All Answers 358093 Answers

When the equation is in this form, the slope is the number multiplying the x.  The other constant (including the sign) is the y-intercept.

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If you meant to write 12x³ - 27x² - 40x + 90 then

$${factor}{\left({\mathtt{12}}{\mathtt{\,\times\,}}{{\mathtt{x}}}^{{\mathtt{3}}}{\mathtt{\,-\,}}{\mathtt{27}}{\mathtt{\,\times\,}}{{\mathtt{x}}}^{{\mathtt{2}}}{\mathtt{\,-\,}}{\mathtt{40}}{\mathtt{\,\times\,}}{\mathtt{x}}{\mathtt{\,\small\textbf+\,}}{\mathtt{90}}\right)} = \left({\mathtt{4}}{\mathtt{\,\times\,}}{\mathtt{x}}{\mathtt{\,-\,}}{\mathtt{9}}\right){\mathtt{\,\times\,}}\left({\mathtt{3}}{\mathtt{\,\times\,}}{{\mathtt{x}}}^{{\mathtt{2}}}{\mathtt{\,-\,}}{\mathtt{10}}\right)$$ 

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You can use the calculator here, noting that there are 60 minutes in a degree:

$$\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{tan}}{\left({\mathtt{29}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{12}}}{{\mathtt{60}}}}\right)} = {\mathtt{0.558\: \!881\: \!109\: \!6}}$$

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I don't think you can solve this.....

Well, the starting value (N₀ in my notation, A in yours) is 2000. This is the value at time t = 0.

At time t = 4 the value of N (my notation) or P (your notation) is 2200. 

So at time t = 4 we have 2200 = 2000*e^k*4

Divide both sides by 2000

2200/2000 = e^k*4

or 1.1 = e^k*4

Now take logs of both sides:

ln(1.1) = ln(e^k*4)

or ln(1.1) = k*4    (because ln(e^x) = x)

Divide both sides by 4

ln(1.1)/4 = k

$${\mathtt{k}} = {\frac{{ln}{\left({\mathtt{1.1}}\right)}}{{\mathtt{4}}}} \Rightarrow {\mathtt{k}} = {\mathtt{0.023\: \!827\: \!544\: \!951\: \!081\: \!2}}$$

Now use this value of k to find N (my notation) or P (your notation) at time t = 9

P = 2000*e^{0.023827544951*9}

$${\mathtt{P}} = {\mathtt{2\,000}}{\mathtt{\,\times\,}}{{\mathtt{e}}}^{\left({\mathtt{0.023\: \!827\: \!544\: \!951}}{\mathtt{\,\times\,}}{\mathtt{9}}\right)} \Rightarrow {\mathtt{P}} = {\mathtt{2\,478.355\: \!127\: \!582\: \!545\: \!6}}$$

or P ≈ 2478

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(X+3)^2$${{\mathtt{X}}}^{{\mathtt{2}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{6}}{\mathtt{\,\times\,}}{\mathtt{X}}{\mathtt{\,\small\textbf+\,}}{\mathtt{9}}$$

it is true. we can write it anyway.

o okay but i still dont understand even after reading the other answer to the question 

You can use the calculator here to find the prime factors:

$${factor}{\left({\mathtt{217}}\right)} = {\mathtt{7}}{\mathtt{\,\times\,}}{\mathtt{31}}$$

If you are after all the factors, not just the prime ones, then, in this case, the only others are 1 and 217 itself.

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Your expression is mathematically the same as mine Anonymous.  You've just used different symbols!

no its P=Ae^kt 

A missing side of what?  And what information do you have for whatever it is?

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Use N = 56e^k*t where t is the time in years from 1995 and k is an. as yet, unknown rate constant.

Find k from the 2002 data:   59 = 56e^k*7   (because 2002 - 1995 = 7)

Divide through by 56, take logs, then divide by 7 to get k = ln(59/56)/7

$${\mathtt{k}} = {\frac{{ln}{\left({\frac{{\mathtt{59}}}{{\mathtt{56}}}}\right)}}{{\mathtt{7}}}} \Rightarrow {\mathtt{k}} = {\mathtt{0.007\: \!455\: \!107\: \!595\: \!795\: \!7}}$$

In 2016 t = 2016 - 1995 = 21, so
N = 56e^0.007455*21

$${\mathtt{N}} = {\mathtt{56}}{\mathtt{\,\times\,}}{{\mathtt{e}}}^{\left({\mathtt{0.007\: \!455}}{\mathtt{\,\times\,}}{\mathtt{21}}\right)} \Rightarrow {\mathtt{N}} = {\mathtt{65.490\: \!604\: \!574\: \!065\: \!260\: \!8}}$$

or N ≈ 65 million

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5/11, 3/7, 4/9, 13/30, 17/39 if these fractions are arranged from least to greatest, which will be the third  ?  

I.  decimal: $$\small{\text{
1. $ \frac{ 3 }{ 7 } = 0.429 \quad $
2. $ \frac{13}{30 } = 0.4\overline{3} \quad $
3. $ \frac{17}{39} = 0.4359 \quad $
4. $ \frac{4}{9 } = 0.\overline{4} \quad $
5. $ \frac{ 5}{11} = 0.\overline{45} \quad $
}}$$

II. fraction:

$$\small{\text{
1. $ \frac{ 3 }{ 7 } = \frac{38619}{90090} \quad $
2. $ \frac{13}{30 } = \frac{39039}{90090} \quad $
3. $ \frac{17}{39} = \frac{39270}{90090} \quad $
4. $ \frac{4}{9 } = \frac{40040}{90090} \quad $
5. $ \frac{ 5}{11} = \frac{40950}{90090} $
}}$$

http://web2.0calc.com/questions/how-do-i-type-in-fractions

Yes Heueka but how do you suggest anon derives this order?

That is a good start anon :)

They are both equally distant from 8.5

They are both real numbers

They are both integers

They are both natural numbers 

They are both positive numbers

They are both factors of 72, 144,....... etc

They are both single digit (base 10)

They are both assumed to be base ten

When raised to the power of 0  they both become 1

When multiplied by 0 they both become 0

When multiplied by infinity they both become infinity

When they are subtracted from themself they both become 0

When divided by themselves they both become 1

there are a few - there are lots more :)

5/11, 3/7, 4/9, 13/30, 17/39

$$\frac{ 3 }{ 7 } < \frac{13}{30 } < \frac{17}{39} < \frac{4}{9 } < \frac{ 5}{11}$$

17/39 will be the third

Well there are different methods

They are all quite close in value and all less than a half.

It is probably easiest to change them into decimals using a calculator and then compare the decimal answers.

They share a common factor: 1

They have the same vowels in their spelling: e and i

Each has a factor which is itself a square: 4 & 9

There is a calc on the home page 

The original pops were 100% of the original - and bot hthe same

in 1995 town A was 100+60= 160%

in 1995 town B was 160-60 =40%

$$\\\frac{40\%}{160\%}*100\%\\\\
=\frac{4}{16}*100\%\\\\
=25\%$$

what two numbers multiply to 394.24 and adds up to 40 ?

$$\small{\text{
\boxed{
\begin{array}{rcl}
x_1+x_2 &=& 40 \\ \quad x_1*x_2 &=& 394.24
\end{array}
}
}}$$

$$\small{\text{
set $x^2 - (x_1+x_2)x + x_1*x_2 = 0$
}}
$\\$ \small{\text{
than we have $x^2 - 40x + 394.24 = 0$
}}
$\\$ \small{\text{
and the solution for $x_1$ and $x_2$ is: $\frac{ -b\pm\sqrt{b^2-4ac} } {2a}$
}}
$\\$ \small{\text{
$x_{1,2}=\frac{ 40\pm\sqrt{1600-4*394.24 } } {2}
= \frac{ 40\pm\sqrt{23.04} }{2}
= \frac{ 40\pm4.8 }{2}
$
}}
$\\$ \small{\text{
$x_1=\frac{ 40+4.8 }{2} = 22.4
$
}}
}}
$\\$ \small{\text{
$x_2=\frac{ 40-4.8 }{2} = 17.6$
}}$$

I think GL has, very sensibly, first considered a single unit:

0.4*x + 0.7*(1-x) = 1

-0.3x +0.7 = 1

-0.3x = -0.1

x = 1/3

so, with 30L you simply require (1/3)*30 L

No doubt GL considered the lead up to the final equation too obvious to be worth spelling out!!

6 + 2y = 5     subtract 6 from both sides

2y = -1         divide both sides by 2

y = -1/2

and there you go.....!!!