All Answers 358180 Answers

How many balls do you get for your ticket ?

If the number of visitors was, say, 100 people in 2003, then in 2005 that number would have gone up to 300 people, which is 200% increase. And that number would have gone up to 900 people in 2007, which is 800% increase.

So, it takes 4 years for daily visitors to grow by 800%.

Another way of looking at it is to find ANNUAL percentage increase as follows:

300 people / 100 people =3-folds increase in 2 years. So the yearly increase would be:

3^1/2 =1.73205 - 1 x 100 = 73.205% average compound annual increase.

900 people =100 x [1 + 73.205%]^N    divide both sides by 100

9 = 1.73205^N             take the log of both sides.

N =Log(9) / Log(1.73205)

N = 4 Years for the number of visitors to grow by 800%.

how much money would i have to save for 2 months to get 3,000$ when i already have 1,541.20$

$3,000 - $1,541.20 =$1,458.80 - this is what you need to save in 2 months, or:

$1,458.80 / 2 =$729.40 - this is what you need to save each month for 2 months.

As best as I can understand the rules:

Your chances of matching 2 white balls are: 20C2 =190, or 1 chance in 190.

Your chances of matching the blue Superball are: 10C1 =10, or 1 chance in 10.

Your chances of matching all 3 balls are =190 x 10 =1,900. or 1 chance in 1,900.

try 78^3  

A:474552

474,552

Match the balls to the chosen numbers. For example, If the Superball number chosen is 25, and you pick 23, you don't win a prize unless you matched at least two white balls.

Match them to what?

I do not understand the rules :/

By opposite do you mean negative? In that case it is -5.

If we suppose point C should be (0, 7) then the centre of the circle lies at infinity, because the three points lie on a straight line!! 

Otherwise we must wait wait for the questioner to post corrected coordinates.

Mistype I think, A is the same as C.

Have a look at http://www.mathpages.com/home/kmath616/kmath616.htm, or do a more general search for "fractional calculus".

474,552

24m is correct.

Maybe the textbook have mistakes ;P

(f/g)(x)

= (f(x))/(g(x))

= (4x - 5)/3x

( "_" )

y'+y=x

\(\begin{array}{|l|rcll|} \hline & y'+y &=& x \\ & y' &=& x -y \\ \text{substitution} \ u=x-y & y' &=& u \\ & 1-y' &=& 1-u \quad & | \quad u' = 1-y'\\ & u' &=& 1-u \\ & \frac{du}{dx} &=& 1-u \\ & \frac{du}{1-u} &=& dx \\ & \int \frac{du}{1-u} &=& \int dx \\ & -\ln|1-u| &=& x + c_1 \\ & \ln|1-u| &=& -x - c_1 \\ & 1-u &=& e^{-x - c_1} = c_2e^{-x} \quad & \quad (c_2=e^{-c_1}) \\ & u &=& 1- c_2e^{-x}=1-ce^{-x} \quad & \quad (c_2=c) \\ \text{back substitution} \ x-y=u & x-y &=& 1-ce^{-x} \\\\ & \mathbf{ y }& \mathbf{=} & \mathbf{ce^{-x} +x-1} \\ \hline \end{array}\)

proof y' + y = x

\(\begin{array}{|rcll|} \hline \mathbf{ y }& \mathbf{=} & \mathbf{ce^{-x} +x-1} \\ \mathbf{ y' }& \mathbf{=} & \mathbf{-ce^{-x} +1 } \\ y'+y &=& -ce^{-x} +1 + ce^{-x} +x-1 \\ y'+y &=& x \ \checkmark \\ \hline \end{array} \)

Here's another way to approach this problem:

.

(3x^3+2x^2-25x-12)/(x+3)=?

\(\dfrac{3x^3+2x^2-25x-12}{x+3}=\ ? \)

The point (-3,-4) divides the line joining point A(-6,-7) and point B in the ratio 1:3.

Find the coordinates of B. 

\(\text{Set } \vec{P} = \binom{-3}{-4} \\ \text{Set } \vec{A} = \binom{-6}{-7} \\ \text{Set } \vec{B} =\ ?\)

Formula:

\(\begin{array}{|rcll|} \hline \vec{P} = (1-\lambda)\vec{A}+\lambda\vec{B} \\ \hline \end{array}\)

Ratio 1:3

\(\begin{array}{|rcll|} \hline \lambda &=& \frac{1}{1+3} \\ &=& \frac14 \\ \hline \end{array}\)

Solution for \(\vec{B}\):

\(\begin{array}{|rcll|} \hline \vec{P} &=& (1-\lambda)\vec{A}+\lambda\vec{B} \\ \lambda\vec{B} &=& \vec{P} - (1-\lambda)\vec{A} \\ \vec{B} &=& \frac{1}{\lambda} \cdot \Big( \vec{P} - (1-\lambda)\vec{A} \Big) \quad & | \quad \lambda &=& \frac14 \\ \vec{B} &=& \frac{1}{ \frac14 } \cdot \Big( \vec{P} - (1-\frac14)\vec{A} \Big) \\ \vec{B} &=& 4 \cdot ( \vec{P} - \frac34 \vec{A} ) \\ \vec{B} &=& 4 \vec{P} - 3\vec{A} \\ \vec{B} &=& 4 \binom{-3}{-4} - 3\binom{-6}{-7} \\ \vec{B} &=& 4 \binom{-3}{-4} + 3\binom{6}{7} \\ \vec{B} &=& \binom{-12}{-16} + \binom{18}{21} \\ \vec{B} &=& \binom{-12+18}{-16+21} \\ \mathbf{ \vec{B} } & \mathbf{=} & \mathbf{\dbinom{6}{5}} \\ \hline \end{array}\)

Point B(6,5)

We can use long division to answer this question:

Therefore, \(\frac{3x^3+2x^2-25x-12}{x+3}=3x^2-7x-4\hspace{1mm},\hspace{1mm}x\neq-3\)

When rounded to the 4th decimal place

\(8500(1-15\%)^5=3771.4952\)

\(43+56=99\)

I'm unsure how this question is geometry-related. My only guess is that you are calculating the area of a triangle.

There you go! I'm glad to help!

There you go!

^ is the symbol denoting an exponent on a keyboard.

\(6\text{^}3=6^3 \)

\(2\text{^}12=2^{12} \)

\(9\text{^}2=9^2 \)

What does an exponent mean? Well, I'll explain with a picture: