All Answers 359051 Answers

x is less than 2

ok happy thanks for the heads up

@ Gar-  I hope you know she's a girl,  and I was kidding

@ Taylor-  Zip it,  lock it,  put it in your pocket

Dude when it's open it stays open. Haha. 

he does not have to unles he` your brother  

Hey......

Tiddle,  close your zipper mouth

hi tiddel and happy

This I can solve.

Find a common denominator for the solution and the problem.

15 is the first common denominator.

3*5=15

5*5=25

x=25

Here's a graph of the position function and the velocity fuction that demonstrates Alan's and Heureka's answers....

Obviously happy . Hello gar.

good and hi

I am on............

(4.5)(5)(-2)=4.5*2*(-2)

4.5*5=22.5

22.5*(-2)=-45

-45 is the solution

Fractions are my specialty.........and the occasional decimal

Excellent, h7....!!!!

I'm impressed.....

Now its just the last one that I cant figure out if its right or wrong:

z = a+bi --> r and θ (degrees)

z = conjugate(4+2i) = 4-2i

$$\small{\text{$\boxed{r=\sqrt{a^2+b^2}\qquad\phi= \left\{ \begin{array}{ll}\arctan{( \frac{b}{a} )}, & a > 0 \text{ and } b \text{ whatever!} \\ \\\arctan{( \frac{b}{a} )} + \pi , & a < 0 \text{ and } b \ge 0 \\\\\arctan{( \frac{b}{a} )} - \pi , & a < 0 \text{ and } b < 0 \\\\\frac{ \pi }{2}, & a = 0 \text{ and } b > 0 \\\\-\frac{ \pi }{2}, & a = 0 \text{ and } b < 0 \\\\\end{array}\right.}$}}$$

$$\\\small{\text{\ $z = 4-2i$}}\\
\small{\text{ $a=4, \ b = -2$}}\\
\small{\text{ $r=\sqrt{(4)^2+(-2)^2} = \sqrt{20}=4.47$}} \\
\small{\text{ $a > 0 :\quad$ $\phi= \arctan{( \frac{b}{a} )} =\arctan{( \frac{-2}{4} )} = -26.5650511771\ensurement{^{\circ}} $}}$$

Multiply 2/3*9/1

18/3 is the answer

18/3=6

It will take 6 days

There is a "long division" method that used to be taught many years ago in schools, but I think that it's pretty tricky to use until you get the hang of it....

Here's a simpler way - the "bisection" method.....this website explains it pretty well

C=15+ 0.10n                      C=0.25n

n=65

15 + .10(65)  = 21.5             .25(65) = 16.25

Company "A" is the better option.....

3. also final velocity v: 

$$v=v_0+at_{\small{\text{stone hits the ground}}} \quad v_0 = 7\quad t = 6.51625939587s \\
v = 7 + 32 * 6.51625939587 = 215.5203 \ \frac{ft}{s}\\$$

The last one is correct.

.

What is the common ratio sequence 6,-3,1.5,-0.75

$$\small{\text{the common ratio is
$\quad \frac{-3}{6}= \frac{1.5}{-3}= \frac{-0.75}{1.5}= -\frac{1}{2} $
\quad \small{\text{or}}\quad $-0.5$
}}$$

1.  Use s = ut + (1/2)at², where s = distance travelled, u = initial velocity, a = acceleration, t = time.

s = 7*3 +(1/2)*32*9 = 165 ft., so the stone is 725 - 165 = 560 ft off the ground.

2. The stone hits the ground when s = 725, so: 725 = 7*t +(1/2)*32*t²

Solving this quadratic we get 

$${\mathtt{16}}{\mathtt{\,\times\,}}{{\mathtt{t}}}^{{\mathtt{2}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{7}}{\mathtt{\,\times\,}}{\mathtt{t}}{\mathtt{\,-\,}}{\mathtt{725}} = {\mathtt{0}} \Rightarrow \left\{ \begin{array}{l}{\mathtt{t}} = {\mathtt{\,-\,}}{\frac{\left({\mathtt{3}}{\mathtt{\,\times\,}}{\sqrt{{\mathtt{5\,161}}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{7}}\right)}{{\mathtt{32}}}}\\
{\mathtt{t}} = {\frac{\left({\mathtt{3}}{\mathtt{\,\times\,}}{\sqrt{{\mathtt{5\,161}}}}{\mathtt{\,-\,}}{\mathtt{7}}\right)}{{\mathtt{32}}}}\\
\end{array} \right\} \Rightarrow \left\{ \begin{array}{l}{\mathtt{t}} = -{\mathtt{6.953\: \!759\: \!395\: \!873\: \!178\: \!7}}\\
{\mathtt{t}} = {\mathtt{6.516\: \!259\: \!395\: \!873\: \!178\: \!7}}\\
\end{array} \right\}$$

The only positive solution is t = 6.516 seconds

3. Use v² = u² + 2as  where v is final velocity.  

v² = 49 + 2*32*725

$${\mathtt{v}} = {\sqrt{{\mathtt{49}}{\mathtt{\,\small\textbf+\,}}{\mathtt{2}}{\mathtt{\,\times\,}}{\mathtt{32}}{\mathtt{\,\times\,}}{\mathtt{725}}}} \Rightarrow {\mathtt{v}} = {\mathtt{215.520\: \!300\: \!667\: \!941\: \!719\: \!5}}$$

v = 215.52 ft/sec

.