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OR on the web2 calc it is '2nd' function on the top row.   

how does $${\left({\frac{{\mathtt{3}}}{{\mathtt{4}}}}\right)}^{{\mathtt{n}}} = {\mathtt{0.05}}$$

The amount of old water y is found with the equation, with n being the number of refills:

 $$y_{n}=\frac{3}{4}*y_{n-1}$$

This can be changed to a version where $$y_{n-1}$$ is irrelevant to $$y_{n}$$:

$$y_{n}=(\frac{3}{4})^{n}*y_{0}$$

With $$y_{0}$$ being the starting amount of water.

We are considering percentages hence we divide $$y_{n}$$ by $$y_{0}$$:

$$\frac{y_{n}}{y_{0}}=\frac{(\frac{3}{4})^{n}*y_{0}}{y_{0}}=(\frac{3}{4})^{n}$$

Now we can equate $$\frac{y_{n}}{y_{0}}$$ with the desired percentage and the amount of required refills:

$$\frac{y_{n}}{y_{0}}=(\frac{3}{4})^{n}=0.05$$

$$n=\frac{\log{0.05}}{\log{\frac{3}{4}}}\approx10.4$$

You'll need to refill 11 times to achieve a pollution level of 5%, you can figure the second percentage out for yourself. :)

what two numbers would multiply to -1040 & add up to be 14

$$\\x^2+px+q=0 \quad
\begin{array}{rcrcr}
x_1+x_2&=&14&=&-p\\
x_1x_2&=&-1040&=&q\\
\end{array} \quad
x^2-14x-1040=0$$

$$\underbrace{
\left(
x-\frac{14}{2}
\right)^2}
_{x^2-14x+\frac{14^2}{4}}
-\frac{14^2}{4}-1040=0$$

$$\left(
x-7\right)^2=1040 + 49$$

$$\left(
x-7\right)^2=1089 \quad | \quad \pm \sqrt{}$$

$$x-7=\pm 33$$

$$x_1 = 33 + 7 = 40$$

$$x_2 = -33 + 7 = -26$$

tg(x)= ???? cos(x)

$$tg{(x)} = \sqrt { \frac{1-\cos{(2x)}}{1+\cos{(2x)}}}$$

Example:

$$tg{(45)} = \sqrt { \frac{1-\cos{(90)}}{1+\cos{(90)}}} = \sqrt{\frac{1}{1}} = 1 \quad ok!$$

The line that passes through (1,5) and (4,-4) 

Point 1: $$x_1 = 1, y_1=5$$

Point 2: $$x_2=4, y_2=-4$$

$$m=\frac{y_2-y_1}{x_2-x_1}=\frac{y-y_1}{x-x_1}$$

$$\begin{array}{rcl}
(x-x_1)(y_2-y_1) & = & (y-y_1)(x_2-x_1)\\
x(y_2-y_1)-x_(y_2-y_1) & = & y(x_2-x_1) - y_1(x_2-x_1)\\
y(x_2-x_1) &=& x(y_2-y_1)-x_1(y_2-y_1) + y_1(x_2-x_1) \quad | \quad : (x_2-x_1) \\\\
y &=& \left(
\frac{y_2-y_1}{x_2-x_1}
\right)x -x_1 \left(
\frac{y_2-y_1}{x_2-x_1}\right) + y_1\\\\
y &=& \underbrace{
\left(
\frac{y_2-y_1}{x_2-x_1} \right)}_{m}
x +
\underbrace{
\frac{y_1x_2-x_1y_2}{x_2-x_1} }_{b}
\end{array}$$

$$y =\left(
\frac{y_2-y_1}{x_2-x_1} \right)
x +
\frac{y_1x_2-x_1y_2}{x_2-x_1}$$

$$y =\left(
\frac{-4-5}{4-1} \right)
x +
\frac{5*4-1(-4)}{4-1}$$

$$y =\left(
\frac{-9}{3} \right)
x +
\frac{20+4 }{3}$$

$$y =-3x +8$$

All you have to do is collect like terms:

9.6y + 1.1y - 18.4 - 6.2

Can you go from here?

sqrt(10) /2 is not rational because sqrt(10) is irrational.

You can use the "-" key located next to the "0" on top of the keyboard.

Alternatively, you can press the "-" under "X" on the calculator on the home page.

4(8-z) - 50 = 26z - 6 (3+5z)      simplify

32 - 8z - 50 = 26z - 18 - 30z     combine like terms

-18 - 8z = -4z - 18     add 18 to both sides

-8z = -4z   divide by -4 on both sides

2z = 0        divide by 2 on both sides

z = 0

1296^3/4 =

(1296^1/4)³ =

(6)³ =

216

Here's a nice method for this....it is easy to understand and apply.....!!!

9 1/6 isn't a whole number...we can write it as an improper fraction or as a decimal.

For the improper fraction, multiply the 6 in the denominator times the whole number 9 = 54 and add the 1 in the numerator = 55....put this result over the denominator and we get 55/6

 And 1/6 = .1666

So....... 9 + .1666  =   9.1666    ...the "6" repeats...!!!

Rate  x Time  = Distance

If he walks x hrs., then he runs  1.5 - x  hours

Then

3mph *(x) hrs. + 5m[h * (1.5 - x) hts  = 6 miles    .....just for the heck of it, let's solve this

3x + 7.5 - 5x  = 6

-2x + 7.5 = 6       subtract 7.5 from each side

-2x = -1.5            divide by -2 on each side

x = -1.5 / -2   =    3/4

So he walks 3/4 of an hour. And he runs for the same time. And the distance he walks is

3mph * (3/4 hr) = 9/4 mi. = 2.25 miles.

And the distance he runs is

5mph * (3/4) = 15/4 = 3.75 miles

And 2.25 mi and 3.75 mi = 6 mi.

7/8 + 1/7t = 2.... solve equation no decimals please

$$\begin{array}{rcl}
\frac{7}{8}
+
\frac{1}{7}t & = & 2 \quad | \quad +\frac{9}{8}\\\\
\frac{16}{8}
+
\frac{1}{7}t & = & 2 +\frac{9}{8}\\\\
\frac{1}{7}t & = & \frac{9}{8} \quad | \quad *\frac{7}{1}\\\\
t & = & \frac{7*9}{8} \\\\
t & = & \frac{63}{8} \\\\
t & = & \frac{64-1}{8} \\\\
t & = & 8-\frac{1}{8}
\end{array}$$

please answer asap i really need to figure this out.. im really bad with fractions

2.5 miles of a mile 

1,760 yards = 1 mile.

Since there are 5280 ft in a mile and 3 ft in a yard, we have

5280 / 3 = 1760 yds

Use the calculator located on the home page --> Click "Home" next to "Forum" on the top of the website.

Do you mean like:

Given ratios of 5:8, 6:7, etc. --> 5/8, 6/7???

Let's use x and y for the two numbers and set up equations:

x*y = -1040

x + y = 14

x + y = 14

y = 14 - x

Let's substitute that into the first equation

x*(14 - x) = -1040.

14x - x^2 = -1040.

Move over everything to the write to get:

x^2 - 14x - 1040 = 0.

Now, let's use the quadratic formula to solve this:

6x+3=2x+8

Subtract 2x and 3 from both sides

4x = 5        divide both sides by 4

x = 5/4

2/3 = 0.66666667 in decimal form so you move the decimal point over two times 66.666667 then you round to the nearest number which would then be 66.7%