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This graph might help:

1+ 1/1+1/1/1+1

\(1+\frac{1}{1}+(\frac{1}{1}\div1)+1\\ =1+1+(1\div 1)+1\\ =2+1+1\\ =4\)

The fifth term can be expressed as

1 / [ a + 4d] =  1/28

And the 13th term can be expressed as

1 / [ a + 12d]  = 1/178

So.......this implies that

a + 4d   = 28   (1)       and

a + 12d  =  178      (2)

Multiply (1) by -1 and add it to (2)

8d  = 150        divide both sides by 8

d = 75/4

Using (1)   to find a, we have

a + 4(75/4)   = 28

a + 75  = 28         subtract   75 from each side

a = -47

The first term is given by 1/a   =    1/ - 47  =   -1/ 47

Replace x, y and z in the equations by a, b and c:

a + b + c = 2

a*b/3 + b*c/3 + a*c/3 = -41.  So.  a*b + b*c + a*c = -123

-a*b*c/(3*5*6) = 6. So. a*b*c = -540

(t - a)(t - b)(t - c) = 0. ⇒ t^3 - (a + b + c)t^2 + (a*b + b*c + a*c)t - a*b*c = 0

Hence:  t^3 - 2t^2 - 123t + 540 = 0

Solving this gives: a = -12, b = 5, c = 9 or variants of these.

So:  x = a/3 → -4,   y = b/5 → 1,  z = -c/6 → -3/2

x + y = -3 This is just one possibility.  The others can be found by interchanging the values allocated to a, b and c.

You spent 3/4 of your time driving on the highway at an average of 60 mph. Or, you drove 1 mile per minute or 45 miles.

But, in 45 minutes you covered 5/6 of the distance. Therefore, you covered the entire distance of 6/5 x 45 =54 miles in 60 minutes.

But, you covered the last 9 miles in 15 minutes. So, your average speed off the highway was:

9/15 x 60 =36mph

Hello dabae!

3x+5y-6z=2 

5xy-10yz-6xz=-41  

xyz=6

x = 1,666666666667
y = 1,8
z = 2

Solved with computers for nonlinear equations.

Probably not the expected. Sorry!

Greeting asinus :- )  !

√(b^2y^5b^36y^2) → √(b^38y^7) → b^19y^3√y

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30=60*sin(pi*x/15-7.5*pi/15)+75

(30 - 75)/60 = sin(pi*x/15 - pi/2)

-3/4 = sin(pi*x/15 - pi/2)

pi*x/15 -pi/2 = asin(-3/4) → -0.848 (4'th quadrant) = 2pi - 0.848

x = (2.5 - 0.848/pi)*15 ≈ 33.45

\(\begin{array}{rl}&\dfrac{2}{3}+\dfrac{4}{5}\\=&\dfrac{10}{15}+\dfrac{12}{15}\\=&\dfrac{22}{15}\\=&1\dfrac{7}{15}\end{array}\)

Example:

\(\color{aqua}e^x\cdot e^{-x}= 1\)

Uh sorry that holds for every values of x XDDDDD

\(\color{blue}e^x=e^{-x}\)

\(\color{blue}\ln e^x = \ln e^{-x}\)

\(\color{blue}x=-x\) \(\color{red}\leftarrow \color{}\boxed{\color{red}\ln x = \log_e x}\\\color{}\boxed{\color{red}\ln e^x=x}\)

\(\color{blue}2x=0\)

\(\color{blue}x=0\)

\(\color{aqua}\left(\dfrac{3}{9x^2}-\dfrac{5}{6x}-14\right)-\left(\dfrac{7}{9x^2}-\dfrac{5}{6x}+1\right)\)

\(\color{aqua}=\dfrac{3}{9x^2}-\dfrac{5}{6x}-14 - \dfrac{7}{9x^2}+\dfrac{5}{6x}-1\\ \color{aqua}=\dfrac{3}{9x^2}-\dfrac{7}{9x^2}-14-1\\\color{aqua} =-\dfrac{4}{9x^2}-15\)

Same as Mellie's answer, only difference is the steps.

\(\begin{array}{rll}\dfrac{3}{12}&=&\dfrac{5}{x}\\\dfrac{1}{4}&=&\dfrac{5}{x}\\\dfrac{5}{20}&=&\dfrac{5}{x}\\x&=&20\end{array}\)

\(\dfrac{1}{2}+\dfrac{1}{4}\\ =\dfrac{2}{4} + \dfrac{1}{4}\\ = \dfrac{3}{4}\)

Same as Mellie's answer.

This could not be the same. 

\(\left(\dfrac{a}{b}\right)^{m\cdot n}\)

\(=\left(\dfrac{a^m}{b^m}\right)^n\)

This is correct, this also equals

\(\dfrac{a^{mn}}{b^{mn}}\)

\(\text{This could not be further simplified.}\)

y = exp(x) = e^x 

Where e = \(1+\dfrac{1}{1!}+\dfrac{2}{2!}+\dfrac{3}{3!}......\)

Which is Euler's number

\(\begin{array}{rl}&28-(-43)\\=&28+43\\=&71\end{array}\)

\(\begin{array}{rl}&-28-(-43)\\=&43-28\\=&15\end{array}\)

Thankyou so much. you're a legend too if you're a different person to the first one. thankyou so so much guys. you's have been a huge help

What do you mean?

P.S. You only get "complex values" for x:

Solve for x:
75-60 sin(1.5708-(π x)/15) = 30

Subtract 75 from both sides:
-60 sin(1.5708-(π x)/15) = -45

Divide both sides by -60:
sin(1.5708-(π x)/15) = 3/4

Take the inverse sine of both sides:
1.5708-(π x)/15 = π-sin^(-1)(3/4)+2 π n_1 for n_1 element Z
 or 1.5708-(π x)/15 = sin^(-1)(3/4)+2 π n_2 for n_2 element Z

Subtract 1.5708 from both sides:
-(π x)/15 = 0.722734+2 π n_1 for n_1 element Z
 or 1.5708-(π x)/15 = sin^(-1)(3/4)+2 π n_2 for n_2 element Z

Divide both sides by -π/15:
x = -3.4508-30 n_1 for n_1 element Z
 or 1.5708-(π x)/15 = sin^(-1)(3/4)+2 π n_2 for n_2 element Z

Subtract 1.5708 from both sides:
x = -3.4508-30 n_1 for n_1 element Z
 or -(π x)/15 = 2 π n_2-0.722734 for n_2 element Z

Divide both sides by -π/15:
Answer: |
 | x = -3.4508-30 n_1 for n_1 element Z
 or x = 3.4508-30 n_2 for n_2 element Z

2) Interest rate =3.86% compounded Bi-weekly or every 2 weeks for 1/2 a year.

3) Interest rate=7.75% compounded annually over a period of 9 years.

4) Interest rate=7.66% compounded monthly over a period of 1.5 years.

OK, young person. Here is the interest rate for your loan:

1) 7.69% compounded semi-annually. This is how you get that rate:

FV=PV [1 + R/2]^N, Where R=Interest rate per period, N=number of periods, PV=Present value, FV=Future value.

64,010=35,000[1 + R/2]^8*2 Divide both sides by 35,000,

1.828857..=[1 + R/2]^16 Take the log of both sides.

0.26218...=16 x log[1 + R/2]

log[1 + R/2] =.26218/16=..0.016386...

[1 + R/2] =10^0.016386=1.0384515

R/2=1.0384515 - 1 =0.0384515

R=2 x 0.0384515

R=0.0769 x 100

R=7.69% compounded semi-annually.

PS. All the rest are calculated the same way. Good luck to you.

Yes thank you heureka, but i already got those parts i just dont know how to do part c and part d, i only know what they are i dont know how to apply them.

comitee-forming: prove this using a commitee of n people and you want to choose k from that n.

block-walking: ho many ways can you get to a certian number on pascals triangle starting from the top and going to dot by dot, each dot representing a number.