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3ⁿ  = 5     log each side

log3ⁿ  = log 5      and we can write

n * log 3  = log 5    divide both sides by log 3

n  = log 5 / log 3  ≈    1.465

On the very top right of the calculator you will see some lines click those lines and you will see a section with multiple options click fractions and voila

The answer is £88.01

The answer is £88.01

Basically just another form of parentheses.

SOmetimes helps keep things clear to not have so many parentheses....

[ x (5^(2/3) )]      is the same thing as having parentheses on the outside....

the sum of two consecutive natural numbers is 55. If the smaller number is x, what is the other?

If the smaller number =x, then the larger number is:

x + 1, so that:

x + [x +1] =55 subtract 1 from both sides,

2x =55 - 1

2x = 54 divide both sides by 2

x = 54/2

x =27 - which is the smaller number. And,

27 + 1 =28 - which is the larger number, so that:

27 + 28 = 55.

You can also use this famous formula for the area of an equilateral triangle:

A =sqrt(3) / 4 x S^2, S=Side. Once you have the area, then just divide by S/2, since the area of ANY triangle is:Base x Height / 2.

1.(2/3)x +50=330

2. (2/3)x =280

3. x = 280 / 2/3

4. x = 280 * 3/2

          or 

5. x = 280 * 1.5

6. x = 420

Therefore, the answer is 420 :)

Hi Max,you have made a mistake with a negative sign. That's what's causing the confusion. Look again at how you found ln(-1).

This says i^i is a member of the set of Reals.  i^i = e^-(pi/2) which is a Real number.

Not exactly rib-ticklingly funny though!

"Irrational" means cannot be expressed as the ratio of two integers (I.e. whole numbers).  So you could never have a circumference divided by a diameter which could be represented by the ratio of two whole numbers.

.

Using the steps I outlined above:

(2/3) x + 50 = 330

2/3  x   = 330 -50

(2/3) x = 280

(3/2)(2/3) x = 280 (3/2)

x = 420

Unfortanitly you are both incorret it is 16.666666667

It is not the sine of a number, but of an angle. Once you know the sine of that angle, then you can easily find the angle(in degrees or radians), using the "inverse sine" or the "arcsine". Similarly, if you konw the angle, you can find its sine by a number of advanced methods, such as Taylor's infinite series, which goes something like this:x - x^3/3! + x^5/5! - x^7/7! + x^9/9!.........and so on. "x" is in radians.

?????

But where?

Very similar problem here as before

First, subtract '50' from both sides

   Then multiply both sides by 3/2

      Done

Use the INVERSE SIN function which is the same as sin^-1  which is the same as arcsin which is the same as asin (on web2.0 calc)

An equalateral  has angles of 60 - 60 - 60

Drop a plumb line down from the vertex (hight point) that BISECTS the base.

Now you have TWO triangles of 60-30-90

You know the length of the shorter leg (it was a side BISECTED) and you know the HYPOTENUSE

Use pythag theorem to calculate the other LEG (which is the HEIGHT)

(you could also use law of sines etc)

OK...I'll tell you the STEPS and then YOU do it

First : Subtract '3' from both sides

Second : Multiply both sides by '4'

Done

Let me know what you find!

Because even though the diameter can be known with ABSOLUTE PRECISION, the same cannot be said about the CIRCUMFERENCE of a given circle!!. Example: If a diameter of a particular circle is 10 units, then the circumference will be only an approximate number. In this case: Pi x 10 =31.41592........etc. units. On the other hand, if you knew the circumference with great precision, such as 30 units, then you can NEVER measure the diameter with absolute precision.

At least, that is my undestanding of it.

Just put '9' into the equation where 'b' is and you will get

5 + 4*9 = ?  

Remember PEMDAS.....the multiplication goes first and you will then have

5 + 36

= 41

NIce table.....that is what Melody was mentioning...BUT if you count the squares in your table , you will see:

There are 6 x 6 = 36 possibilities for the two dice (not 48) , so the possibility of a 12 ( 6 & 6 ) is 1/36

1/36 = 2.77 %

there are TWO 11s possible out of 36    2/36 = 5.55 % chance of rolling an 11

etc...

Counting the number of blocks on the table excluding the zero, there is 48 for both dices which means there's a 2.173913043. percent of rolling a twelve, and 4.347826087 percent of rolling a 11, and so on. All you have to do is to multiply 2.173913043 by the number of your number given on the table. That's my answer for it.

If you move the origin from (0,0) to the point (a,b) then the new x and y co-ordinates translate to

(x-a)   (y-b)

here you are moving the origin to the point (0,1)  so all points now translate to (x-0)   (y-1)

or just    x   , (y-1)

So (a) is your answer.

In general,if you have a function y=f(x)  then by moving the origin to the point (a,b) the new (translated or shifted) function becomes  (y-b) = f(x-a).This is very useful to remember,and is commonly used to simplify some types of problems. (Like the equations of circles) You can check this with your original problem,  you get the function shifting to (y-1) =f(x) which of course gives you the set of points

(x,  {y-1}  )