All Answers 358110 Answers

the rates at which they can solve problems are combined

$$rate_{Beth}=\dfrac p 2 ~\mbox{problems/hr}$$

$$rate_{Molly}=\dfrac x h~\mbox{problems/hr}$$

$$rate_{both}=\dfrac p 2 + \dfrac x h = \dfrac {p h + 2 x}{2h}$$

the time it takes for both of them to do 400 problems is 400 divided by their combined rate.

$$t_{both}=\dfrac {400}{rate_{both}}=\dfrac {800h}{ph + 2x}$$

CODING!

Just hit return on your keyboard

$$\dfrac 1 R = \dfrac 1 {r1} + \dfrac 1 {r2} ~mho$$

$$\dfrac 1 R = \dfrac 1 1 + \dfrac 1 3 = \dfrac 4 3~mho$$

$$R = \dfrac 3 4~ohm$$

D=3 yd

R=1.5 yd

$$Area=\pi R^2=\pi (1.5)^2$$

$${\left({\mathtt{1.5}}\right)}^{{\mathtt{2}}}{\mathtt{\,\times\,}}{\mathtt{\pi}} = {\mathtt{7.068\: \!583\: \!470\: \!577\: \!034\: \!8}}$$

so 7.1 sq yds is correct

$$C = \pi D = 3 \pi$$

$${\mathtt{3}}{\mathtt{\,\times\,}}{\mathtt{\pi}} = {\mathtt{9.424\: \!777\: \!960\: \!769\: \!379\: \!7}}$$

and 9.4 yds is correct for the circumference

well done

Friday 30/5/14

Manipulating logs (Thanks for the demo Alan)

73√3 over in²

3/4{4}

3/{4*4} (by changing 4 to its inverse of 1/4, you have a like denominator)

3/16

Or ride your bike around the haaaaaalls?

(Provided I have like a half-hour, I could probably sing this and post it here.)

I assume you might mean..... (2x-8)/(5x-20)=2

OK...note that we can factor the top and bottom of this as

[2(x -4)] / [5(x-4)] = 2  ...... Note that this simplifies to

(2/5) = 2 ...... which is never true

BTW...."solving" this gives x =4....however, that answer won't work either, because it makes the numerator and the denominator 0 in the original equation.

Thus....this has no solution
 

Not agreed, we have a huge number of immigrants who have become nationalized.  they belong to our nation but they were not born here.  Sorry reinout-g I only just read your next sentence.

I am nit picking too.  The world population is still irrelevant.

Stupid illogical school problems.  Just give the teachers what they want - that's how you pass a test!

you could always be clever and state why the question is stupid and then give the teachers what you think they want  (or vice versa).  I'd probably do that!

I don't know. To me, it is really the mystery of life. The question that describes my life is, is 2+2, not, normal? When I look at 2+2, I see myself, and when I look into the eyes of 2+2, I see, life. So you tell me, what is 2+2?

Well 4. Unless you want us to say that it's fish.

I believe 1 + 1 is equal to the square root of 49 divided by 7 plus a negative 4 multiplied by 6 plus 19. Am I correct?

Look here and all will be explained.

It is the second button on the top row 

but you can just type in pi, that is what i do!

And the solution point is (-1,2)

$${{\mathtt{x}}}^{{\mathtt{2}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{7}}{\mathtt{\,\times\,}}{\mathtt{x}}{\mathtt{\,\small\textbf+\,}}{\mathtt{53}} = {\frac{{\mathtt{11}}}{{\mathtt{3}}}} \Rightarrow \left\{ \begin{array}{l}{\mathtt{x}} = {\mathtt{\,-\,}}{\frac{\left({\sqrt{{\mathtt{1\,335}}}}{\mathtt{\,\times\,}}{i}{\mathtt{\,\small\textbf+\,}}{\mathtt{21}}\right)}{{\mathtt{6}}}}\\
{\mathtt{x}} = {\frac{\left({\sqrt{{\mathtt{1\,335}}}}{\mathtt{\,\times\,}}{i}{\mathtt{\,-\,}}{\mathtt{21}}\right)}{{\mathtt{6}}}}\\
\end{array} \right\} \Rightarrow \left\{ \begin{array}{l}{\mathtt{x}} = {\mathtt{\,-\,}}\left({\frac{{\mathtt{7}}}{{\mathtt{2}}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{6.089\: \!608\: \!635\: \!484\: \!241\: \!2}}{i}\right)\\
{\mathtt{x}} = {\mathtt{\,-\,}}{\frac{{\mathtt{7}}}{{\mathtt{2}}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{6.089\: \!608\: \!635\: \!484\: \!241\: \!2}}{i}\\
\end{array} \right\}$$

$$3x^2+21x+148=0\\\\
x=\frac{-21\pm\sqrt{1335}}{6}\qquad \mbox{That bit is correct}\\\\
\mbox{so it is only the coefficient of i that is in question}$$   

From my hand held casio calculator it is   6.089608635  so to 10 significant figures it is correct.

Okay, from further checking it appears to be correct to 12 significant figures the last 5 digits may have rounding error.

If you want an exact answer your would leave it as a surd.  

Simple interest is given by:

I = Prt     where

I = accumulated interest

P = amount invested = $200

r = the interest rate = 10% = .10

r = the time = 5 years

So we have

I = 200(.10)(5) =  $100

3x/5+2=8  

Let's multiply through by 5 on both sides to "clear" the fraction

5(3x/5) + 5(2) = 5(8)

3x + 10  = 40      Subtract 10 from both sides

3x = 30               Divide both sides by 3

x = 10

And that's it.....you should check to see that this answer is correct by substituting it back into the original equation.

For the first one, we have

cos²x - sin²x = -1

Note that sin²x = 1 - cos²x       So we have

cos²x - (1 - cos²x ) = -1

2cos²x - 1 = -1            add 1 to both sides

2cos²x = 0                   divide by 2 on both sides

cos²x = 0                     take the suare root of both sides

cosx = 0                       So x = pi/2 and x =3pi/2

For the second one, we have

1 + √(3) tan(2x)  = 0       Subtract 1 from both sides

√(3) tan(2x)  =-1             Divide both sides by √(3)

tan(2x) = -1/√(3)

Note that tan(x) = -1/√(3) at  150 degrees and at 330 degrees

So tan(2x) = -1/√(3) at 75 degrees and at 165 degrees

And converting these to rads, we have x = (5pi)/12 and x = (11pi)/12

1+1=2