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I turned x into x^-1 which differentiates to -x^-2 which I then multiplied by the numerators (2x and -5).  Is that wrong?

it is the derivative of   [ x^2-5x-24] / x       Note the red part.....

I thought the derivative of x²-5x-24 would be 2x-5 (the 24 is zero)? 

The point C will be    x = 2

y = (2+3)(2-8) /2   = -15         2,-15

the slope (m) is given by the derivative at x = 2 

    Then just use   y = mx + b   to find your line.....can you do that?

Slope of the original line is   2-4  / 1-7 =  1/3

y = mx + b     

2 = 1/3 (1) + b   b= 5/3

original line is     y = 1/3 x + 5/3      perpindicular slope is   -3

Midpoint of original line is 4, 3

New line    3 = -3(4) + b    b = 15

New perpindicular line    y = -3x + 15 

Here is a graph:

https://www.desmos.com/calculator/nljlb5kiy8

CPhill: Did you forget 20 km/h when cycling uphill?

I'm getting y = 5x - 7.

Actually, a = 7k, b = 4k, c = k, so (a - b)/c = (7k - 4k)/k = 3.

Anyone?

Now I'm getting (u + 2v)*w = 10, (w - u)*v = 7, (3v - 2w)*u = -3.

just learn all the topics.

*you can practice math problems in Aops online.*

At 9:00, the hands form a right-angle (90°) or you can think of it as 270° if you look at the angle between the minute and the hour hand.

MINUTE HAND RATE:

Now the minute hand moves 1/60 of the way around the circle each minute. 1/60 of 360° is 6°

The minute hand moves 6° per minute.

HOUR HAND RATE:

The hour hand moves 1/12 of the way each hour. Dividing by 60, that means the hour hand moves 1/720 of the way around the circle each minute. 1/720 * 360° = ½°

The hour hand moves ½° per minute.

Thus the minute hand is getting 6° closer, but the hour hand is moving away at a rate of ½° per minute. That's a net of 5½° per minute that they are getting closer together.

You want to figure the minutes until the 270° angle is down to 28°.

Set up an equation:

270 - 5.5t = 28

270 - 28 = 5.5t

242 = 5.5t

t = 242/5.5

t = 484/11

t = 44

Answer: 

In 44 minutes (at 9:44).

Let the top of the statue  be point A

Let the bottom be point B

Place  the mirror between Kiran and the statue such that from  Kiran's point of view, the whole statue shows in the mirror....call this  point, C

Call the top of Kiran's head point D

Call the place where he stands  point E

Because  the angle of  incidence of light  = its angle of reflection, then angle ACB   =Angle DCE

And Angle  ABC  =  Angle DEC  = right angles

So..........by AA congruency.....triangle  ABC  is similar to triangle DEC

Here's the idea   {using a palm tree rather than a statue ]  : 

Now....note something else.....if the mirror is placed  305 ft from the statue = BC   and Kiran stands exactly 5.8 ft from the mirror = EC....we have this relationship

AB / BC  =   DE / EC

305 / 305  =  5.8  / 5.8

Which is true

Furthermore

The tangent of angle ACB [ angle of incidence]  =   AB / BC  = 305/305  =  1

And

The tangent of  angle DCE  [angle of reflection ]  = 5.8 / 5.8  = 1

So....since the tangents are equal.....then  we know that the angle of  incidence  = angle of reflection

Let (a x b x c) / (a + b + c) = 341 be an equation where a, b and c are consecutive positive integers. What is the least possible value of a?

Sei (a x b x c) / (a + b + c) = 341 eine Gleichung, in der a, b und c aufeinanderfolgende positive ganze Zahlen sind. Was ist der geringstmögliche Wert von a?

Hello Guest!

\((a\times b \times c)/ (a + b + c) = 341\\ a\times (a+1)\times (a+2)/(a+a+1+a+2)=341\\ \color{blue}a=31\\ \color{blue}(31\times 32\times 33)/(31+32+33)=341\)

  !

or   +31    since it has to be positive     31   32  and 33

One solution is a = 6, b = 2, c = 4, so (a - b)/c = (6 - 2)/4 = 1.

Let x be the middle number

a = x-1

c = x+1

(x-1)(x)(x+1) / [(x-1)+(x)+(x+1)]   = (x^3 +x)/3x =====>  (x^2-1)/3

(x^2-1) /3 = 341

x^2 = 1024

x= +- 32

smallest x would be  -32    smallest a would be - 33

I put numbers in there to see what you mean but I only understand this a little. I will work on it some more later when I have time. 

Thanks CPhill with your help I’ll pass the quiz tomorrow and maybe I’ll pass the class.  

it's dot product not normal product

It actually is, 53 - 43 = 10

10 should be the answer.

oopsies

(u + 2v)*w = 14, (w - u)*v = 7, (3v - 2w)*u = -5

You didn't say what language are you using in your class project? Here is a short code in C++, but you can easily write the code similarly in any language. The % symbol stands for "mod".

n=?;s=0;p=0;cycle: if(n%10)%2==1, goto4, goto6);s=s+(n%10);p=p+1;n=int(n/10);if(n!=0, goto cycle,0);print"Total Sum =",s;print"Total Num =",p

1 - First, you have to print 1,000 digits of e from whatever source you want.
2 - You would copy and paste that 1,000 digits under "n" in the code above. The conditional statement: if(n%10)%2==1, sums up the odd digits only. If you wish to sum up the even digits, then change the "1" to "0" in the above conditional statement.

Sum total of all odd digits in the first 1,000 digits of e= 2,549
Total Num = 501
And for your own curiosity, the sum total of all even digits =2010
Total Num =499

Notice that the total number of odds + evens =1,000. Now, since the digits are supposed to be "random", you would expect the total of the "odds" to be very close to the total of "evens". Why is there such a big gap? I will leave that question for you to answer !!.

The only way that we can get two  positive roots is if we have something like this :

(x  - a)^2   =   0             take both roots

x  - a   =  0    [  both roots of   0   are  -0   and  + 0   =  0   ]

x  = a           (assuming that  a  >  0  )