Mathematical Analysis

If the leading coefficient is 1 (or you don't see any number in front of x^2) then find 2 factors f1,f2 which multiply to get the constant term, c, and add to get the coefficient of x, or b,. Then the factors would be (x+f1)(x+f2). Always watch for negatives. Example: x^2 + 2x - 8 B= 2 C= -8 We want 2 numbers that multiply to -8 and add to 2. Since they multiply to a negative number, one must be positive and one must be negative. Since the sum is positive, the larger must also be positive. Analyzing signs can help with determining the factors. With our example, the factors would be 4, -2 so the factor of x^2 + 2x - 8 is (x + 4)(x - 2) To factor quadratic trinomials with a coefficient of the quadratic term , other than 1, I would try the AC method. Here is an example Factor 2x^2 - 3x - 2 With the AC method, find the product of the a, the coefficient of the quadratic term, and c, the constant Here AC = 2*-2 = -4 Then find your b, or coefficient of x B = -3 AC = -4 B = -3 To factor, you need to find a pair of factors that multiply to get AC but adds up to B Our factors would be -4 and 1 since -4*1 = -4 and -4 + 1 = -3 Then rewrite your factors (Ax + f1)(Ax + f2) where f1, f2 are the factors you just found. For our example, (2x - 4)(2x + 1). Finally, factor out any common factor from each binomial (here we can factor 2 out of 2x-4 to get (x - 2)(2x +1)) If this doesn't work, resort to the Quadratic Formula. The factors are then (x - (-b + sqrt(b^2-4ac))/2a)(x - (-b - sqrt(b^2 - 4ac))/2a)

The prime factors of 24 are 2,2,2 and 3

The prime factors of 36 are 2,2,3 and 3

Thus the common factors are 1,2,3,4,6 and 12.

An empty set is this { }

It's just a set with nothing in it.

They are: 8 times 17 = 136

It is to convert a function into a sum of sine (or cosine) functions so as to simplify its analysis.

speed 13 miles, 36 yards and 2 feet per hour

All the digits!

Muhammad ibn Musa al-Khwarizmi gave the West all of the Hindu digits and much more besides. Please see the link.

When expanded, 2/3 becomes 4/6, being one-sixth lower than the other. So, 5/6 is greater.

1 minute = 60 seconds

4.05 minutes = 4.05 x 60 seconds = 243 seconds

When you integrate by parts, you generally want to select part of a function that can be differentiated easily (and also, simplifiable), and the rest of it be easily integrable. For example, the integral of x2sin(x) dx is quite simple since we can choose u = x2 --> du = 2xdx, and dv = sin(x)dx, v = -cos(x), and go on from there. However this would require applying parts twice.

Bronze is a widely available alloy made from copper and tin, so it is not particularly hard to find. It has been used for thousands of years and can be found in various artifacts, sculptures, and architectural elements around the world.

Most people who multiply mentally are using some form of the distributive property. If you wanted to do something like 47 x 5 in your head, that's (40 x 5) + (7 x 5) = 200 + 35 = 235

Because you can't divide nothing by something

A Fourier series is a set of harmonics at frequencies f, 2f, 3f etc. that represents a repetitive function of time that has a period of 1/f.

A Fourier transform is a continuous linear function. The spectrum of a signal is the Fourier transform of its waveform. The waveform and spectrum are a Fourier transform pair.

10 000

It is: 25.

YES. Every whole number is a real number too.

As we know,

1 ft = 30.48 cm

1 square ft=(30.48)2 square cm

=30.48*30.48 square cm

=929.0304 square cm

Multiply the rate by 100, then express it as a decimal number, followed by the % sign.

it helps in many ways

There are 10 sides to a dodecagon and there are 12 sides on a dodecahedron.

* * * * *

There are, actually 12 sides to a dodecagon, not 10.

Maths is EVERYWHERE in the real world ! Take the simple act of buying a newspaper. How will you know (a) what money to give the vendor, and (b) if the vendor has given you the correct change. OR - how will you know if you've been paid the correct wages for your job ! And they're just simple examples !

The answer depends on what precisely the question is.

tentukan dimensi bagi kek berbentuk bulat berjisim 5 kg yang memerlukan jumlah krim segar yang minimum untuk dihias.gunakan sekurang-kurangnya dua kaedah penyelesaian yang berbeza termasuk penggunaan kaedah kalkulus.nyatakan sama Ada kek dengan dimensi tersebut sesuai untuk dibakar atau tidak.berikan penerangan bagi menyokong jawapan anda.

Let me rephrase it. You mean take a bounded subset of real numbers, S, and find a subset of all the upperbounds of S, say D, such that sup S is not in D?

If I get you right, then yes.

Take D := {a : a = sup s + n, n is natural and n < 4} so the first element is sup s + 1 > sup s, and the remaining two terms are even larger than the first one.

But I think I got you wrong, go through the Completeness Axiom.

That is for any two set A and B such that for all a in A, b in B, a <= b, and they share a maximum of one element, then there exist at least one number x such that a <= x <= b

In particular, A have a supremum, sup A <= x and B have an infimum inf B > = x

sup A <= inf B if they are equal then they must be x.