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it takes a very long time

it takes a very long time

Solve:  3x + 4  =  20

Subtract 4 from both sides:     3x  =  16

Divide both sides by 3:              x  =  16/3

One set of steps in solving  3(3x - 8)  =  4x + 6  is:

1)  Use the distributive property on the left hand side:  3(3x - 8)  =  9x - 24:

                                              9x - 24  =  4x + 6

2)  Get all the x-terms to one side by subtracting 4x from both side:

                                               5x - 24 =  6

3)  Get the x-term alone on the left side by adding 24 to both sides:

                                                     5x  =  30

4)  Divide both sides by 5:

                                                      x  =  6

Wait so is it (C * F)(x)= 9/5(x-273.15)+32 or (F * C)(x)=9/5(x-273.15)+32

I'm confused...

Find  (f*g)(x)  when  f(x)  =  [ sqrt(x + 3) ] / x  and  g(x)  =  [ sqrt(x + 3) ] / (2x)

   (f*g)(x)  =  f(x) * g(x)  =  { [ sqrt(x + 3) ] / x }  *  { [ sqrt(x + 3) ] / (2x) }  

                                     =  [ sqrt(x + 3) * sqrt(x + 3) ] / [ x * 2x ]

                                     =  (x + 3) / ( 2x² )

Determine the domain of  (f/g)(x)  when  f(x)  =  -1/x  and  g(x)  =  sqrt(3x - 9)

     (f/g)(x)  =  f(x) / g(x)  =  [ -1/x ] / [ sqrt(3x - 9) ]  =  -1 / [ x * sqrt(3x - 9) ]

Two restrictions:

     Since x is in the denominator  x  can't be zero.        

     Since  3x - 9  is under the square root sign,  3x - 9 >= 0     --->     3x >= 9     --->     x >= 3.

Combining these two restrictions,  x >= 3.                   

For that you will need  f( c(x) )    the c(x) will convert the degrees kelvin to celcius, then the f (  ) will convert the resultant celcius degrees to farenheit

f ( c (x) )  =   f ( x-273.15)     =   9/5 (x-273.15) + 32      Where 'x' is Kelvin degrees and the result is Farenheit degrees

Come on MaxWong, a very smart young man like you couldn't figure this one out!!? I just don't believe it:

[1.25 x 10^200]^1/3 =[125 x 10^198]^1/3 =5 x 10^66

\sqrt[3]{1.25\times10^{200}}

\(\sqrt[3]{1.25\times10^{200}}\\ =\sqrt[3]{1.25}\times\sqrt[3]{10^{200}}\\ =\frac{\sqrt[3]{125}}{\sqrt[3]{100}}\times\sqrt[3]{10^{198}}*\sqrt[3]{100}\qquad \text{I have used Alan's hit here}\\ =\frac{\sqrt[3]{125}}{1}\times\sqrt[3]{10^{198}}*1\\ =5\times 10^{66}\\\)

So yes your answer is correct :)

What am I doing? Solving for x or y?

I don't see where he went wrong...

Hi Max, technically you have answered a different question although it may well be was the asker intended :)

\(\begin{array}{rl}f(x)=\dfrac{2x+6}{3x}&g(x)=\dfrac{\sqrt x - 8}{3x}\\\end{array}\\ (f-g)(x) = f(x) - g(x) = \dfrac{2x - \sqrt x + 14}{3x}\)

The slope of the required graph is negative reciprocal of 2 which is -1/2.

Its y-intercept is 3(Given).

Equation of the required graph is y = -x/2 + 3.

Correct. 

Is it 5 x 10^66?

Come on Max, cant you work it out from Alan's answer - or do you need more help??

I thought Alan's answer was a good one :))

If you need more help just say so :))

-18/8

= -9/4

= - 2.25

Oops i thought it was |x+8| = -3

As |x + 8| is always greater than zero it must also always be greater than -3. Hence the relation is true for all real numbers.

.

No solution.

An absolute value of a number will never be negative.

Whole number part remains unchanged.

2 3/5 = 2 + 3 ÷ 5 = 2 + 30 ÷ 5 ÷ 10 = 2 + 6 ÷ 10 = 2.6

Hint: 

5^3 = 125

(10^66)^3 = 10^198

.

f divided by 3

= \(\dfrac{f}{3}\)

It is not going to move - 30 degrees...... Thats anticlockwise......

Amendment by myself: The hour hand of a clock moves 30 degrees, How many degrees does it moves in 2 1/5 hours?

2 1/5 x 30

= 66 degrees.