Linear Algebra

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The answer depends on

1. how good you are,

2. where in the world you work,

3. how many lucky breaks you get.

These are the general math courses in an undergraduate program of Mechanical Engineering. Actually, these are also the math courses required in ANY undergraduate Engineering curriculum:

Algebra

Trigonometry

Analytic Geometry

Differential Calculus

Integral Calculus

Mutivariable Calculus

Differential Equations

Lis - linear algebra library - was created in 2005.

i have always questioned this myself but it is necessary to solve everyday problems. for example: you need to split 24 apples evenly among 8 people. so you use the equation

8x = 24 to find an answer of 3 apples per person.

4

The decimal notation for 418/580 is 0.7206896552

if any one of the vectors is a null vector or if A is the angle between the two vectors then tanA =1

No engine likes being pushed too hard. The biggest problem most have is that people do not let the engine warm up first before driving this means letting the car idle for at least 5 minutes before driving anywhere. So in answering your question an engine will perform in both circumstances as long as you keep it regularly seviced and warm it up first before driving and you will have many more trips to go.

1/2=1/3 false

154a - 5 is not an equation, as there is no relation between two unknowns, or an unknown or a known.

But to answer your question, 5 is always equal to 5, except when 5 is a constant function, in which case it is a function which is always equal to 5, but is not 5 itself - because 5 itself is a scalar while the function 5 is a function.

y - 2 = 0

The expression is 3b - 1. Not very helpful, but that IS the answer to the question!

x - 2 is an expression, not an inequality.

Y = 5X - 3

It form a linear function; a line.

There are many possible answers.

The simplest polynomial solution is

Un = (20n3 - 90n2 + 160n - 75)/3 for n = 1 , 2, 3, ... and accordingly, the next few terms are 325, 655, 1165, etc.

An alternative is a geometric sequence of the form

Vn = 5*3n-1 where n = 1, 2, 3, ...

so the next few terms will be 405, 1215, 3645, etc.

No. They can have none, one, finitely many or infinitely many.

The important of Math to language is the same as Math to Language. In particular to English.

First Math is just a method of conveying thoughts, it's another language. Sometimes, regular words cannot be used to describe things (how much money your earned today? I earned "k" dollars), we need to use a different language, namely Math. Same vice versa (Hey, what's are you typing on? 5 + 9 = 14!) It's a tool.

secondly, not as important or as obvious, is that Math is a practice of critical thinking. While it certainly won't help you write a better article right away (use induction to prove your essay!), it will help you think critically on what to write about and how to make it better (logically speaking, we cannot "assume" A, but we can easily see that the author's choice of word here "implies" it)*.

* "assume" and "implies" are commonly used math language in analysis and abstract math. THey are basically logic courses with balls instead of events.

9 (and 15)

It depends on what you divide them by!

Although the history of algebra can be traced back several millennia, the first systematic study of the subject was entitled "Al-jabr wa'l muqabalah" or "The Compendious Book on Calculation by Completion and Balancing". The book was written by the Muslim Persian mathematician Muhammad ibn Mūsā al-Khwārizmī , in Baghdad in the middle of the 9th Century.

A banana is a good non-example. Even a banana republic is not likely to be confused with an empire!