CPhill

4 sec (pi/6)+5 cot(pi/4)

sec(pi/6)  = 1/cos(pi/6) = (1)/(√3/2) =  2/√3

cot(pi/4) = 1/tan(pi/4)  = 1/1 = 1

So we have

4(2/√3) + 5*1 =

8/√3 + 5 =

8√3/3 + 15/3 =

[8√3 + 15] / 3

I doubt  that is correct, Melody...there is no purpose in writing the first fraction on the right side of the equation over 1......besides, the poster claims that the answer on his sheet was the same as I got......

Thanks, Melody...I like your answer better, too.....

Ok...here's an example

Let's suppose that we have

10^{log₁₀ 100}

Notice that log₁₀100    just evaluates to "2"

So we really have

10²  = 100       which was just the number that we were taking the log of in the exponent!!!

And since 10^10 was the number that we were taking the log of in the exponent, the answer just ends up being just..... 10^10

I think we have.....

.08 = [(.75x)/(1- .75x)]   subtract the expression from the right hand side to set the expression = 0  .....and using the on-site solver, we have......

$${\mathtt{0.08}}{\mathtt{\,-\,}}\left({\frac{{\mathtt{0.75}}{\mathtt{\,\times\,}}{\mathtt{x}}}{\left({\mathtt{1}}{\mathtt{\,-\,}}{\mathtt{0.75}}{\mathtt{\,\times\,}}{\mathtt{x}}\right)}}\right) = {\mathtt{0}} \Rightarrow {\mathtt{x}} = {\frac{{\mathtt{8}}}{{\mathtt{81}}}} \Rightarrow {\mathtt{x}} = {\mathtt{0.098\: \!765\: \!432\: \!098\: \!765\: \!4}}$$

10^{log₁₀ (10^10)}

Whenever we have something like this...... a^log_ab   the answer is just "b"

So we have

10^{log₁₀(10^10)}

And the answer is just .....  10^10

Assuming that "?" retains the same value, let it = 'x"

So

x*x*x = 25

x³ = 25     take the cube root of both sides

x = ³√25

5^-2 = 1/5² = 1/25

10log10(10^10)

If we have

10log[10(10^10)]   ......then we have

10log(10)¹¹ =

log[(10)¹¹]¹⁰ =

log(10)¹¹⁰ =

110

If we have

10log₁₀(10^10)   .....then we have

10*log₁₀(10¹⁰) =

log₁₀(10¹⁰)¹⁰ =

log₁₀10¹⁰⁰ =

100

14.9*sin(22)/sin(113)   = about 6.064