x from both sides: 6 = 2x - 20

Add 20 to both sides: 26 = 2x

Divide both sides by 2: 13 = x

A subset of a given set is simply any set, all of whose elements are contained in the other. Since the empty set has no elements, all of its elements are in any other set! It sounds weird, but that's the way logic works. To put it another way, a set A is NOT a subset of B if there is some element x of A that is not in B. Since the empty set has no elements that are not in your given set, we can't say it is NOT a subset. That means that it is. To select a subset, we must look at each member of the set and decide whether to keep it. If we say "yes" to every member, we have the set itself; if we say "no" to all of them, we have the empty set. We could choose to exclude these from the definition of subset, but it makes a lot of things easier if we include them. That way there are no special cases to deal with when we state theorems.