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The mistake occurs in the first line:  \(\sqrt{\frac{1}{-1}}\ne\frac{\sqrt1}{\sqrt{-1}}\)  

Your subsequent development shows that equality here leads to an inconsistency.

We need to look at this as follows:  \(\sqrt{\frac{1}{-1}}\rightarrow\sqrt{(\frac{1}{-1})}\rightarrow\sqrt{-1}=i\)

.

x/y = 5    so  5y = x

x-y =64

substitute

5y - y = 64

4y=64

y=16    then  x = 5y = 80

x * y = 16*80 = 1280

Oh but my school reader says that it doesn't form an A.P

Then how is it forming an A.P?

heureka's 126 should be 126x of course!

That is correct though :)

lol

3+2+1+2+5+2+2+3+12+2+3+2+3+4+5+3+3+5+6+3+2+1+5+3+2+2+3+3+1+5+3+2+22+2+2+3+4+5+3+2+5+3+3+1+5+2+3+2 = 170

Alan was correct with, g(x)=x^2+4 and f(u)=sqrt(u)

Take the integral:
 integral7 (2 x + 6) (x^2 + 6 x + 3) dx
Factor out constants:
 = 7 integral(2 x + 6) (x^2 + 6 x + 3) dx
Expanding the integrand (2 x + 6) (x^2 + 6 x + 3) gives 2 x^3 + 18 x^2 + 42 x + 18:
 = 7 integral(2 x^3 + 18 x^2 + 42 x + 18) dx
Integrate the sum term by term and factor out constants:
 = 14 integral x^3 dx + 126 integral x^2 dx + 294 integral x dx + 126 integral1 dx
The integral of x^3 is x^4/4:
 = (7 x^4)/2 + 126 integral x^2 dx + 294 integral x dx + 126 integral1 dx
The integral of x^2 is x^3/3:
 = 42 x^3 + (7 x^4)/2 + 294 integral x dx + 126 integral1 dx
The integral of x is x^2/2:
 = 147 x^2 + 42 x^3 + (7 x^4)/2 + 126 integral1 dx
The integral of 1 is x:
 = (7 x^4)/2 + 42 x^3 + 147 x^2 + 126 x + constant
Which is equal to:
Answer: |= 14 (x^4/4 + 3 x^3 + (21 x^2)/2 + 9 x) + constant

ʃ (2x + 6)(x2 + 6x + 3)7 dx

\(\begin{array}{|rcll|} \hline && \int (2x + 6)(x^2 + 6x + 3)\cdot 7\ dx \\ &=& 7\cdot \int (2x + 6)(x^2 + 6x + 3)\ dx \\ &=& 7\cdot \int (2x^3+12x^2+6x+6x^2+36x+18)\ dx \\ &=& 7\cdot \int (2x^3+18x^2+42x+18)\ dx \\ &=& 7\cdot \left( \frac24x^4+\frac{18}{3}x^3+\frac{42}{2}x^2 + 18x \right) \\ &=& 3.5x^4+42x^3+147x^2+126 + c \\ \hline \end{array} \)

Express the function \(\sqrt{x^2+4}\) as a composition of y=f(g(x)) of the two simpler functions y= f(u) and u=g(x}

f(u)=

g(x)=

I know how to put a function into another function but I don't know what this thing is asking :S

.     \(y=\sqrt{x^2+4}\)

.     \(y=Root\ from \ ( x^2+4)\) 

.               u                    g

f(u)=\(\sqrt{g(x)}\)

\(g(x)=(x^2+4)\) 

I hope I could help.

  !

.  

If the least common multiple of A and B is 1575, and the ratio A of B to 3 is 7 ,

then what is their greatest common divisor?

\(\begin{array}{rcll} \hline lcm(a,b) = 1575 &=& 3^2\times 5^2\times 7 \\ \hline \end{array} \)

\(\begin{array}{rcll} a &=& 3^2\times 5^2 \\ b &=& 3\times 5^2 \times 7 \\\\ \dfrac{a}{b} = \dfrac{3^2\times 5^2}{3\times 5^2 \times 7 } &=& \dfrac{3}{7}\\ \end{array} \)

\(\begin{array}{rcll} gcd(a,b) &=& 3\times 5^2 \times 7^0 = 75 \\ \end{array}\)

So will I need new power supply or not? I'm frustrated. 

Even after your "correction", it turns out that it is exactly the same as Alan's answer!!. Did you plagiarize from him? Or, did you even check his answer first, before you offered your "brilliant" solution? It appears to me that you are as phony as a $3 bill !!. Cheers and have some Canada dry!!.

Try  \(g(x)=x^2+4\)  and  \(f(u)=\sqrt u\)

or  \(g(x)=x^2\)   and  \(f(u)=\sqrt{u+4}\)

or ...

The same question:

So I think I've got it....

I believe the y function is doing the square root so...

f(u) = x+4

g(x)= x^2

??

I was trying to figure out how long it would take to type them in Roman numerals.  A long time, but not as long as Sir CPhill’s quest. 

JK....

Don't waste the bandwidth...

As of January 2017 , the largest known prime number is 274,207,281 − 1, a number with 22,338,618 digits. It was found in 2016 by the Great Internet Mersenne Prime Search (GIMPS). Plot of the number of digits in largest known prime by year, since the electronic computer.

You're not gonna tell us what it is?

That number is the largest currently known Mersenne Prime.

Whats 5+(3/5)x8 ??????

\(5+\frac{3}{5}\cdot 8\)

\(=5+\frac{3\cdot 8}{5}\)

\(=5+\frac{24}{5}\)

\(=\frac{5\cdot 5+24}{5}\)

\(=\frac{49}{5}\)

\(=9\frac{4}{5}\)

\(=9.8\)

  !

There are often MANY different ways to solve a problem you may post....that is why there are often several answer methods with the same result....We do not know what you are being taught, how far along you are in your math studies or how old you are.....often the posted questions are incomplete or rather ambiguous, so everyone gets to post THEIR methods of getting a final answer and hopefully one will be compatible and congruent with your level of math knowledge.....

Just sayin'    ......

Corrected error (and clarified math for the hoary hair tortuous).

\(\text {(a)}\\ \small v_f \small \text { velocity of father. } v_s \text { velocity of son. } \\ \frac{1}{2} m_f(v_f + 1.0)^2 = (2)* \frac{1}{2} m_fv^2_f \\ (v_f + 1.0)^2 = 2v^2_f \hspace{2em} \small \text {| Divide by } m_f \text { and reduce}\\ v_f +1 = \sqrt{2}v_f \hspace{3em} \text { | square root of both sides}\\ v_f + 1 \approx 1.4142v_f \\ 0.4142v_f \approx 1 \hspace{4em} \text{ | subtract and divide}\\ v_f \approx 2.4142m/s \\\)

-----

\(\text {(b)}\\ \text { } \\ \frac{1}{2}(m_f/2)v_s^2 = (2) * \frac{1}{2} (m_fv^2_f) \\ \frac {1}{4}v_s^2 = v^2_f \hspace{3em} \small \text {|Divide by } m_f \text { and reduce}\\ v_s^2 = 4v_f^2 \hspace{3em} \small \text { |Multiply through by 4)}\\ v_s = 2v_f \hspace{3em} \small \text { |Take square root }\\ v_s = 2*(2.4142) \approx 4.8284 m/s\)

Sometimes I need a second application of the Tortoise & Hair dye AI formula – especially when the blarney banker is nearby.  If you had used it, then this wouldn’t have been a "W T F" meltdown moment –it would be just a mistake.

VERY friggin' big....why?