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y = .65 %  = .0065

.0065 = [100(.02) + x(.005) ] /(100+x)      ( your question has the equation incorrectly written)

.0065 (100+x)   =  2 + .005x

.65 +.0065x = 2 + .005x

.0015 x = 1.35

x = 900 ml  of    .5 % solution

I was never taught this.

I had to teach a unit of nursing maths at college.

Nurses use the most bizarre 'formulas' that make no sense.  

    Nurses just memorize these 'formulas'. it is not proper maths by any stretch.

I could not get my head around them. I cannot remember things that don't make sense.

However, the units are horrendous. I had to 'invent' some method to deal with all the rates.

This is what I came up with.  It worked a treat.  I thought I was very clever 'inventing' this.

Of course, the students went on to other teachers that demanded they use these ridiculous archaic nursing 'formulas'

So although I gave them an easy to use method that actually made sense, it probably didn't help them a lot in the long run.  What a pity.

Yes, this is correct.

The linear velocities must be the same because they are connected by the chain. The same amount of chain must be traveled by each gear. 

The angular velocities aren't the same, for the smaller gear must travel faster to "keep up", so it must have a faster angular velocity.

The answer of 648p cm per minute is correct because:

-- the smaller gear has a radius of 3 cm, which gives it a circumference of 6 pi cm.

-- therefore, in each revolution, it moves 6 pi cm in a linear distance.

-- since it completes 36 revolutions, it completes 36 x 6 pi cm  =  216 pi cm

-- since it completes 216 pi cm in 20 seconds, it will complete 216 pi x 3  = 648 pi cm in one minute.

I appreciate you! 

These are two EXPRESSIONS....they are not EQUATIONS...infinite solutions.

Perhaps you meant?

3w+45 = 7w+5  subtract 5 from both sides

3w + 40 = 7w     subtract  3w from both sides

40 = 4w              divide both sides by 4

w = 10

Hey Melody ! 

   Hope your liquor is supply is holding out .....

   That is the way  I do these (and other) questions too.....I 've been putting all of the dimensions down and striking through them to show how they cancel and you're left with what you are questioning...but I wonder if anyone out there 'gets it' sometimes !       Is dimensional analysis no longer taught?   HOW will anyone EVER become an ENGINEER ?!  ....and get calculations correct        Haha     ......   

∑[ 2 / (n^3 + 3 n^2 + 2 n) , n, 1, ∞] =It converges to 1/2

Here is the "Partial Sum Formula"

sum_(n=1)^m 2/(n^3 + 3 n^2 + 2 n) = (m^2 + 3 m)/(2 (m + 1) (m + 2))

Ok I will show you how I tackle these.  Once you get the hang of it, my way is really easy.

First make a list of all the rates you know that are relevant.

\(\frac{6.2 radians}{1 sec},\qquad\frac{60sec}{1min},\qquad \frac{2\pi radians}{1 revolution},\qquad \frac{1.6minutes}{1}\\ ~\\find\qquad \frac{?revolutions}{1}\\\)

Since the first 3 of these fractions have units top and bottom they can be turned upside down.

So, for example, it is correct to say   1sec/6.2 radians

You can only turn a fraction upside down if there are units both top and bottom!

Now I want to end up with revolutions on the top and I want all the other units to cancel out.

So I start with revolutions on the top and then I keep multiplying by the correct thing to cancel out the units on the bottom.

like this:

\(\frac{1 revolution}{2\pi radians}\times \frac{6.2 radians}{1 sec}\times \frac{60sec}{1min}\times \frac{1.6minutes}{1}\\ \\~\\ =\frac{1 revolution\times 6.2\times 60 \times 1.6}{2\pi\times 1\times 1\times 1}\\~\\ =\frac{6.2\times 60 \times 1.6}{2\pi}\;\;revolutions\\~\\ =94.7\;\;revolutions.\)

Coding:

\frac{1 revolution}{2\pi radians}\times \frac{6.2 radians}{1 sec}\times \frac{60sec}{1min}\times \frac{1.6minutes}{1}\\
\\~\\
=\frac{1 revolution\times 6.2\times 60 \times 1.6}{2\pi\times 1\times 1\times 1}\\~\\
=\frac{6.2\times 60 \times 1.6}{2\pi}\;\;revolutions\\~\\
=94.7\;\;revolutions.

1.6 minutes is 1.6 x 60 = 96 seconds.

Its angular velocity is 6.2 radians per second:  6.2 radians/second x 96 seconds = 595.2 radians.

One revolution of the fan is one circumference of the fan, which is 2pi radians.

Dividing 595.2 radians by 2pi radians gives us an answer of 94.7 revolutions.

9 ft is 9 x 12 = 108 in

12 ft is 12 x 12 = 144 in.

The area of the floor is 108 in x 144 in = 15,552 sq in.

Each tile is 4 in x 6 in = 24 sq in.

Dividing  15,542 sq in by 24 sq in gives an answer of 648 tiles.

However, we should check to see if the answer is possible.

Is it possible to have the tiles arranged so that the 4 in side of the tiles fits the 108 in length of the room and the 6 in side of the tiles fits the 144 in length of the room?

   108 in divided by 4 in gives us 27 tiles

   144 in divided by 6 in gives us 24 tiles

   27 tiles in one direction and 24 tiles in the other direction gives us 27 x 24 = 648 tiles.

Also, it is possible to have the tiles arranged so the the 6 in side of the tiles fits the 108 in length of the room and the 4 in side of the tiles fits the 144 in length of the room?

   108 in divided by 6 in gives us 18 tiles

   144 in divided by 4 in gives us 36 tiles.

   18 tiles in one direction and 36 tiles in the other direction gives us 18 x 36 = 648 tiles.

So, we can fit them either way.

Cal,

You are doing a really good job of finding things.

I should hire you as my own personal research officer.  LOL

Let's find where   y  =  3x² - 14x   and   x  =  y   intersect by replace the y-term in the first equation with x:

      x  =  3x² - 14x      --->     0  =  3x² - 15x    --->   0  =  3x(x - 5)   --->   x = 0   or   x = 5

The value of  a  is  5.

Oh okay! i was using the equation incorrectly. thank you for providing that!

Nicely answered Cal :)

Long way:  find the slope of the original line and use the point-slope form:

    Original line:  5x - 2y  =  6 

         solve for y:     -2y  =  -5x + 6

                                   y  =  (5/2)x - 3

         slope  =  5/2

    Use point-slope form to find the equation of the new line: 

                   y - y₁  =  m(x - x₁)

        --->     y - -4  =  (5/2)·(x - -2)

                    y + 4  =  (5/2)(x + 2)

                    y + 4  =  (5/2)x + 5

                         y  =  (5/2)x + 1

       Rewriting:  2y =  5x + 2                             (multiplied both sides by 2)

               -5x + 2y  =  2

                 5x - 2y  =  -2

Short way:     notice that the old equation   5x - 2y  =  6   and the new equation   5x - 2y  =  -2

have the same coefficients of the x-term and the y-term and their only difference is the constant.

So, to find the new equation, start with  5x - 2y  =

and put in the point (-2, -4) and solve:   5(-2) - 2(-4)  =  -10 + 8  =  -2

This will give us the new constant, so the new equation is  5x - 2y  =  -2  

Last time I answered your question you did not bother to respond with anything other than a thumbs down.

You do this regularly to people, not just me.

Why would i answer your question?

10 and -2

10+-2=8

10 X -2=-20

The total area of the frustum is (1200 - 400)/2 + 400 + 200 = 1000.

If you were to flip the discs on the side so that the height is 1.6 cm, you cannot fit 16 of those in the 20 cm high box. The most you can fit is 12.