All Answers 358455 Answers

That is a good answer radio.  

you can set it up as an equation if you want. 

$$\\\sqrt{x-10}=1\qquad $ Now square both sides$\\\\
x-10=1\\\\
x=11$$

That is like saying what is the difference between a flower and a rose.

Well, a rose is a flower but a special kind of a flower.  A flower can be a rose but id doesn't have to be.

OR

What is the difference between a square and a rectangle.

Well a square IS a rectangle it is just a special type of rectangle.

-------------------------

A Function is a relation but it is a special type of relation.

I know that students are often asked "Is it a function or a relation?" This wording is extremely poor. 

A relation is just a set of x and y values that are related to one another in some way.

Now a function is a special type of relation where every x value has at most one UNIQUE y value that corresponds to it.

So you put x into the forumula.  It either makes no sense and there in no real y value or there is exactly one y value.

If you draw the graph then functions pass the "Vertical line test"    This means that if you draw a vertical line anywhere on the number plane it will pass through the graph at most once.

Look at this for more discussion.

negative infinity

The same logic would be used for

2-2-2-2-2-2-2.........

$$\\log_5(7)+log_5(3)\\\\
=log_521\\\\
=\frac{log_{10}21}{log_{10}5}\\\\
=1.8917\qquad $correct to 4 decimal places$$$

11

The only number that factorises into 1 is 1 because 1x1=1

1 + 10 = 11, so 10 less than 11 rooted is 1

Expanded would be

x^2-8x-9

This cubic cannot be factorised so this is its simplest form.

There is only one real value for x and 2 imaginary.

Good answer radio. 

Reiteration. 

On the web2 calc  asin is used instead of sin^-1

I like your logic Geno 

Click the 2nd button then asin which is the same as sin-1 or inverse sine.

You want to add in the given domain [0,1] because that is what the question asked for.   

Hi 315  

You have picked me up on an error - that is good  

No 26 

"f(x)=ln(sinx)

sinx must between -1 and 1

okay, ln must be greater than 0

so ln(sinx) must be between 0 and 1       WRONG     sinx must be between 0 and 1.

------------------------------

I think I have made a 'wording' error here - It actually means that sinx must be between 0 and 1 because you cannot find the log of a negative number.

sin x is only positive in the first and the second quadrant.    etc

Does that make sense now?  

right ? 

Melody, I don't understand the last part 

x must be in the 1st or second quadrant.

thanks Rosala.  

Thank you for sharing your great city with us Rosala.  It is really interesting.

I wonder if other members would be interested in sharing a little of their heritage as well.

It would be good if they did don't you think?    

1.  2(4n - 5) = 6

Simpify

8n - 10 = 6     add 6 to both sides

8n = 16           divide both sides by 8

n = 2

2. Let x be the first number and y be the second.  And we're told that   x+ y = 2.... and let x be the smaller number

So

(8-2x) + 2 = 4y  ......... (1)

And using x + y = 2      let y = 2-x  

So, substituting for y in (1), we have

8-2x + 2 = 4(2-x)     simplify

8-2x + 2 = 8 - 4x

10-2x = 8-4x    add 4x to each side and subtract 10 from both sides

2x = -2            divide both sides by  2

x = -1

And  y = 2 - x = 2-(-1) = 2 + 1 = 3

So, the two numbers are -1 and 3

"Eight increased by a number"  = (8 + n)   = (A)

"The difference between the number and 2" = (n -2).....and twice this = 2(n-2) = (B)

And...... (A) "added to" (B)  =  (8 + n) + 2(n-2)

The volume of a hemisphere is given by

V_h = (2/3)*pi*(r)³    where r is the radius....so we have

V_h = (2/3)*pi*(8.2)³  =  about 1154.78 units³

To add or subtract fraction you need a common denominator:  3 x 8  =  24

(-1/3)(8/8) + (-3/8)(3/3)  = -8/24 + -9/24                     Now, add their numerators:  -8 + -9  *  -17

    =  -17/24                                                                 and write that answer over the common denominator 

the problem rounds to:  (10^20) x (7.5 x 10^14)  =  7.5 x 10^34

The integral of  cosh(ax) dx  is  (1/a)sinh(ax) + C

IN this case  a  =  1/361;   (1/a)sinh(ax) + C   =  (361)sinh( (1/361)x ) + C

LOL        

If you want to write this as a decimal, without scientific notation, move the decimal point 31 places to the left.

You will have a decimal point followed by 30 zeros and then the number 910...

Logs are exponents.

You add exponents when you have a multiplication problem with the same bases.

So, if you have added logs, it was a multiplication problem.

log7 + log3  =  log21   (for every base)

Do you need a decimal answer?  If you do, use the change-of-base formula. Any question? Post back.