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Hi, InfoChan!

I am pretty new here too, but it's full of great people and helpers.

I'll answer your questions too, as long as I know the answer and I don't feel lazy.  :)

Well, since you cannot be both alive and dead at the same time (not talking about zombies...), a person must either be alive or dead. The definition of Infinity can be controversial. 

1. infinity can describe a number that is so large that nobody can count up to it. So if the unimaginably large amount of health was greater than the damage dealt, then the person would still be alive. Opposite result with the opposite case.

2. But here's another possibility. Infinity has no end. So...if you have no end of health, then you cannot die. No matter how much damage (even infinite damage), your health will not run out, so the person will always be alive.

3. Here is the final one. There is no answer to this question. Infinity is (arguably) not a number. So my answer would be 'none of the above.'

I don't really know how to answer this question, so I included three possible answers. 

Thank you!

Both answers above forget to include n = 0.

Answers should be 417 and 384 resp.

Creating Linear Equation

Write a linear function that passes through both (a,0) and (0,b).

\(\begin{array}{lcll} \dfrac{x}{a} +\dfrac{y}{b} = 1 \begin{array}{rcll} & \text{if } y = 0 \text{ then } x = a \\ & \text{if } x = 0 \text{ then } y = b \\ \end{array} \end{array}\)

\(\begin{array}{|rcll|} \hline \frac{x}{a} +\frac{y}{b} &=& 1 \quad & | \quad - \frac{x}{a} \\\\ \frac{y}{b} &=& 1 -\frac{x}{a} \quad & | \quad \cdot b \\\\ y &=& b - \frac{b}{a}\cdot x \\\\ \mathbf{y} &\mathbf{=}& \mathbf{ -\frac{b}{a}\cdot x + b } \\ \hline \end{array}\)

density area people

About 1.15 million people live in a circular region

with a population density of about 18,075 people per square kilometer.

Find the radius of the region

Let A = area of the circular region
Let r = radius of the circular region

\(\mathbf{A = \ ?}\)

\(\begin{array}{|rcll|} \hline A &=& 1500000\ \text{people} \times \frac{1\ km^2}{18075\ \text{people} } \\ &=& \frac{1500000}{18075} \ km^2 \\ &=& 82.9875518672 \ km^2 \\ \hline \end{array}\)

\(\mathbf{r = \ ?}\)

\(\begin{array}{|rcll|} \hline \pi \ r^2 &=& A \\ r^2 &=& \frac{A}{\pi} \\ r &=& \sqrt{ \frac{A}{\pi} } \\ &=& \sqrt{ \frac{82.9875518672}{\pi} } \\ &=& \sqrt{ 26.4157581895 } \\ \mathbf{r} &\mathbf{=}& \mathbf{ 5.13962626944 \ km } \\ \hline \end{array}\)

The radius of the region is \(\mathbf{\approx5.14\ km}\)

-3( 2x + 5 )=-21 

pls answer tq

y = (x)^7 * (2x + 5)^10

We want to use the product and chain rules, here...remember that if

y = u * v  ......then   y'  =  u' * v + u * v'       where u, v are functions....so we have.....

dy / dx  =   7(x)^6 * (2x + 5)^10  + (x)^7 * 10 * (2x + 5)^9 *(2) 

Note that we used the chain rule  in the last part [ in red ]

We can simplify thus.....factor out GCF of [ x^6 * ( 2x + 5)^9]

[ x^6 * ( 2x + 5)^9] * [  7 (2x + 5)  +  20x ]  

[ x^6 * ( 2x + 5)^9] * [ 14x  + 35 + 20x ] 

[x^6 * (2x + 5)^9 ] * [ 34x + 35 ] 

Are you wanting to solve for y or x?

When you're writing a fraction in the calculator (for example: 1/2), put parentheses around what you are trying to make a fraction (for example: (1/2)). When you do this, it will show up as a fraction.

Hope this helps!

-MagikalRedNiteTiger 

Solving parentheses we have \({11 \over 4}\over{16 \over 3}\)

Then, tranforming in multiplication \({11 \over 4}\times{3 \over 16}\)

Solving: \(33 \over 64\)

\(\frac{3}{7}\) is a rational number. 

In order to be classified as a rational number, a number must meet the following condition:

A number is rational if and only if you can represent that number with \(\frac{a}{b}\) where \(a,b\in\mathbb{Z}\). 3/7 meets this rule; a=3 and b=7.

Another way to think about it is the following:

A number is rational if and only if its decimal expansion either terminates OR repeats indefinitely. \(\frac{3}{7}=0.\overline{428571}\), which repeats indefinitely. This is a rational number. 

Clever indeed!

Thank you so much, this really helped!

1.)William fills 1/3 of a water bottle in 1/6 of a minute. How much time will it take him to fill the bottle?

(1/6) / (1/3)   =  x / 1      cross-multiply

1/6 =   (1/3)x      mutiply both sides by   3

3/6 minutes  =  x  =  1/2  of a minute 

2.) Michael plays 1/5 of a song in 1/15 of a minute. How much timw will it take him toplay an entire song?

(1/15) / (1/5)  =  x / 1     cross-multiply

(1/15)  = (1/5) x           multiply both sides by 5

5/15 minutes = x  = 1/3 minutes  

3.) Gabriel used 1/3 of a liter of milk to make 1/9 of a jug of tea. How much milk is required to fill the jug?

 (1/3) / (1/9)  =  x / 1      cross-multiply

(1/3) =  (1/9)x     multiply both sides by 9

(9/3) liters of milk  = x  =  3 liters of milk

( g  o  f)  

This is equal to   g [ f ( a) ] 

f (a) =  f ( .25)  =   sqrt (.25)  =  .5  =  1/2 =   b

So

g [ b ] = g [ 1/2 ]  =  1  / [ 1/2]  =   2

 Note that  triangle XOY  is similar to triangle  YPZ .....so....

 XO / OY  = YP /  PZ  →  XO * PZ  =  YO * YP

Also, triangle XOW  is similar to triangle WPZ ...so.... 

XO / OW  = WP / PZ  →  XO * PZ  = OW * WP

Which implies that

YO * YP  =  OW * WP

But YO  = YP + PO     and WP = OW + PO

Therefore....by substitution.....

[ YP + PO ] YP  =  OW [ OW + PO ]   simplify

YP^2 - OW^2  =  PO [ OW - YP ]     subtract the right side from both sides

[ YP + OW] [ YP - OW ] - PO [ OW -YP]  = 0      factor out a negative

[ YP + OW ] [ YP - OW] + PO [ YP - OW] = 0    factor out  [ YP - OW]  

[ YP - OW] [ YP + OW + PO ]  = 0

So, by the zero factor property,  either

[ YP + OW + PO ]  = 0

But this is impossible since  YP, OW and PO  are all > 0

Or

[ YP - OW]  = 0   

Which implies that  YP = OW    →  PY  = OW

In order to convert an equation in slope-intercept form (\(y=mx+b\)) into standard form, you must understand a few rules. I will list them for you:

1. \(Ax+Bx=C\) is the form of the linear function

2. \(A,B,C\in\mathbb{Z}\) (A, B, and C must be integers)

3. \(A\geq0\)

4. A,B, and C must be co-prime

Knowing these rules, let's now convert \(y=-\frac{2}{5}x-5\) into standard form:

This process is more or less the same when you have 2 arbitrary points (such as (4,6) and (-9,1)). This time, however, we must take into account  that there are variables involved. Let's remind you of slope-intercept form of a line.

\(y=mx+b\)

 m = slope of the line 

b = y-intercept

In this particular case, we know the x- and y-intercepts because those points are given in the original problem. We know that the y-intercept is located at \((0,b)\). Since b is the y-intercept, fill that in! That's the easy bit, I think you'd agree.

\(y=mx+b\)

We know that the x-intercept is at the point when y=0, so plug that in:
 

We have determined, with the above algebraic work that when \(y=0,\hspace{1mm}x=\frac{-b}{m}\), which means that the x-intercept is located at \(\left(\frac{-b}{m},0\right)\). However, we also know that the x-intercept is located at \((a,0)\), which means that \(a=\frac{-b}{m}\):

We now know the value for b and for m, so fill it in to get the equation. 

\(y=\frac{-b}{a}x+b\)

Beats me, I do not even know what country Henry lives in.

Maybe there is no sales tax!

The answer is wrong, I tried those answers before too. IDK why it won't work...

Thanks asinus,

You want the length of the interval CD. Lines do not have ends :)

9 is equal to or is greater then -2m + 2 - 3

\(9\ge -2m + 2 - 3\\ 9\ge -2m -1\\ 10\ge -2m \\ 10\ge -2m \\ -2m\le10 \qquad \text{I turned the sign around because I swapped sides}\\ m\ge-5 \qquad \text{I turned the sign around because I multilplied both sides by a negative number}\\\)

You don't - you can just use the divide bar.

If you need full fration mode I suggest you use a different calc.

Karly has 1 1/3 packets of biscuits. She eats 1/6 of a packet and her friend eats 1/2 of a packet.
What fraction of the biscuits have been eaten?

Hello Guest!

\(\frac{\frac{1}{6}packet+\frac{1}{2}packet}{1\frac{1}{3}packets}=\frac{x}{100\%}\\ \frac{\frac{1+3}{6}}{\frac{4}{3}}=\frac{x}{100\%}\)

\(\frac{4}{6}:\frac{4}{3}=x:100\%\\ x=\frac{100\%\times 4\times 3}{6\times 4}\)

\(x=50\%\)

Karly and her friend ate 50% of biscuits,

these are 2/3 packages biscuits.

  !