hectictar

Okay, I'll give this one a try also...

Let  t  be the number of 6 month periods in the term.

7000( 1 + 4% * t )   =   1400 + 7000( 1 + 4% * t/2 )

                                                         Divide through by  7000.

1 + 4% * t   =   0.2 + 1 + 4% * t/2

                                                         Subtract  1  from both sides.

4% * t   =   0.2 + 4% * t/2

                                                         Subtract  4% * t/2  from both sides.

4% * t  -  4% * t/2   =   0.2

t(4%  -   4% / 2)   =   0.2

t(4% - 2%)   =   0.2

t( 2% )   =   0.2

t   =   0.2 / ( 2% )   =   10

There were  10  periods of 6 months in the term. That is  5  years.

Here's my best guess, but I could easily be wrong.....

Let  c  be the starting capital,  and let  i  be the annual interest rate.

accumulated capital after  27  months   =   c(1 + i * 27/12)   =   6600

accumulated capital after  28  months   =   c(1 + i * 28/12)   =   6600 + 0.75% * c

Now we have two equations and two variables.

c(1 + i * 28/12)   =   c(1 + i * 27/12) + 0.75% * c         Divide through by  c .

1 + i * 28/12   =   1 + i * 27/12 + 0.75%                       Subtract  1  from both sides.

i * 28/12   =   i * 27/12 + 0.75%                                   Subtract  i * 27/12  from both sides.

i * 1/12   =   0.75%                                                      Multiply both sides by  12 .

i   =   9%

If I have interpreted the question correctly, this makes sense because it tells you that an additional month of interest adds 0.75% of the capital. That means that 0.75% is the annual rate / 12 . I might have not interepreted the question correctly.

Now....using this value of  i  , we can find  c .

c(1 + 9% * 27/12)   =   6600

c( 1.2025 )   =   6600                      Divide both sides of the equation by  1.2025 .

c   ≈   5488.57

What do you want to solve for? What do the instructions say? 

arccos( 1/2 )   =   60°   =   π/3   radians

The  $\frac{sqrt2}{2}$  does not display in LaTeX for me.

\(\frac{a}{b}\,=\,\frac{\sqrt{10}}{\sqrt{21}} \qquad\text{so}\qquad a\,=\,\frac{b\sqrt{10}}{\sqrt{21}}\\~\\ \frac{b}{c}\,=\,\frac{\sqrt{135}}{\sqrt8}\qquad\text{so}\qquad c\,=\,\frac{b\sqrt{8}}{\sqrt{135}} \\~\\ \ \\~\\\frac{a}{c}\,=\,(\frac{b\sqrt{10}}{\sqrt{21}})\,/\,(\frac{b\sqrt{8}}{\sqrt{135}}) \,=\,(\frac{b\sqrt{10}}{\sqrt{21}})(\frac{\sqrt{135}}{b\sqrt{8}}) \,=\,(\frac{\sqrt{10}}{\sqrt{21}})(\frac{\sqrt{135}}{\sqrt{8}}) \\~\\ \frac{a}{c}\,=\,\frac{\sqrt{10\,\cdot\,135}}{\sqrt{21\,\cdot\,8}} \,=\,\frac{\sqrt{2\cdot5\cdot5\cdot3\cdot3\cdot3}}{\sqrt{3\cdot7\cdot2\cdot2\cdot2}} \,=\,\frac{\sqrt{2}\cdot\sqrt{5\cdot5}\cdot\sqrt{3\cdot3}\cdot\sqrt{3}}{\sqrt{3}\cdot\sqrt{7}\cdot\sqrt{2\cdot2}\cdot\sqrt{2}} \,=\,\frac{\sqrt{5\cdot5}\cdot\sqrt{3\cdot3}}{\sqrt{7}\cdot\sqrt{2\cdot2}} \\~\\ \frac{a}{c}\,=\,\frac{5\,\cdot\,3}{2\sqrt{7}} \,=\,\frac{15\sqrt7}{14} \)

\(\quad\,\frac{1}{\sqrt{8}+\sqrt{50}+\sqrt{18}} \\~\\ =\,\frac{1}{2\sqrt{2}\,+\,5\sqrt{2}\,+\,3\sqrt{2}} \\~\\ =\,\frac{1}{10\sqrt{2}} \\~\\ =\,\frac{1\,\cdot\,\sqrt2}{10\sqrt2\,\cdot\,\sqrt2} \\~\\ =\,\frac{\sqrt2}{10\,\cdot\,2} \\~\\ =\,\frac{\sqrt2}{20}\)

\(\quad\,\frac{3}{\sqrt[5]{16}}\,+\,\frac{1}{\sqrt3} \\~\\ =\,\frac{3}{\sqrt[5]{2^4}}\,+\,\frac{1}{\sqrt3} \\~\\ =\,\frac{3}{2^\frac45}\,+\,\frac1{3^\frac12}\\~\\ =\,\frac{3\,\cdot\,2^\frac15}{2^\frac45\,\cdot\,2^\frac15}\,+\,\frac{1\,\cdot\,3^\frac12}{3^\frac12\,\cdot\,3^\frac12}\\~\\ =\,\frac{3\,\cdot\,2^\frac15}{2}\,+\,\frac{3^\frac12}{3}\\~\\ =\,\frac{3\,\cdot\,2^\frac15\,\cdot\,3}{2\,\cdot\,3}\,+\,\frac{3^\frac12\,\cdot\,2}{3\,\cdot\,2}\\~\\ =\,\frac{3^2\,\cdot\,2^\frac15}{3\cdot2}\,+\,\frac{3^\frac12\,\cdot\,2}{3\cdot2}\\~\\ =\,\frac{3^2\,\cdot\,2^\frac15\,+\,3^\frac12\,\cdot\,2}{3\cdot2}\\~\\ =\,\frac{3^2\sqrt[5]{2}\,+\,2\sqrt3}{3\cdot2}\)

a = 3    and    b = 2     so     a + b  =  3 + 2  =  5

That is really weird!!

The question you linked to does not display properly for me.

I see dollar signs around the LaTeX, like this

$\frac{\sqrt2}{2}$     That might show up for you!

But this website I think uses  \ (  and  \ )  , without spaces, around the LaTeX.

Sometimes I've noticed that the LaTeX does not display in the question at first, but then after somebody posts an answer with LaTeX in it, the question displays properly.