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I hope you take the time needed to actually learn from my answer  

Find the derivative of the function by using the definition of the derivative.

f(x)=(x+1)/(x-1)

REMEMBER: The first derivative  IS  the gradient of the tangent to the curve

Basically when you find this from first principals you take the gradient of the secant.

I want the gradient of the tangent at (x,f(x))

So I have found the gradient of the SECANT  from  (x,f(x)) to the point   (x+c, f(x+c))

THEN I find the limit of this as c tends to 0

This limit will be  the gradient of the TANGENT at (x,f(x)).

In my case this is

    (That is not written technically at all)

This can be expressed in a couple of different ways.  This is one of them.

\(f'(x)=\displaystyle \lim _{c\rightarrow 0} \frac{f(x+c)-f(x)}{(x+c)-x}\\ f'(x)=\displaystyle \lim _{c\rightarrow 0} \frac{\frac{x+c+1}{x+c-1}-\frac{x+1}{x-1}}{c}\\ f'(x)=\displaystyle \lim _{c\rightarrow 0} \frac{\frac{(x+c+1)(x-1)}{(x+c-1)(x-1)}-\frac{(x+1)(x+c-1)}{(x-1)(x+c-1)}}{c}\\ f'(x)=\displaystyle \lim _{c\rightarrow 0} \frac{\frac{(x+c+1)(x-1)-(x+1)(x+c-1)}{(x+c-1)(x-1)}}{c}\\ f'(x)=\displaystyle \lim _{c\rightarrow 0} \frac{\frac{x(x+c+1)-1(x+c+1) -x(x+c-1)-1(x+c-1)}{(x+c-1)(x-1)}}{c}\\ f'(x)=\displaystyle \lim _{c\rightarrow 0} \frac{\frac{2x-2(x+c) }{(x+c-1)(x-1)}}{c}\\ f'(x)=\displaystyle \lim _{c\rightarrow 0} \frac{-2c}{(x+c-1)(x-1)}\times \frac{1}{c}\\ f'(x)=\displaystyle \lim _{c\rightarrow 0} \frac{-2}{(x+c-1)(x-1)}\\ f'(x)=\frac{-2}{(x-1)^2} \)

Check using quotient rule.

f(x)=(x+1)/(x-1)

\(f(x)=\frac{(x+1)}{(x-1)}\\ f'(x)=\frac{(x-1)*1-(x+1)*1}{(x-1)^2}\\ f'(x)=\frac{-2}{(x-1)^2}\\\)

Great :)

10/3 is not equal to 3.3333333333333333 whatever your calculator might say!  It is equal to 3.3333..... where the 3's repeat without end. This means that when you multiply this by 3 you get 9.9999.... where the 9's repeat without end.

Now if we let

x = 9.99999....               (where the 9's repeat without end), then

10x = 99.99999.....      ((where the 9's repeat without end).

Subtract the first from the second to get:

9x = 90          (as all the 9's behind the decimal point cancel each other)

So, dividing both sides by 9 we get x = 10.   That is:  3*3.33333..... = 10

Similar reasoning applies to your second example.

If tc/tf =max(3.3-1.1*0.104-0.34*4.5, 1.1) then tc/tf = max( 1.6556, 1.1), since 3.3-1.1*0.104-0.34*4.5 = 1.6556;  so tc/tf = 1.6556

Multiply both sides by tf:    tc = 1.6556*tf  or  tc = 1.6556*2.9 or tc = 4.8012   or tc ≈ 4.8

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The lcm of 12 and 10 is 60, which is the largest value in the set.

Well I am pleased that you answered them yourself Danny.

You should use this forum to help you with questions AFTER you know you need help.

If you have already answered them then you do not need our input.

If you have not seriously attempted them yet then they should not be here or on any other help site.

Maybe you feel overwelmed by maths and that is why you post before you think but it is not a good thing to do.  Not good for you or for us (us = answerers on forums).

You would probably be better off to look for you tube clips where these things are explained.

If you want to learn, rather than have answers freely supplied, there are many good, free teachers who post excellent clips on youtube.

When I want to learn something new, I almost always start with you tube.

I am sure you also now know that it is unacceptable to post a lot of questions all at once.

You should not make a habit of getting answerers here to check your answers either  but if you want to do that occasionally then state that is what you are doing.

Give your logic and your answer.  Don't give the answerers the impression that you have no idea or that you have not even thought about it yet.

I wish you, and everyone on the planet, good luck with your studies. I hope you study hard and acheive well.  

I'm not sure I understand the question, but I'll go with 92. 

I started at 99 and checked each succeeding lesser integer for divisibility by 4 but not by 3. 

What I'm not understanding is the wording of the problem; i.e., 4 is not the greatest divisor of 12.  6 is. 

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I wish I knew how to draw the picture, but I don't.  I'll try to describe it. 

Draw the rhombus.  Draw the diagonals.  This creates four right triangles inside. 

Label each half of the short diagonal as X.  Label each half of the long diagonal as X+3. 

Label the sides of the rhombus as sqrt(89). 

Each of the internal triangles will be figured the same, so I'll just describe one.

You have a right triangle with one side X, one side X+3, and the hypotenuse sqrt(89).

Pythagoras' Theorem   (X)² + (X+3)² = sqrt(89)²  

                                      X² + X² + 6X + 9 = 89 

                                      2X² + 6X – 80 = 0  

This will factor to           (2X + 16)(X – 5) = 0

Disregard the negative solution.  Half of the short diagonal is 5 units.  Can you take it from there?

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I can see that (for example) they treat stat and atst as two different combinations.

They aren't.

They are both the combination astt.

I have......... I nearly flooded the house.

so on the last post i couldn't reply cause it was locked, but i already answered them on my own. i don't know how to delete the questions sorry about that, and i wasn't really expecting to gett an answer but courage the cowardly dog helped so i was able to solve the other one's by myself

but for any other person having a hard time answering the questions these were my answers

1. A normal distribution has a mean of 103 and a standard deviation of 2.7.
What is the z-score of 105?

Answer: 0.74

2. A normal distribution has a mean of 103 and a standard deviation of 2.7.

What is the z-score of 105?

Answer: 17.8

3. Use technology or a z-score table to answer the question.

The weights of logs in a wood pile are normally distributed with a mean of 17 pounds and a standard deviation of 3.4 pounds. The wood pile is composed of 325 logs.

How many of the logs will weigh 15 pounds or more

Answer: 235

4. The ages of members of a policy action group are normally distributed with a mean of 33 years and a standard deviation of 2 years.
There are 400 members in the group.
About how many members are expected to be between 29 years old and 37 years old

Answer: 380

5. Use technology or a z-score table to answer the question.

The expression  P(z<1.71) represents the area under the standard normal curve below the given value of z.

What is  P(z<1.71)?

Answer: 0.9564

6.  Use technology or a z-distribution table to find the indicated area.

The weights of tomatoes in a bin are normally distributed with a mean of 120 grams and a standard deviation of 4.3 grams.

Approximately 40% of the tomatoes weigh less than which amount?

Answer: 119 g

7. Suppose the scores on a grammar quiz are normally distributed with a mean of 76 and a standard deviation of 8.

Which group describes 16% of the population of grammar quiz scores?

Answer: scores below 68

8.

Select Yes or No to state whether each data set is likely to be normally distributed.

Data Set

the weights of the babies born at a hospital yes/no

the number of babies born each month at a hospital yes/no

the number of rooms on each floor of a hospital yes/no

the lengths of the babies born at a hospital yes/no

Answer: yes, yes, no, yes

9. The masses of the oranges on sale at a farm stand are normally distributed with a mean of 239 grams and a standard deviation of 25 grams

Answer 0.8

10. The heights of the peach trees in an orchard are normally distributed with a mean of 12.5 feet and a standard deviation of 1.8 feet.

What is the height of a peach tree with a z-score of −0.5−0.5 ?

Answer: 11.6

11. Use technology or a z-distribution table to find the indicated area.

The masses of the eggs collected on a farm are normally distributed with a mean of 55 grams and a standard deviation of 4.2 grams.

Approximately 80% of the eggs on the farm have a mass greater than which mass?

Answer: 51.5 g

12. Use technology or a z-score table to answer the question.

The weights of boxes of rice produced at a factory are normally distributed with a mean of 24 ounces and a standard deviation of 1.3 ounces. Consider a shipment of 1200 boxes of rice.

How many of the boxes will weigh 25 ounces or less?

Answer: 935

btw wont post the other 50 questions on the study guide , any onlookers just look at pavlov's formula and the way he/she answered it

 Hope ya feel better.....i was miserable for a week when I had the flu back in December....I was hoping to die...but somehow suffered through!

Emphasis on how he said thought

If you are doing slope, plug in the formula whenever you find out the properties.

slope, or m, is the coefficient of x. B is your y intercept.

Im sorry if you dont think i speak english, i also speak math.

Simple. Plug in the formula

Love, Gabe

Nice, Nickolas....but don't forget your UNITS.     120  ounces    

  In future years...if school is anything like it 'used to be'   ....only partial credit will be given for answers without the units! 

Breakthrough amen halleluajah

(I concur)