Algebra

SLAE 100,48CM CUBICOS

10

Examples are discussing the relationship between the surface area and volume of a rectangular prism to its height, length and width. For geometric examples, it's usually a good idea to draw the object and label what you call each thing (especially in 2d, since any 2 of base, height, length and width can be used to describe most objects)

Step 1: define your symbols. If you're in a class, do this even if it's dead obvious; it's good practice for when things get a lot more complex (viscosity, for instance is denoted by the greek letter 'mu' in fluid dynamics), plus math teachers tend to give marks (or take marks off) based on the presence/absence of each step

ie:

W=width

L=length

H=height

A=surface area

V=volume

Step 2: Determine how the input and output parameters are related.

ie:

surface area=sum of area on faces

2 faces are width by length, 2 are length by height and 2 are width by height

volume is base area times height; base area is area of a face not including height, therefore area of the width by length face.

Step 3: Convert relationships into symbolic form

2 faces of width by length=2WL

2 faces of width by height=2WH

2 faces of length by height=2LH

Base area=width by length area => B=WL

Volume = base area times height => V=BH

Since surface area is the sum of all face areas:

A= 2WL + 2WH + 2LH

And since we want to define volume in terms of input parameters rather than intermediates:

V= WLH

In algebra classes, you should be given the relationship in non-equation form if you're asked to do this, or it should be something quite simple like the example I used.

There are methods for determining the relationship between variables if you only have a data table, but that's Calculus, not Algebra.

There is also a method called Pi Notation for determining a relationship between parameters based on what is being measured (for instance, one cannot determine the amount of light being generated by an object from knowing its dimensions, unless one can determine a conversion factor that tells you how much light is generated by some dimensional parameter (unit of surface area or volume), but that's even further beyond this than Calculus; I learned it in second year (university) fluid dynamics. However, the basic principles aren't that complex - if you're interested in science, I suggest checking it out, since it's a very useful tool in scientific work.

Reciprocal is the multiplictive inverse. For example, 1/x when multiplied by x gives 1. x is the reciprocal of 1/x. Thus, if a number, when multiplied by a given number, produces 1 as the product, then that number is called the reciprocal of the given number.

It is: 2*2*5*5 = 100

9x^(2) + 25

(3x)^(2) + 5^(2)

This does NOT factor in REAL numbers.

Remember two squared terms with a positive(+) between them does NOT factor.

NB Two squared terms with a negative (-) between the does factor .

e.g.

(3x)^(2) - 5^(2) factors to

(3x - 5)(3x + 5)

The reciprocal of a fraction is found by flipping the numerator and denominator. So, the reciprocal of 17/7 is 7/17. This means that if you were to multiply 17/7 by its reciprocal, the result would be 1, as the two fractions are multiplicative inverses of each other.

Let the integers be, n , n+1 , & n+2

Hence their sum is

n + n+1 + n + 2 = 300

3n + 3 = 300

3n = 297

n = 297/3 = 99

N+ 1 = 100

n + 2 = 101.

7/9 - 2/3 =

7/9 - 6/9 = 1/9 The Answer!!!!!

First, find the least common multiple of 4 and 3 (the denominators). This is 12. 3/4 = 9/12 and 2/3 = 8/12 So the revised question is: 9/12 minus 8/12 easy enough? (pssst. the answer is one twelfth)

1,000 multiplied by 1,000 is 1,000,000.

A Rectangle ( or a square)

The cube root of the number 8 is 2(two).

Cube Root-a number when multiplied 3 times equals a given number.

4

cu.rt.(342) = 342^(1/3) = 6.993190657.... ~ 6.99 (2 d.p.).

The number 45 can be expressed as a ratio in various ways. For example, it can be represented as the ratio 45:1 or simplified to 9:1 by dividing both sides by 5. Additionally, it can also be expressed as a fraction, such as 45/1, which is equivalent to the same value.

A posteriori knowledge refers to understanding that is derived from experience or empirical evidence, making it a key component of empiricism. Empiricism is the philosophical stance that emphasizes the role of sensory experience in the formation of knowledge, asserting that all knowledge is ultimately grounded in observation and experimentation. Therefore, a posteriori knowledge supports the empiricist view by highlighting how our understanding of the world is shaped by our experiences. In contrast, a priori knowledge is independent of experience, relying instead on reason or intuition.

Can you ell me how much all this is worth???

2/15

Infinite!!!!

'pi' is an irrational number, which means that the decimal digits recur to infinity(go on forever), AND there is no regular order in the decimal digits.

'Supa - Dupa' Computers have calculated 'pi' to 50 billion places and still going.

When you are given pi = 3.14 or 3.1416 etc., these are only approximate values.

Well, darling, the answer to 2X times 3X is 6X^2. Just multiply the coefficients and add the exponents because math doesn't have time for drama. So there you have it, simple and straight to the point.

Curved surface area includes the area of the length of the cylinder only whereas surface area includes the two bases as well...

Agreed with anonymous 14 y ago.

However,

2pir^(2) + 2pirh

can be factor to

2pir(r + h)

So S.A.(Cyl) = 2pir(r + h)

e.g. a cylinder of radious 2 cm and a height/length of 24 cm

Has a surface area of

SA(cyl) = 2(3.14)(2(2 + 24) =>

SA(Cyl) = 3.14(4)(26)

SA(Cyl) = 3.14(104)

SA(Cyl) = 326.56 cm(2)

There are 40 (5 x 8) pints in a 5 gallon vessel.

An imperial pint (20 fl oz) is 0.020068 cu ft. Thus 40 x 0.020068 = 0.80272 cu ft.

QED

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