$\displaystyle \dfrac{1}{2}+\dfrac{1}{4}+...+\dfrac{1}{14}=\sum_{k=1}^{k=7} {\dfrac{1}{2k}}\\\\=\dfrac{1}{2}\dfrac{420+210+140+105+84+70+60}{5*7*3*2*2}\\\\=\dfrac{1}{2}\dfrac{1089}{420}\\\\=\dfrac{1089}{840}=1.296429...$

Thank you.

3 0

3 years ago

You cut a 54-inch rope into four pieces. Twoof the pieces are the same length, a thirdpiece is twice as long as each of the twoe

antiseptic1488 [7]

Let's use the variable x to represent the length of the first and second pieces.

If the third piece has twice the length of the first and second, its length is 2x.

If the fourth piece has half the length of the first and second, its length is 0.5*x.

Adding all four pieces and equating to 54 inches, we have:

$\begin{gathered} x+x+2x+0.5x=54 \\ 4.5x=54 \\ x=\frac{54}{4.5} \\ x=12 \end{gathered}$

So the length of each piece is:

12 inches, 12 inches, 24 inches and 6 inches.

5 0

1 year ago

-9x+8=26 i need help

Flura [38]

The answer is -2.

im sorry if the work is messy.

4 0

3 years ago