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0.346 recurring as a fraction?

\(\begin{array}{|rcll|} \hline 1000\cdot 0.\overline{346} &=& 346.\overline{346} \\ 1\cdot 0.\overline{346} &=& 0.\overline{346} \\\\ 1000\cdot 0.\overline{346} - 1\cdot 0.\overline{346} &=& 346.\overline{346}-0.\overline{346} \\ 999\cdot 0.\overline{346} &=& 346 \\ 0.\overline{346} &=& \frac{346}{999} \\ \mathbf{ 0.346\ recurring } &\mathbf{=}& \mathbf{ \frac{346}{999} }\\ \hline \end{array}\)

0.2 recurring as a fraction?

\(\begin{array}{|rcll|} \hline 10\cdot 0.\bar{2} &=& 2.\bar{2} \\ 1\cdot 0.\bar{2} &=& 0.\bar{2} \\\\ 10\cdot 0.\bar{2} - 1\cdot 0.\bar{2} &=& 2.\bar{2}-0.\bar{2} \\ 9\cdot 0.\bar{2} &=& 2 \\ 0.\bar{2} &=& \frac{2}{9} \\ \mathbf{ 0.2\ recurring } &\mathbf{=}& \mathbf{ \frac{2}{9} }\\ \hline \end{array} \)

V= Wurzel Fz *r/m Was mach ich,wenn ich m nicht weiß.

Muss ich dann anstatt m

g nehmen?

\(\begin{array}{|rcll|} \hline v&=& \sqrt{ \frac{F_z \cdot r} {m} } \quad & | \quad F_z = m\cdot g \\ v&=& \sqrt{ \frac{ m\cdot g \cdot r} {m} } \\ v&=& \sqrt{ g \cdot r } \quad & | \quad g=9,81 \frac{m}{s} \\ \hline \end{array} \)

Zwei Erntehelfer ernten zusammen an drei Tagen 270 Kilogramm Birnen.

Wie viele Birnen ernten dann fünf Erntehelfer an 4 Tagen?

\(\begin{array}{|rcll|} \hline \dfrac{270\ \text{kg}} { 2\cdot 3\ \text{Tage} } &=& \dfrac{x} {5\cdot 4\ \text{Tage}} \\\\ \dfrac{270\ \text{kg}} { 6 } &=& \dfrac{x} {20} \\\\ 45\ \text{kg} &=& \dfrac{x} {20} \\\\ 20\cdot 45\ \text{kg} &=& x \\\\ 900\ \text{kg} &=& x \\ \hline \end{array} \)

Es werden von 5 Erntehelfern an 4 Tagen 900 kg Birnen geerntet.

a television is on sale for $449.95.this is $30 off the original price.

what is the percent of the discount?

\(\begin{array}{|rcll|} \hline (449.95+30)\cdot (100\ \%-x) &=& 449.95 \\ 479.95\cdot (100\ \%-x) &=& 449.95 \\ 479.95\cdot (1-x) &=& 449.95 \\ 479.95 -479.95x &=& 449.95 \quad & | \quad \cdot (-1) \\ -479.95 +479.95x &=& -449.95 \quad & | \quad +479.95\\ 479.95x &=& 479.95-449.95 \\ 479.95x &=& 30 \\ x &=& \frac{30}{479.95} \\ x &=& 0.06250651109 \\ x &=& 6.250651109 \ \% \\ \hline \end{array} \)

The percent of the discount is \(\approx\) 6.25 %

how to multiply mixed numbers 5 5/8 x 8 5/6

\(\begin{array}{|rcll|} \hline && 5 \ \frac{5}{8} \times 8 \ \frac{5}{6} \\ &=& \frac{5\cdot 8+5}{8} \times \frac{8\cdot 6 + 5}{6} \\ &=& \frac{40+5}{8} \times \frac{48 + 5}{6} \\ &=& \frac{45}{8} \times \frac{53}{6} \\ &=& \frac{45\cdot 53}{8\cdot 6} \\ &=& \frac{2385}{48} \\ &=& 49\ \frac{33}{48} \\ \hline \end{array}\)

The tires on your bicycle have a diameter of 22 inches.
How many rotations does each tire make when you travel 800 feet?
Round your answer to the nearest whole number.

Let p = perimeter circle
Let d = diameter circle
Let n = number of rotations

perimeter circle:
\(\begin{array}{|rcll|} \hline p &=& d\cdot \pi \quad &| \quad d = 22\ in. \\ p &=& 22\cdot \pi \ in. \\ \hline \end{array}\)

rotations:

\(\begin{array}{|rcll|} \hline n &=& \dfrac{ 800\ feet \cdot \frac{12\ in.}{1\ feet}} {p} \quad &| \quad 1 feet = 12\ inches \\ n &=& \dfrac{800\cdot 12}{22\cdot \pi} \\ n &=& 138.898859426 \text{ rotations } \\ \hline \end{array}\)

Round your answer to the nearest whole number: 139 rotations

What is 4i^2

\(\begin{array}{|rcll|} \hline && 4i^2 \quad &| \quad i^2 = -1 \\ &=& 4\cdot(-1) \\ &=& -4\\ \hline \end{array}\)

What is (x+4)^4 expanded

\(\small{ \begin{array}{|rcll|} \hline (x+4)^4 &=& [(x+4)^2]^2 \quad &| \quad (x+4)^2 = x^2+8x+16 \\ &=& (x^2+8x+16)^2 \\ &=& [x^2+(8x+16)]^2 \\ &=& (x^2)^2 + 2\cdot x^2 \cdot (8x+16)+(8x+16)^2 \quad &| \quad (8x+16)^2 = (8x)^2+2\cdot 8x \cdot 16 + 16^2 \\ &=& (x^2)^2 + 2\cdot x^2 \cdot (8x+16)+(8x)^2+2\cdot 8x \cdot 16 + 16^2 \\ &=& x^4 + 2\cdot x^2 \cdot 8x +2\cdot x^2 \cdot 16 +64x^2+ 256x + 256 \\ &=& x^4 + 16 x^3 +32x^2 +64x^2+ 256x + 256 \\ &=& x^4 + 16\ x^3 +94x^2+ 256x + 256 \\ \hline \end{array} }\)