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The second case:

Correct identity is: Sin 3x = 3 sin x - 4 sin^3 x

Start with sin (2x + x), use sin (A + B) = sin A cos B + cos A sin B

Then use cos 2x = 1 - 2 sin^2 x

...

Hi:

How do I read an XML file?

I downloded XMLViewer, but when I click on it (Windows ME), it gives an error.

How do I read the file?

Thanks

First step:

Find Maxima and Minima

Equate first derivative to zero, to get the values of x to be tested

When second derivative is negative, you have maxima

...

PolluxCastor:

Technically you are correct, it is a vector.

But my experience is that at junior levels all they want is the speed when they talk of velocity.

We should let the querist decide...

What is the QUESTION?

We can solve it this way too, without vectors.

Velocity = SQRT[(X-Component)^2 +(Y-Component)^2]

Flying South-West. Hence making an angle of 45 degrees with West as well as with South.
...

Furthermore, we were to "solve this question algebratically".

Not only Maxima/Minima are not needed in this case, their determination requires Calculus!

CONCLUSION:

To determine Range of...

I did not substitute the end points of the domain! At the end points of the domain, values of the function are simply 1 at both points! If I substituted the end points of the domain, the result...

When A is between 0 an pi, Sin A is between 0 and 1

Hence least value of Sin A = 0, Greatest = 1

Hence least value of -SinA = -1, Greatest = 0

Hence least value of -3 SinA = -3, Greatest =...

The question is unclear.

COSTS:

Assuming his aim is to minimise Expected Loss:


COST CONSIDERATION: MAYBE WE CAN LOOK AT IT LIKE THIS:

1. Lets suppose he tries 3 employees.

Cost: 75000

1. "He notes that the probability of a trainee actually becoming a master is only 1 in 6.".

You take 3 trainees. (A, B, C)

a. Chances that none becomes maser is: (5/6)^3

...

Use the following example:

9 + (5-1)4/9

= 9 + (4*4)/9

= 9 + 16/9

etc.

FURTHER: See P-value - Wikipedia, the free encyclopedia

"In statistical hypothesis testing, the p-value is the probability of obtaining a result at least as extreme as a given data point, under...

"P-Value of a statistical test is a probability number that measures the extent to which the sample data are consistent with the Null hypothesis. It represents a compact summary of sample findings in...

Eddington was a very great Astronomer and conducted one of the first definitive Astronomical observations that confirmed the Theroy of Relativity.

He was also one of the first great exponents of...

Asymptote

Asymptotes are formally defined using limits.

The line x = a is a vertical asymptote of a function f

Lim f(x) = (+ or -) infinity as x approaches a

In your case find...

Domain:

Logs are defined for only positive real values.

Hence Domain of log x is R+

log x can have any real values

Hence Range of log x is R

f(x)=5-2cos(x)

Least value simply means Least value! (Look up a dictionary)

If you mean minimum, that's a different matter.

If you want to know WHAT is the least value in this case:

Cos...

I wonder if Newton believed there was actual Attraction between bodies.

Is it possible that all he meant in his Law of gravitation was that:

To calculate motion of bodies we may assume that...

By "our part of the universe" I mean the curvature and geometry of Space-Time around us.

The configuration or Space-Time geometry (which gets modified by presence of matter)
In our part of the...

FURTHER:

See Gravitation - Wikipedia, the free encyclopedia

"In general relativity, the effects of gravitation are ascribed to spacetime curvature instead of a force. .....

To deal with...

General Theory of Relativity.

See "Mathematical Theory of Relativity" by A.S. Eddington, the Chapter on Einsten's Law of Gravitation, which has nothing to do with "Attraction".

In this...

I am even more confused!

Perhaps you should attach a diagram.

Where are A, B, C, D and G?

Are talking of a circle?

Which is the arc and which is the chord?

According to the Theory of Relativity, there is no real attraction, only seems to be so in our part of the universe.

It is not attraction between bodies but the geometry of the universe near us...

Assuming base for log is 10:

log (x + 17) - log (x - 1) + log (x) = 1

[Log A + Log B - Log C = Log [(AB)/C] and 1 = Log 10 , assuming base is 10]

Log [(x +17)x/(x -1) ] = Log 10

(x...

For the automobile :

Acceleration is rate of change of velocity.

In this case:

Average acceleration = (Final Velocity - Initial Velocity)/Time

Free Fall:

Use the following formula for velocity:

v = u + at

v = final velocity u = initial velocity = 0

a = acceleration = g, t = time

B = E, A = F

Hence C = D (Because A + B + C = D + E + F = 180 degrees)

A = F, a = f,

Hence triangles are congruent.

When 3 corresponding angles are equal, and a = f (Sides...

See attachment - May clarify further.

I am confident you will have no problem.

Remember, however, the following probability theorem which I used:

P(A|B) = P(A intersection B)/P(B)

P(A|B) means Probability of A when B is true.
...

AT LAST!

Using VENN diagrams, I get the following results (No presumption of Independence!)

P(AUB) = P(A) + P(B) - P(A INTERSECTION B) = .75 (A or B: At least one grant)

Hence .75 = .5 +...

"The probabilities are based on Billy's feelings, it might be best not to assume the events are independent."

In case of "feelings", Billy has to make sure that his "feelings" are not...

Deleted because of wrong answer.

See below for the correct answer.

Hi PolluxCastor:

Thanks for taking the time.

One other thought: I wonder whether your first (intuitive) answer be considered acceptable in an examination or test?

Jiten

VECTORS

A vector is something which has magnitude and direction.

For example, Speed is a scalar because it is just a number without direction.

Velocity is always in a certain direction, so...

Very good, Polluxcastor. Makes sense but not perfect mathematical sense!

Hence I would stick to my laboured solution!

I wonder whether you (now or in the past) have actually verified your...

If you mean 2 different functions, (x + 2) and (x^2 -1), they being defined for all real numbers, their domain is (-infinity, +infinity).


If you mean y = (x + 2)/(x^2 -1)


The function is...

Here are some examples to help you:

(-3)^4 = 3^4 (raising to an even power makes it positive)

= 3*3*3*3 = 81

(4)^-1 = 1/(4^1) = 1/4

Find 2 integers, a and b, whose product is 5 and whose sum is 6.

i.e. ab = 5, a + b = 6

Then factors are (x + a) (x + b)

Sit in an aeroplane!

From your standpoint you are at rest.

From standpoint of someone on the ground, you are in motion.

Look at it like this:

First letter of the password can be selected in 7 ways, then Second in 6 ways, then 3rd in 5 ways, then fourth in 4 ways.

Hence: 7*6*5*4 = 840

OR

Formula for...

5^(x+3) - 5^(x+1) = 600

5^(x+1) (5^2 -1) = 600

5^(x+1) = 25

x + 1 = 2

x = 1

Gravity is due to another Law, Law of gravitation which says that every body attracts every other body with a certain force.

In case of a falling body, the external force is the attraction by the...

In how many ways can we arrange the non-Red balls?

We have to select (100-r) postions out of 100

Answer: 100P(100-r) = 100!/r! (P means Permutations) (nPr = n!/(n-r)! )

In how...

Each person can select any of the seven floors.

Hence Number of All possibilities = 7^5 = 16807

(This is the number of possibilities when each person selects any floor)

If each passenger...

If you need an equation:

let Price before tax = P

Price after tax = P + 6% of P = P + .06 P = 1.06 P

Hence:

1.06 P = 360.40

Newton' Second Law

Application of external force on a body causes acceleration in the latter that is proprtional to the applied force.

Remember external force when falling is mg (mass times g,...

Dear EAWOODALL:

You may wish to rethink your following steps:

log y = x log a. (where the base is 4).
and when log (base 4) y = 0 x = 0.
and when log (base 4) y = 3, x = 6.
when is log...