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1.1=m-0.9. 1.1+0.9=2   2-0.9=1.1 

(-8)^-6 =

1 / (-8)⁶ =

1 / 262144

$$\\28 log(x) = 48\\\\
log(x)=48/28\\\\
10^{log(x)}=10^{48/28}\\\\
x=10^{48/28}\\\\$$

$${{\mathtt{10}}}^{\left({\frac{{\mathtt{48}}}{{\mathtt{28}}}}\right)} = {\mathtt{51.794\: \!746\: \!792\: \!312\: \!1}}$$

this is an approximation.

you need to find the square root of 412.

The square root of 412 is 20.297783130184.

The area of a square is just = (side length)²

So we have.........

412cm² = s²

To find the side length, we would take the square root of 412

But, the square root of 412 must be between 20 and 21, because 20² = 400 and 21² = 441

So the side length estimate is between 20 and 21 cm in length

(x + y)^2  =  (x + y)(x + y)  =  x² + xy  + xy + y²  =  x² + 2xy + y²

(x + y)^3  =  (x + y)(x + y)(x +y)                                                                                                                                =  (x + y)(x² + 2xy + y²)  =  x³ + 2x²y + xy² + x²y + 2xy² + y³  =  x³ + 3x²y + 3xy²+ y³ 

(x + y)^4  =  (x + y)(x + y)(x +y)(x + y)  =  (x + y)(x³ + 3x²y + 3xy²+ y³)                                                                 =  x^4 + 3x³y + 3x²y² + xy³ + x³y + 3x²y² + 3xy³ + y^4                                                                           = x^4 + 4x³y + 6x²y² + 4xy³ + y^4

Look at the coefficients:

(x + y)^2  -->  1  2  1

(x + y)^3  -->  1  3  3  1

(x + y)^4  -->  1  4  6  4  1

Can you find the pattern?  You may want to look up "Pascal's Triangle" for a fuller explanation.

If you're still confused, ask again ...

35 x 26  =  910

(1/2) · (8 - x)  =  (8 - x) / 2

So, we have:         (8 - x) / 2  =  8 - x / 2

Multiply each term by 2 to eliminate fractions:    8 - x  =  16 - x

Add  x  to both sides:  8  =  16

Since this is not possible the original "equation" was not really an equation.

Thank you so much for explaining, this helped me not only with that problem but with all the others!

-Linlee Y.

Thank you! This answered my question completely!

Thank you! This helped a lot!

-Linlee Y.

If the diameter is  1.905 cm  then the radius is  0.9525 cm.

V  =  π · (0.9525 cm)² · (0.124 cm)   =  0.335 cm³

That's interesting. what grade are you in?

Cats have eyes; potatoes have eyes; so count the number of eyes on the potato and divide by 2.

These seem to be the three sides of a triangle. Is it a right triangle; and, if so where is the right angle?

A rational number is a number that can be put into the form  a/b  where  a  and  b  are integers and b ≠ 0.

Every common fraction is a rational number. Every mixed fration is a rational number.

Decimals that terminate (such as 12.375) or repeat (such as -2.34343434...) are rational numbers.

12.375  =  12 3/8  =  99/8.                -2.3434...  =  -2 34/99  =  -232/99  

Decimals that neither terminate nor repeat, such as √2 and π are not rational.

The square root of 121= 11.....and any integer is a rational quantity....

√121 =  11    because   11 x 11 = 121

It is a rational number; not an irrational number.

The Pythagorean Theorem is  c²  = a² + b²

where  c  is the hypotenuse and  a  and  b  are the other two sides.

For this problem,  c = √74  and  a = 5:    ( √74 )²  =  ( 5 )² +  b²

     --->  74  =  25 + b²

     --->  49  =  b²

     --->  b  =  √49

     --->  b  =  7

[The sides  a  and  b  are interchangeable.]

The numbers multiplied together to equal 36 are 1 and 36, 2 and 1, 3 and 12, 4 and 9, and 6 and 6.

-Linlee Y.

you multiply that number by itself 3 times

If you are divisible by 9, then you are divisible by 3. Then, the sum of your digits is also divisible by 3.

But you must be even, since you are divisible by 2.

And if you're divisible by 2 and 9, then you are divisible by 18, as well.

So the possibilities are 426, 432, 438, 444 and 448

And 432 is the answer.  No other answers are possible because all of the other numbers lie within 18 integers - positive or negative - from 432.

This is another example where reading the question properly is paramount.

Thanks Chris.

Thanks to anon and Alan as well.  Mistakes like this are easy to make.

If tan x = 2, then y / x = 2 / 1

Then, using, √(x² + y² ) = r 

√(2² + 1²) = √5 = r

So sin x = y/r =  2/√5

And using

cos 2x = 1 - 2(sin x)²

cos 2x = 1 - 2(2/√5)²

cos 2x = 1 - 2 (4/5)

cos 2x = 1 - 8/5

cos 2x = -3/5 = -(.6)     .....as geno found   !!!!!!!

$${\frac{{\mathtt{5}}}{{\mathtt{x}}}} = {\mathtt{5}}{\mathtt{\,\times\,}}{\mathtt{x}}{\mathtt{\,-\,}}{\frac{{\mathtt{6}}}{{{\mathtt{x}}}^{{\mathtt{2}}}}}{\mathtt{\,-\,}}{\mathtt{4}} \Rightarrow \left\{ \begin{array}{l}{\mathtt{x}} = {\frac{{\mathtt{91}}{\mathtt{\,\times\,}}\left({\frac{{\sqrt{{\mathtt{3}}}}{\mathtt{\,\times\,}}{i}}{{\mathtt{2}}}}{\mathtt{\,-\,}}{\frac{{\mathtt{1}}}{{\mathtt{2}}}}\right)}{\left({\mathtt{225}}{\mathtt{\,\times\,}}{\left({\frac{{\sqrt{{\mathtt{8\,434}}}}}{\left({\mathtt{25}}{\mathtt{\,\times\,}}{{\mathtt{3}}}^{\left({\frac{{\mathtt{3}}}{{\mathtt{2}}}}\right)}\right)}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{2\,539}}}{{\mathtt{3\,375}}}}\right)}^{\left({\frac{{\mathtt{1}}}{{\mathtt{3}}}}\right)}\right)}}{\mathtt{\,\small\textbf+\,}}{\left({\frac{{\sqrt{{\mathtt{8\,434}}}}}{\left({\mathtt{25}}{\mathtt{\,\times\,}}{{\mathtt{3}}}^{\left({\frac{{\mathtt{3}}}{{\mathtt{2}}}}\right)}\right)}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{2\,539}}}{{\mathtt{3\,375}}}}\right)}^{\left({\frac{{\mathtt{1}}}{{\mathtt{3}}}}\right)}{\mathtt{\,\times\,}}\left({\mathtt{\,-\,}}{\frac{{\sqrt{{\mathtt{3}}}}{\mathtt{\,\times\,}}{i}}{{\mathtt{2}}}}{\mathtt{\,-\,}}{\frac{{\mathtt{1}}}{{\mathtt{2}}}}\right){\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{4}}}{{\mathtt{15}}}}\\
{\mathtt{x}} = {\left({\frac{{\sqrt{{\mathtt{8\,434}}}}}{\left({\mathtt{25}}{\mathtt{\,\times\,}}{{\mathtt{3}}}^{\left({\frac{{\mathtt{3}}}{{\mathtt{2}}}}\right)}\right)}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{2\,539}}}{{\mathtt{3\,375}}}}\right)}^{\left({\frac{{\mathtt{1}}}{{\mathtt{3}}}}\right)}{\mathtt{\,\times\,}}\left({\frac{{\sqrt{{\mathtt{3}}}}{\mathtt{\,\times\,}}{i}}{{\mathtt{2}}}}{\mathtt{\,-\,}}{\frac{{\mathtt{1}}}{{\mathtt{2}}}}\right){\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{91}}{\mathtt{\,\times\,}}\left({\mathtt{\,-\,}}{\frac{{\sqrt{{\mathtt{3}}}}{\mathtt{\,\times\,}}{i}}{{\mathtt{2}}}}{\mathtt{\,-\,}}{\frac{{\mathtt{1}}}{{\mathtt{2}}}}\right)}{\left({\mathtt{225}}{\mathtt{\,\times\,}}{\left({\frac{{\sqrt{{\mathtt{8\,434}}}}}{\left({\mathtt{25}}{\mathtt{\,\times\,}}{{\mathtt{3}}}^{\left({\frac{{\mathtt{3}}}{{\mathtt{2}}}}\right)}\right)}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{2\,539}}}{{\mathtt{3\,375}}}}\right)}^{\left({\frac{{\mathtt{1}}}{{\mathtt{3}}}}\right)}\right)}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{4}}}{{\mathtt{15}}}}\\
{\mathtt{x}} = {\left({\frac{{\sqrt{{\mathtt{8\,434}}}}}{\left({\mathtt{25}}{\mathtt{\,\times\,}}{{\mathtt{3}}}^{\left({\frac{{\mathtt{3}}}{{\mathtt{2}}}}\right)}\right)}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{2\,539}}}{{\mathtt{3\,375}}}}\right)}^{\left({\frac{{\mathtt{1}}}{{\mathtt{3}}}}\right)}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{91}}}{\left({\mathtt{225}}{\mathtt{\,\times\,}}{\left({\frac{{\sqrt{{\mathtt{8\,434}}}}}{\left({\mathtt{25}}{\mathtt{\,\times\,}}{{\mathtt{3}}}^{\left({\frac{{\mathtt{3}}}{{\mathtt{2}}}}\right)}\right)}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{2\,539}}}{{\mathtt{3\,375}}}}\right)}^{\left({\frac{{\mathtt{1}}}{{\mathtt{3}}}}\right)}\right)}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{4}}}{{\mathtt{15}}}}\\
\end{array} \right\} \Rightarrow \left\{ \begin{array}{l}{\mathtt{x}} = {\mathtt{\,-\,}}{\mathtt{0.478\: \!747\: \!068\: \!016\: \!753\: \!2}}{\mathtt{\,-\,}}{\mathtt{0.673\: \!492\: \!074\: \!363\: \!498\: \!9}}{i}\\
{\mathtt{x}} = {\mathtt{\,-\,}}{\mathtt{0.478\: \!747\: \!068\: \!016\: \!753\: \!2}}{\mathtt{\,\small\textbf+\,}}{\mathtt{0.673\: \!492\: \!074\: \!363\: \!498\: \!9}}{i}\\
{\mathtt{x}} = {\mathtt{1.757\: \!494\: \!136\: \!033\: \!506\: \!4}}\\
\end{array} \right\}$$

Yuk!  Let's look at this

$${\frac{{\mathtt{5}}}{{\mathtt{x}}}} = {\mathtt{5}}{\mathtt{\,\times\,}}{\mathtt{x}}{\mathtt{\,-\,}}{\frac{{\mathtt{6}}}{{{\mathtt{x}}}^{{\mathtt{2}}}}}{\mathtt{\,-\,}}{\mathtt{4}}$$

There are no real roots.

More inspection here.