Alan

Remember  SOHCAHTOA

Sin is Opposite/Hypotenuse

Cos is Adjacent /Hypotenuse

Tan is Opposite/Adjacent 

B∪C is the set of all the items in B and C put together. {b, c, d, e, f}

A∩(B∪C) is the set of items that are common to A and to B∪C.  In this case that is {b, d}

B` is everything in the universal set that is not in B, namely {a, c}

B`∩C is the set of items common to B` and C, namely {c}

(B`∩C)` is everything in the universal set not in B`∩C.  So {a, b, d, e, f}

(B`∩C)`-A is the set of items left when you take those in A away from (B`∩C)`, so you are left with  {e, f}

To find za/2 from 0.58*0.42*(za/2 /0.04)² = 718 first divide both sides by 0.58*0.42

(za/2 /0.04)² = 718/(0.58*0.42)

Take the square root of both sides

za/2/0.04 = ±√(718/(0.58*0.42))

Multiply both sides by 0.04

za/2 = ±0.04*√(718/(0.58*0.42))

$${\mathtt{0.04}}{\mathtt{\,\times\,}}{\sqrt{{\frac{{\mathtt{718}}}{\left({\mathtt{0.58}}{\mathtt{\,\times\,}}{\mathtt{0.42}}\right)}}}} = {\mathtt{2.171\: \!618\: \!693\: \!604\: \!038}}$$

So za/2 ≈ ±2.1716

zegroes said: well i tried giving him the easiest way i suppose......

Yes, but unfortunately you forgot part of the equation.  If you put x = 6 in the left-hand side you get 6(6+6) which is 6*12, which is not 36. The equation isn't one which factors nicely!  

Good try, but always check your answer by plugging it back into the original equation!

These are known as parametric equations.  Choose a range of values for t, calculate the corresponding values of x and y and plot y vs. x.  The graph below was calculated from 10000 values of t from 0 to 100 in steps of 0.01.

You can use the calculator here to solve this:

$${\mathtt{x}}{\mathtt{\,\times\,}}\left({\mathtt{x}}{\mathtt{\,\small\textbf+\,}}{\mathtt{6}}\right) = {\mathtt{36}} \Rightarrow \left\{ \begin{array}{l}{\mathtt{x}} = {\mathtt{\,-\,}}{\mathtt{3}}{\mathtt{\,\times\,}}{\sqrt{{\mathtt{5}}}}{\mathtt{\,-\,}}{\mathtt{3}}\\
{\mathtt{x}} = {\mathtt{3}}{\mathtt{\,\times\,}}{\sqrt{{\mathtt{5}}}}{\mathtt{\,-\,}}{\mathtt{3}}\\
\end{array} \right\} \Rightarrow \left\{ \begin{array}{l}{\mathtt{x}} = -{\mathtt{9.708\: \!203\: \!932\: \!499\: \!369\: \!1}}\\
{\mathtt{x}} = {\mathtt{3.708\: \!203\: \!932\: \!499\: \!369\: \!1}}\\
\end{array} \right\}$$

Note there are two solutions.

People who use trigonometric functions:

Surveyors

Navigators

Electrical engineers

Mechanical engineers

.... etc.

Depends on what career you adopt.  You probably won't need them if you stack shelves in a supermarket!

The polar representation of cartesian point (x,y) is (r,θ) where 

$$\\
r=\sqrt{x^2+y^2}\\ \theta=\tan^{-1}(\frac{y}{x})$$

So, with x = 4 and y = 30

$${\mathtt{r}} = {\sqrt{{{\mathtt{4}}}^{{\mathtt{2}}}{\mathtt{\,\small\textbf+\,}}{{\mathtt{30}}}^{{\mathtt{2}}}}} \Rightarrow {\mathtt{r}} = {\mathtt{30.265\: \!491\: \!900\: \!843\: \!111\: \!9}}$$

$${\mathtt{theta}} = \underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{tan}}^{\!\!\mathtt{-1}}{\left({\frac{{\mathtt{30}}}{{\mathtt{4}}}}\right)} \Rightarrow {\mathtt{theta}} = {\mathtt{82.405\: \!356\: \!631\: \!409^{\circ}}}$$

What you have said is not correct!  Remember that raising to a power takes precedence over negation, so -3² without brackets is the same as -(3²).  Suppose this were not the case, then you could have the following strange situation:

-3² = 9

0 - 3² = -9

Yet most of us think of -3² as the same thing as 0 - 3².

If you don't like this convention (namely, that -3² is different from (-3)²), then use Microsoft Excel, which treats them as the same!  Most proper scientific calculators and mathematical software treat raising to the power as a higher priority than unary negation.

On the calculator on this site, if you enter -3², the calculator even puts brackets around the 3² to reinforce the fact that it is making the standard assumptions on hierarchy!

$${\mathtt{\,-\,}}\left({{\mathtt{3}}}^{{\mathtt{2}}}\right) = -{\mathtt{9}}$$

Don't forget the other solution!

If (2x+1)² = 16 then 2x+1 = ±4

Taking the negative value we have 2x+1 = -4;  2x = -5;  x = -5/2 or x = -2.5