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5/6*13/30=

1/6*13/6=

13/36

yes, I'm pretty sure.

(g⁷)·h⁴·g·h⁵  =  ( g⁷ · g ) · ( h⁴ · h⁵ )  =  ( g^{7 + 1} ) · ( h^{4 + 5} )  =  ( g⁸ ) · ( h⁹ )  =  g⁸ · h⁹ 

z-score  =  ( score - average ) / ( standard deviation )

z-score  =  (15 - 10.8) / 7.2  =  0.5833

11000(1.333)^84

11,000 x 1.333^84

11,000 x 30,600,783,817.021

=$336,608,621,987,230.89  !!!!!

P.S. There is something wrong with your interest rate !!. You can't have 33.3% per month !!!. Even 3.33% is too high.

Remember: 3% means =3 / 100 =0.03......and so on.

We can use the sine for this :

sin (25)  =  2.8 / L        multiply both sides by L, divide by sin (25)

L  = 2.8 / sin (25)   ≈ 6.63 m

Thanks Alan,

I would not have got that either without you showing me.

I just want to finish it.

Let

\(u = e^{-st} \;\; then\;\; \\\frac{du}{dt} = -se^{-st} \\e^{-st}dt = \frac{-1}{s}du \)

so we can write the integral as:

\(\int te^{-st}dt \rightarrow -\frac{1}{s}\int tdu \rightarrow -\frac{1}{s}\int td(e^{-st})\)

\(u=e^{-st}\\ ln(u)=-st\\ t=\frac{-ln(u)}{s}\)

So

\(\frac{-1}{s}\int t\;du\\ =\frac{-1}{s}\int \frac{-ln(u)}{s}\;du\\ =\frac{1}{s^2}\int 1*ln(u)\;du\\ \qquad \text{integrate by parts}\\ \qquad \frac{da}{du}=1\quad b=ln(u)\\ \qquad a=u\quad \frac{db}{du}=\frac{1}{u}\\ =\frac{1}{s^2}\left( [ab]-\int a*\frac{db}{du}\:du\right)\\ =\frac{1}{s^2}\left( [uln(u)]-\int u*\frac{1}{u}\:du\right)\\ =\frac{1}{s^2}\left( [uln(u)]-\int 1\:du\right)\\ =\frac{1}{s^2}\left( [uln(u)]-u\right)+c\\ =\frac{u}{s^2}\left( ln(u)-1+k \right)\)

Why would you ever want to present it with the extra step in the question? 

As follows:

\(2x^2+5x+12=19-7x\rightarrow 2x^2+12x-7=0\\ \text{ use the quadratic formula to find x } x= \frac{-12\pm \sqrt{12^2+4\times 2\times 7}}{2\times2}\\ x = \frac{-12\pm\sqrt{200}}{4}\\ \text{ positive difference: }\sqrt{200}/2\rightarrow 5\sqrt2\)

FV=P{[1 + R]^N - 1/ R}

FV = 200 x {[ 1 + .03/12]^(4*12) - 1 / (0.03/12)}

FV = 200 x {[ 1.0025]^48 - 1 / 0.0025}

FV = 200 x      {0.127328            / 0.0025}

FV = 200 x                       50.9312

FV =10,186.24 - Riyals - David will have after 4 years or 48 months @ 3% compounded monthly.

Excellent, thank you for explaining.

Let u = e^-st  then du/dt = -se^-st or e^-stdt = -(1/s)du so we can write the integral as:

\(\int te^{-st}dt \rightarrow -\frac{1}{s}\int tdu \rightarrow -\frac{1}{s}\int td(e^{-st})\)

Hi again Julius,

I just tried a different calculator and it would not do it either.

You may have to leave out the Payment and then  'guess' the interest rate, you guess will get closer and closer until it is within the desired 2 decimal places.

I shall try it with your calculator....

PV = 4800-500 = 4300

Periods = 36

monthly

FV=0

The PMT that you want is $156.64  but you cannot put that in.

You have to try different rates (these are nominal annual rates) until you find the one that will give you a PMT of $156.64.

So to two decimal places the nominal rate is 18.55%  and that is using your calculator :)

Julius, I tried using your calculator and it refused to work out the nominal (or any other) interest rate.

Maybe you'd do better with a different calculator. :/

Thanks Guest :)

\(\frac{31}{3}\\ 3\times 10=30 \;\;so\\ \text{3 goes into 31, 10 times with remainder 1 }\\ \text{You have to put the 1 over the 3 that you are dividing by}\\ \frac{31}{3}=10\frac{1}{3} \)

This is what answer guest did - it is right too :)

\(\frac{31}{3}=\frac{30+1}{3}=\frac{30}{3}+\frac{1}{3}=10\frac{1}{3}\)

I think there is a bit of a language problem here asinus  

What is 3/4 of 8/9 less than 2/5 of 20?

(3/4)*(8/9) = 2/3

(2/5) of 20 = 8

What is 2/3  less than 8 ?

8 - 2/3  = 7 and 1/3

Pretty Simple:

Take a mixed number, for example \(\frac{31}{3}\)

When you are converting a mixed number to a fraction we use 

\(a+\frac{N}{D}=\frac{aD+N}{D}\)

So, lets split up 31, into 2 parts: The multiple and the remainder. 31 divided by 3 gives 10, with a remainder of one. Lets write this:

\(\frac{31}{3} = \frac{30+1}{3} = \frac{(10\cdot3)+1}{3} = 10+\frac{1}{3}\)

Hope this helps!

-M

So, the way I lile to answer these is starting with a mixed fraction, with the non-decimal digits, plus the decimal part as the numerator of the fraction. The numerator will be a 1 followed by 0, the number times equal to the digits in the numberator, then you can bring up the non-decimil digits, and simplify. For example:

\(3.625 = 3+\frac{625}{1000} = \frac{(3\cdot 1000)+625}{1000}=\frac{3625}{1000}=\frac{73}{200}\)

Your example is a little harder, but the algorithim still works :P

\(10.3896029812186073\\ =10+\frac{3896029812186073}{10000000000000000}\\ =\frac{(100\cdot10000000000000000)+3896029812186073}{10000000000000000}\\ =\frac{1003896029812186073}{10000000000000000}\)

Hope this helps lol

-M

If what?

If tan theta is equal to 3. Calculate cos theta.

Draw a right angled triangle

mark an acute angle as theta.

opposite is 3

adjacent is 1

work out the hypotenuse using pythagoras's theorum

read  cos(theta)  off the triangle.

BUT tan is positive in the 1st or third quadrant so cos(theta) can be pos or neg.

I actually cannot see a question here at all but other people seem to be able too :/

Thanks I just added this calculator reference to our reference material thread in the 'sticky topics' :)

\(v_o=30\\ x_0=0\\ \ddot{x}=-9.8\\ \dot{x}=-9.8t+k_1\\ when\;\;t=0,\;\;\dot{x}=30\;\;so\;\;k_1=30\\ \dot{x}=-9.8t+30\\ x=\frac{-9.8t^2}{2}+30t+k_2\\ when\;\;t=0,\;\;x=0\;\;so\;\;k_2=0\\ x=-4.9t^2+30t\\~\\ Max\;\;reached \;\;when\;\;\dot{x}=0\\ \dot{x}=-9.8t+30=0\\ t=30/9.8\approx3.06sec\\ When\;\;t=3.06sec\\ x=-4.9*3.06^2+30*3.06\\ x\approx 45.9\;metres \)

I have not checked this fro errors but the method is correct :)

F(a, b, c, d)  =  a^b + c^d        Replace  a  with  4  ,  c  with  2  ,  and  d  with  3  .

F(4, b, 2, 3)  =  4^b + 2³

F(4, b, 2, 3)  =  12               Replace   F(4, b, 2, 3)   with   4^b + 2³

4^b + 2³  =  12                       2³  =  8

4^b + 8   =  12                       Subtract  8  from both sides of the equation.

4^b  =  12 - 8

4^b  =  4

4^b  =  4¹

 b  =  1

Account 1 will be worth =$2,000 x 1.06 =$2,120 in exactly one year

Account 2 will be worth=2,000 x [1 + 0.06/12]^n =$2,120, solve for n

$2,120 =$2,000 x 1.005^n     divide both sides by 2,000

1.06 = 1.005^n                           take the log of both sides

n =Log(1.06) / Log(1.005)

n =11.68 months. After 11.68 months, or round it to 12 months, account 2 will be worth more than account 1.