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I'm assuming that Log (x)   is base 10

This can get a little messy.....here's WolframAlpha's answer........

https://www.wolframalpha.com/input/?i=fifth+derivative++%5Bsin+(x)+*+Log+(x)%5D&rawformassumption=%7B%22FunClash%22,+%22Log%22%7D+-%3E+%7B%22Log10%22%7D

Go to Mathpapa.com for help with problems like this! Helped me out a lot back in algebra, and still in geometry

Thanks a lot. And very happy birthday to one of nicest and very competent people on this forum. Many healthy and happy returns.

See my answer under the original post......

Suppose our train left the station at 12 midnight.  [every hour on the hour]....we  would meet no train at that time because the other train would have had to have left at 7:30AM the previuos evening....but this is impossible because it would not have left "on the hour"

Instead, 15 minutes later  [ at 12:15 AM].....we have met the train the left the other station at 8AM  the previous evening  [ and would arrive at our station of departure 15 minutes later....at 12:30 AM ]

Then......30 minutes later  [ at 12:45 AM]  we would meet the train that left at 9 AM the previous evening.......it has been traveling for 3 hrs, 45 min....and since we are 45 minutes from our station of departure......it's 45 min from its station of arrival......and it will arrive at 1:30 AM.....4 1/2 hours after its departure

Note the remaining patterns :

Our Time  → Time that the train we meet left the station of departure [our station of arrival ]

1:15 AM →  10 PM

1:45 AM → 11AM

2:15 AM → 12 AM

2:45 AM → 1 AM

3:15 AM → 2 AM

3:45 AM → 3 AM

4:15 AM → 4 AM 

Note that we don't meet any more trains after 4:15 AM.......we arrive at the station at 4:30AM, but the next train that departs that staion won't happen for 30 more minutes [ at 5 AM]

So....we pass a total of 9 trains......

Hi Mr Prime-Fred,

You have introduced yourself as a new member of the forum and as such you are very welcome here.

However,

We are here to facilitate learning, it does not appear that you are trying to learn anything.

It appears only that you are being a total smart a**e who is trying to get pre-trained trained monkeys to perform tricks of your choice.

Categorize me as you please. Your opinion is of no consequence to anyone!

7(2e-1)-3=6+6e Solve for e

distribute the "7(2e-1)"

= 14e - 7 -3 = 6 + 6e

subtract the 6 from both sides,

= 14e -7-3-6=6e

clean it up a little,

=14e -16=6e

add 16 to both sides,

=14e=6e+16

subtract 6e from both sides,

=

8e= 16

divide 8 from both sides,

e= 16/8

e= 2

smile :)

21

625 /  10,000 =

[ 125 * 5]  /  [ 2000 * 5]  =

125 / 2000  =

[ 5 * 25] /   [ 5 * 400]  =

25 / 400  =

[5 * 5]  /  [ 5 * 80 ] =

5 /  80  =

[1 * 5 ] /  [ 16 * 5 ]  =

1 / 16

It's also undefined when 3x^2 - x - 2 =1 or -1, since then the log will be zero, and we are not allowed to divide by zero.

[ 32 + 1/2 ] * 4  =

32 * 4   +  (1/2) * 4  =

128  +  2   =

130

|3 - x | = 5

We have two equations

3 - x  = 5                        and          3 -  x    = -5

Subtract 3 from both sides

-x  =  2                                            -x =  - 8

Multiply though by  -1

x = -2                       and              x = 8

If i'm 13 years old, how old i will be in 2061?

\(Life \ age=(2061-2016)years+13years=58years\)

  !

-4x-5y=-21

−4x+5y= 69   add the equations

-8x  = 48     divide both sides by -8   

x = -6

And using either equation and substituting for x, we have

-4(-6) - 5y  = -21

24 - 5y  = -21   subtract 24 from both sides

-5y =  -45    divide both sides by  -5

y = 9

sin a =  0.84

Use the arcsin to find the angle

arcsin (0.84)   ≈  57.14° ,  122,86° , 417.14° , 482.86°  on   (0, 720°)

And  ≈  -237.14° , -302.86° , -597.14° , -662.86°    on  ( -720, 0 )

This is really a dumb idea!

Anyone too dumb or indifferent to know or care about clicking the previous page of questions is too dumb or indifferent to answer them anyway. Common sense dictates that answering any question is much more involved than a simple click. 

Questions do get “lost” on here, but displaying a hundred questions at a time will not change that. A hundred-question default will cause more “clutter” and this is more likely to cause them to be lost.

Most of these questions are abandoned, not lost, anyway. The hundred-question display option is available for any who care to us it.

CPhill

I tried plugging that in but it wouldn't work

obviously 4

The absolute value bars mean that this is only undefined when :

3x^2 - x - 2  = 0     factor

(3x + 2) (x - 1)  = 0     set each factor to 0   and x = -2/3    or x =  1

Thus....all x values are in   the domain except  x = -2/3   and x = 1

Here's the graph :  https://www.desmos.com/calculator/uuzamhwcht

-4 - (-22)

Means

-4 + 22

Rearranged: 22 - 4 = -4 + 22

22 - 4 = 18 = -4 + 22 = -4 - (-22)

This is the complicated answer given by Wolfram/Alpha:

{x element R : 6 x + sqrt(37)<1 or (6 x + sqrt(13)>1 and 6 x<1 + sqrt(13)) or 6 x>1 + sqrt(37) or 1/6 (1 - sqrt(37))<x<-2/3 or -2/3<x<1/6 (1 - sqrt(13)) or 1/6 (1 + sqrt(13))<x<1 or 1<x<1/6 (1 + sqrt(37))}
(assuming a function from reals to reals). See the link here:

http://www.wolframalpha.com/input/?i=Domain++y%3D+1+%2F+Log(abs%5B3x%5E2+-+x+-+2%5D)&rawformassumption=%7B%22C%22,+%22Domain%22%7D+-%3E+%7B%22DomainAndRangeWord%22%7D&rawformassumption=%7B%22FunClash%22,+%22Log%22%7D+-%3E+%7B%22Log10%22%7D

"a"  would be the answer if we assumed that a ,b and c > 0

However......to cover all situations......assume that  a < 0    and bc < 0

Then the answer is   l a l

To see why :

√ [abc] * √ [ a / (bc) ]  =  √  [ (a^2 * bc ) / ( bc)]  =  √  a^2

If  "a"  <  0   and we wrote down  "a"  as a result......we would be obtaining a negative value from a positive root.......which isn't possible

The first farmer was asking 1/2 cent for an egg, thus he should have received 1/2 x $3=$1.50(for 300 eggs). The second farmer was asking 1/3 cent for an egg, hence, he should have received 1/3 x $3 =$1.00 (for 300 eggs.) Therefore, both together should have received: $1.50 + $1.00 =$2.50. However, by combining their eggs, they got only 2/5 cents per egg. That is, the rate was changed, so that they received: 2/5 x $6.00 =$2.40 (for 600 eggs). Hence, together they lost:$2.50 -$2.40 =0.10 cents. However, the second farmer received $1.20 - $1.00 =0.20 cents more, while the first farmer lost: $1.50 - $1.20 =0.30 cents. Boy, pretty cheap eggs!!