All Answers 358128 Answers

$$\begin{array}{lcl}
2x^4+3x^3-17x^2-27x-9&=&(\underline{x}+1)(\underline{x}-3)(\underline{ax}+b)(\underline{x}+c) \\
2x^4&=&x*x*ax*x\\
2x^4&=&ax^4 \quad \mbox{(Coefficient comparison 2=a)}
\end{array} \\
\boxed{a=2}$$

$$\begin{array}{rcl}
2x^4+3x^3-17x^2-27x-9&=&(x+\underline{1})(x-\underline{3})(ax+\underline{b})(x+\underline{c}) \\
-9&=&1*(-3)*b*c\\
-9&=&-3bc
\end{array} \\
\boxed{c=\frac{3}{b}}$$

$$\begin{array}{lcl}
(x+1)(x-3)(ax+b)(x+c)&=& (x+1)(x-3)(2x+b)(x+\frac{3}{b}) \quad | \quad x+\frac{3}{b}=0 \quad | *b \quad bx+3=0\\
&=&(x+1)(x-3)(2x+b)(bx+3)
\end{array}$$

$$\begin{array}{lcl}
2x^4+3x^3-17x^2-27x-9&=&(\underline{x}+1)(\underline{x}-3)(\underline{2x}+b)(\underline{bx}+3) \\
2x^4&=&x*x*2x*bx\\
2x^4&=&2bx^4 \quad \mbox{(Coefficient comparison 2=2b)}
\end{array} \\
\boxed{b=1}$$

$$\boxed{c=\frac{3}{b}=\frac{3}{1}=3}$$

$$\boxed{(x+1)(x-3)(ax+b)(x+c)=(x+1)(x-3)(2x+1)(x+3)}$$

Yes Melody i am very well introduced to her !i have read about her in newspapers!thank u so much for it!And thanks to u also anonymous,the ghost of web2.0calc i am very much enlightened by ur words, they have made me felt really very greatful!u know i was just searching a simple moral poem on the net and then i found this one and on clicking on it it lead me to the website of it and that website and the poem gave me an idea to share it to all! i am still unable to get that why on alternate days im posting something fun , interesting and all!but im liking it so i think i should continue it which ill try becoz i was happy seeing reinout doing something like this but i cant post everyday so i may be able to post alternately!btw thanks to all of u !i dont know why ive got the habbit of writing alot for everything !lol! 

but still Thanks to all of u !

Here is another young woman that Rosala probably knows all about.

Rosala, our Web2 ghost is right.  How can we do justice to something so powerful?

What you have shared with us is truly moving.  I am so glad that you chose to share this .  

You are already are a diplomat.  On this forum you are dealing with people from all over the world and it would have been impossible for you to have made a better impression.  You represent your country, in particular you represent the girls of your country.  There could be no better representative.  Thank you so much for being amoung us.

Melody.

In modern society, converting fat percentage to grams is like converting the mass of water in the Pacific Ocean to imperial minims.

Tuesday 24/6/14

This one is special.  Thank you Rosala.

if (x+2) is a factor of f(x) =x^3+3x^2-kx+4

then

(x+2)(something)=x^3+3x^2-kx+4

consider if x=-2  then

(-2+2)(something)=x^3+3x^2-kx+4

But -2+2=0 and if you multiply anything by zero then the answer is zero, that is;

(-2+2)(something)=x^3+3x^2-kx+4=0

So what this is saying is that  (x+2) is a factor IF x=-2 is a root, that is, f(-2) =0

so 

$$f(x)=x^3+3x^2-kx+4\\\\
f(-2)=(-2)^3+3(-2)^2-k(-2)+4\\\\
f(-2)=-8+12+2k+4\\\\
f(-2)=8+2k\\\\$$

Now if (x+2) is a factor then f(-2)=0 so

$$8+2k=0\\

2k=\:-8\\

k=\:-4\\$$

BY THE WAY this is called remainder theorum

If (x+a) is a factor of f(x) then f(-a)=0

I've just explained why.  If you have a good maths brain this will help a lot.

Well, One million is essentially 1000000. So 6 Zeros. Between the millions is multiplication. So writing what you said in as an equations would be:

$${\mathtt{10}}{\mathtt{\,\times\,}}{\mathtt{1\,000\,000\,000\,000\,000\,000\,000\,000\,000\,000\,000\,000\,000\,000}} = {\mathtt{10\,000\,000\,000\,000\,000\,000\,000\,000\,000\,000\,000\,000\,000\,000}}$$

I am sure Heureka ( or someone else) will come along with a beautifully laid out explanation but in the mean time 

$$(x+1)(x-3)=x^2-2x-3$$

so you need to divide your polynomial by that to get the product of the 2 brackets containing a,b,and c.

You can so this with a polynomial long division.  There are lots of you tube videos explaining thiase techniques.  I can find one if you need me to.   (I've included one below)

after that you just factorise what is left by ordinary techniques to get the value of a,b and c.

---------------------------------------

Long division

(12.01) ÷ 6.022*10²³

12.01 is the same thing as 1.201 x 10¹

(1.201 x 10¹) ÷ (6.022 x 10²³)

(1.201 ÷  6.022)(10¹ ÷  10²³)

.1994354 x 10^-22

this is the same as

(1.994354 x 10¹) x 10^-22

1.994354x 10^-21

Round down to 4 significant digits.

1.994 x 10^-21

This method is known as scientific notation. It helps when your dealing with really big or really small numbers. You could also write this as 0.0000000000000000000000199435

3x

By dividing both sides by 3, this can be simplified to:

x<4

This is saying that x could be any number below 4.

x could even be -99999999 for that matter!

74$${\mathtt{X}}{\mathtt{\,\small\textbf+\,}}{\mathtt{69}}{\mathtt{\,\small\textbf+\,}}{\mathtt{420}} = {\mathtt{489}}{\mathtt{\,\small\textbf+\,}}\underset{{\tiny{\text{Error: Unknown Identifier}}}}{{\mathtt{X}}}$$

If you mean the "Origin" of the Perpendicular Lines (Cartesian Plane) Then it would be (0,0)

NinjaDevo is correct, i'd just like to add one more thing. You will need to specify what you are rounding it to. For example, Round 4.8282 to the nearest tenth.

The rule for rounding is that if it is 5 or higher, round up. If it is 4 or lower, round down.

But...this depends where your rounding too.

If you wanted to round to the nearest whole number, you would get:

3

If you wanted to round to the tenths place, you would get:

2.9

If you wanted to round to the hundredths place, you would get:

2.90

If you wanted to round to the thousandths place, you would get:

2.897

If you wanted to round to the ten-thousandths place, you would get:

2.8974

To solve this, we need to set up two equations and solve them like you would solving inequalities by elimination.

N + Q = 60          ---This one is telling us that 60 coins are made up of nickles and quarters.

.05N+.25Q = 7.40      ---This one is telling us that the total balance is $7.40 and quarters are worth 25 cents,                                                        and nickles are worth 5 cents.

If we move the decimal place over on all three numbers, we can write the second equation as:

5N+25Q=740

Now, to solve with elimination we need to have 5N in both the equations. Let's multiply everything in the first equation by 5 so we have 5N in both equations.

5(N + Q = 60)

5N+5Q=300

Now, we solve by elimination with our two new equations.

5N+25Q=740

-5N -5Q= -300

20Q=440

Q = 22                    ---Divide both sides by 20

There are twenty-two quarters!

To find how many nickles there are, put in 22 instead of Q for one of the equations (we can do this because Q = 22)

Let's take our original first equation.

N + Q = 60

N + 22 = 60

N = 38                  ---Subtract 22 from both sides

There are 38 nickles!

To check this, let's put in these values of N and Q into our original second equation.
.05N+.25Q = 7.40

.05(38)+.25(22) = 7.40

1.9+5.5 = 7.40

7.4 = 7.4

It works!

To type in a division sign on this calculator, you can click the little ÷ button, or you can type in a backslash which looks like this: /

The reason you use / is because there is no divided by sign on most keyboards, and the / symbol is on almost every keyboard.

Hi Rosala,

This is why you are like springtime and flowers.

The lack of response is not because no one liked your post. It is because your post is emotionally powerful, and people have a fear of saying the wrong thing, or they think it may dilute what you wrote. This is true for young persons and adults.

Your polite and pleasant manners and your willingness to communicate sincere, compassionate empathy, ranks you among the most unique of human beings.

I am sure, someday, no matter what you choose to do in life, you will be a diplomat – an ambassador to the world. Your posts represent a great beginning.

Happiness to you.

The ghost of web2.0calc

Can you clarify this question?  It seems unclear. 

First recognize that this is the same as (sin(3))^2 so if you know what sin(3) is you just have to square it.  After typing it in a calculator i see that sin(3) is about 0.05244596

Typing in (sin(3))^2 i get .002739

Generally we prefer radians for such a measurement because radians make calculations for things like circumference, arc length, etc. very easy.  That said is is not necessarily wrong to use degrees, it just requires more mental aerobics. 

As an example lets say you wanted to find how far a dump truck rolls when its tires with a 2 ft radius roll 135 degrees =3pi/4 rad

The radians calculation is simple.  (3pi/4)4=4pi ft

The degress calculation is a touch less friendly but gives the same result  (135/360)2pi(4)=4pi ft

this means that there is some function called "f" and when you input the x value x=1 into the function the function value or y value is y=1.728. 

Another way of looking at it is that the point (1,1.728) is a solution to, or is on the graph of the f function.

-6 / (1/2) =

-6 x (2/1) =

-12