(1/27) x+2 +1=(1/3) x-3 +1
(Headline of the task)
\(\frac{1}{27}x+2+1=\frac{1}{3}x-3+1\)
\((\frac{1}{3}-\frac{1}{27})x=2+1+3-1\)
\(\frac{8}{27}x=5\)
\(x=\frac{5\times 27}{8}\)
\(x=16\frac{7}{8}\) !
It is 1/343, or 0.0029154518950437
\(95+25\div 83\times 64\\ = 95 + 25\times 64 \div 83\\ = 95 + 1600 \div 83\\ = 95 + \dfrac{1600}{83}\\ = 95 + 19\dfrac{23}{83}\\ =114\dfrac{23}{83}\)
\(\color{blue}{\begin{array}{rll}(\dfrac{1}{27})^{x+2}+1&=&(\dfrac{1}{3})^{x-3}+1\\ (3^{-3})^{x+2}&=&(3^{-1})^{x-3}\\ 3^{-3x-6}&=&3^{3-x}\\ -3x - 6&=& 3-x\\ -2x&=&9\\ x&=&-\dfrac{9}{2}\end{array}}\)
#BlackLaTeXIsBoring.
Use your own calculator!! Each IP only have 3 chances to ask a question here using the identity 'Guest' so seize your asking chance unless you want to register to be a member!!
\(\color{olive}{\dfrac{\sqrt{71.15}}{107.9-70.4}\\ = 0.224934558}\\ \color{orange}\text{according to my calculator}\)
I assume you mean \(\pi\) by 3.14.
\(\begin{array}{rll}131 &=& \dfrac{1}{3}\cdot \pi \cdot r^2 \cdot 10\\ 393&=&10\pi r^2\\ r^2 &=& \dfrac{393}{10\pi}\\ r&=&\sqrt{\dfrac{393}{10\pi}}\end{array} \)
which is approx. 3.53688825481142
Thanks everyone :)
Probability of getting 3 odd numbers from the set {1,3,5,7,9,11,13,15} is 1
But Probability of adding 3 odd numbers and getting an even number is 0.
Therefore this problem is impossible.
Assuming that x does not equal zero, translate the following according to exponent law: 5x/5x
\(x\ {\in \mathbb R }\)\(\) \ 0
\(\frac{5x}{5x}=5^1\times x^1 \times 5^{-1}\times x^{-1}=5^{1-1}\times x^{1-1}\)
\(=5^0\times x^0 =1\times 1=1\)
\(\frac{5x}{5x}=1\) !
asinus without login
-x+y=1 2x + y=4
what is the solution?
\(-x+y=1\)
\(y=x+1\)
\(2x+y=4\)
\(2x+(x+1)=4\)
\(3x=3 \)
\(x=1\) !
\(y=2\) !
There's no indication that this is a recurring decimal, so technically it's equal to 333333333/1000000000 .
log2(x)=-3
2-3=1/23=1/8
Hallo, JonathanB
I think it's right.
If the spring extension changes by a small (infinitesimal) distance, dx, then the energy change, dE, is given by Fs*dx.
i.e. dE = Fs*dx or dE/dx = Fs or dE/dx = -kx
Hence E = -(1/2)kx^2
.
Any Help !
Simplify c**p with radicals
\(\begin{array}{|rcll|} \hline && 2\cdot[~\frac14 (\sqrt{5}-1)~]\cdot \sqrt{\frac18\cdot (5+\sqrt{5}) } \\ &=& \frac24\cdot (\sqrt{5}-1)\cdot \sqrt{\frac18\cdot (5+\sqrt{5}) } \\ &=& \frac12\cdot (\sqrt{5}-1)\cdot \sqrt{\frac18\cdot (5+\sqrt{5}) } \\ &=& \frac12\cdot (\sqrt{5}-1)\cdot \frac{\sqrt{ 5+\sqrt{5} } } { \sqrt{8} } \\ &=& \frac{1}{2\cdot \sqrt{8} } \cdot (\sqrt{5}-1)\cdot \sqrt{ 5+\sqrt{5} } \\ &=& \frac{1}{2\cdot \sqrt{8} } \cdot \sqrt{ (\sqrt{5}-1)^2\cdot (5+\sqrt{5}) } \\ &=& \frac{1}{2\cdot \sqrt{8} } \cdot \sqrt{ (5-2\sqrt{5}+1)\cdot (5+\sqrt{5}) } \\ &=& \frac{1}{2\cdot \sqrt{8} } \cdot \sqrt{ (6-2\sqrt{5})\cdot (5+\sqrt{5}) } \\ &=& \frac{1}{2\cdot \sqrt{8} } \cdot \sqrt{ 30+6\sqrt{5}-10\sqrt{5}-2\cdot 5 } \\ &=& \frac{1}{2\cdot \sqrt{8} } \cdot \sqrt{ 30+6\sqrt{5}-10\sqrt{5}-10 } \\ &=& \frac{1}{2\cdot \sqrt{8} } \cdot \sqrt{ 20-4\sqrt{5} } \\ &=& \frac{1}{2\cdot \sqrt{8} } \cdot \sqrt{ 4(5-\sqrt{5}) } \\ &=& \frac{\sqrt{4}}{2\cdot \sqrt{8} } \cdot \sqrt{ 5-\sqrt{5} } \\ &=& \frac{2}{2\cdot \sqrt{8} } \cdot \sqrt{ 5-\sqrt{5} } \\ &=& \frac{1}{ \sqrt{8} } \cdot \sqrt{ 5-\sqrt{5} } \\ &=& \frac{1}{ \sqrt{4\cdot 2} } \cdot \sqrt{ 5-\sqrt{5} } \\ &=& \frac{1}{ \sqrt{4}\cdot \sqrt{2} } \cdot \sqrt{ 5-\sqrt{5} } \\ &=& \frac{1}{ 2\cdot \sqrt{2} } \cdot \sqrt{ 5-\sqrt{5} } \\ &=& \frac{\sqrt{2}} {\sqrt{2}}\cdot \frac{1}{ 2\cdot \sqrt{2} } \cdot \sqrt{ 5-\sqrt{5} } \\ &=& \frac{\sqrt{2}}{ 2\cdot 2 } \cdot \sqrt{ 5-\sqrt{5} } \\\\ &\mathbf{=}& \mathbf{ \frac{\sqrt{2}}{ 4 } \cdot \sqrt{ 5-\sqrt{5} } } \\ &=& 0.58778525229 \\ \hline \end{array}\)
(\(\qquad (\sqrt{10}-\sqrt2)^2\\ \qquad =10+2-\sqrt{40}\\ \qquad=12-2\sqrt{10}\\ \\~\\ \frac{\sqrt{(12-2\sqrt{10})(5+\sqrt5)}}{8}\\ =\frac{\sqrt{60+12\sqrt5-10\sqrt{10}-2\sqrt{50}}}{8}\\ =\frac{\sqrt{60+12\sqrt5-10\sqrt{10}-10\sqrt{2}}}{8}\\\)
Let's see :)
\(2\left(\frac{-1+\sqrt5}{4}\right)\left(\sqrt{\frac{5+\sqrt5}{8}}\;\right)\\ =\left(\frac{-1+\sqrt5}{2}\right)\left(\frac {\sqrt{5+\sqrt5}}{\sqrt8}\;\right)\\ =\left(\frac{-1+\sqrt5}{2}\right)\left(\frac {\sqrt{5+\sqrt5}}{2\sqrt2}\;\right)\\ =\frac{(-1+\sqrt5) \sqrt{(5+\sqrt5) }}{4 \sqrt2 }\\ =\frac{\sqrt2(-1+\sqrt5) \sqrt{(5+\sqrt5) }}{8 }\\ =\frac{(\sqrt{10}-\sqrt2) \sqrt{(5+\sqrt5) }}{8 }\\\)
I haven't checked it. :/
1. Work out the Mean (the simple average of the numbers)
2. Then for each number: subtract the Mean and square the result.
3. Then work out the mean of those squared differences.
4. Take the square root of that and we are done!
thank you so much!
Actually it's right, my other calculator was just wrong.
!
