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Hi 

BasicMaths

  I agree the forum s my FAV Math help site super useful.... 

a)

Maybe this drawing will help...

The thing at the bottom right corner of the triangle is supposed to be somebody riding the Ferris wheel x)

All the lengths are in meters, and  t  is the number of seconds after the ride starts.

height of person  =  b + 1

height of person  =  8 - 8 cos θ  + 1

height of person  =  9 - 8 cos θ

height of person  =  9 - 8 cos( \(\frac{\pi t}{10}\) )

h(t)  =  -8 cos( \(\frac{\pi t}{10}\) ) + 9

If you have a question about where any part of this came from, please ask

You didn't suffer ....

It counts

Welcome to the FORUM BASICS MATH what your are very welcomed here and will find it an excellent community of way's to learn and help the ones that need assitance : )

Nothing much... unless watching dragons hidden world counts. (Which was a highly exceptional movie)

We can use the Law of Cosines to find the missing side, S

S^2  = 143^2 + 220^2 - 2(143)(220)cos(75.7)

S^2  = 53307.8

S = √53307.8  ≈  231 ft

Thank you

a. Are the events "Chocolate" and "Adults" independent? Why or why not?

If independent.... P (Chocolate l Adult )  = P(Chocolate and Adult) /P(Chocolate)

                                      .21/ (.21 + .39 + .60)  =  .21/ .35  ???

                                       .21   =  .60   ????    not independent

b. Are the events "Children" and "Chocolate" independent? Why or why not?

P(Children l Chocolate)  =  P(Children and Chocolate) / P(Children)  ???

                        .14/ (.14+ .21+ .35)     =   .14 / .40  ???

                         .20  = .35  ???   not independent

c. Are the events "Vanilla" and "Children" independent? Why or why not?

P(Vanilla l Children)  = P(Vanilla and Children) / P(Vanilla)      ???    

      .26 / (   .14 + .26 + .40)  =  .26 / .65    ???

                  .325 = .40 ???    not independent

2) Alex from Ayden and Bob from Beaufort are driving towards each other at the same time. They meet at a first point 32km away from Ayden. After Alex arrives at Beaufort and Bob arrives ay Ayden, they turn around right away. They meet at a second point 64km away from Ayden. Find the distance from Ayden to Beaufort.

Let the distance be D

Let Alex's Rate = A

Let Bob's Rate = B

Distance / Rate = Time

When they meet the first time  Alex has traveld 32 km  and Bob has traveled (D - 32) km

So.....from the start until they meet the first time we have that the times are equal

32/ A  =  (D - 32) / B    ⇒   A/B  = 32 / (D - 32)

And after the first meeting.....Alex has traveled (D - 32 + D -64)  = (2D - 96)

And Bob has traveled (32 + 64) = 96

So......equating the time again

(2D -96) /A  = (96) /B ⇒   A/B  = (2D - 96) / 96

And A/B  =A/B   so

32 / (D -32)  = (2D -96) / 96     cross-multiply

96 * 32  = (2D - 96) ( D - 32)     simplify

96*32  = 2D^2 - 160D + 96*32

2D^2 - 160D = 0

2D ( D - 80)  = 0     so

2D = 0                                 D - 80  = 0  

D = 0   reject                       D = 80km

Thank you so much!

Here you go for the first one : https://www.desmos.com/calculator/ofobm3u4af

For the second

You have the correct graphs...the intersection points are  ( -1, -3)  and ( 3,5)

Algebraically....set the functions equal

x^2 -4  = 2x - 1       rearrange as

x^2 - 2x - 3  = 0   factor

(x - 3) ( x + 1)  = 0

Set each factor and solve for x

x -3  = 0          x + 1  = 0

x = 3                  x = -1

Put these values into either function for x and you should get the same intersection points as above

Hope that helps  !!!

Congrats man I don't think I ever seen anyone type that big of a number in words  ; )

Let's see.

(x+1)(x+1)-(x+2)(x-3)

(x^2+2x+1)-(x^2-x-6)

x^2+2x+1-x^2+x+6

3x+7

We can see how he didn't distribute the negative sign in -(x^2-x-6) to the -x and -6.

You are very welcome!

:P

(r+3)/(r-2)=(r-1)(r+1)

(r+3)(r+1)=(r-1)(r-2)

r^2+4r+3=r^2-3r+2

7r=-1

r=-1/7

You are very welcome!

:P

It is around 27,295,538,859,730,818.34465860927220128658, or around twenty-seven quadrillion two hundred ninety-five trillion five hundred thirty-eight billion eight hundred fifty-nine million seven hundred thirty thousand eight hundred eighteen and thirty-four quintillion four hundred sixty-five quadrillion eight hundred sixty trillion nine hundred twenty-seven billion two hundred twenty million one hundred twenty-eight thousand six hundred fifty-eight hundred quintillionths.

why did i make myself suffer like that?

You are very very very very very welcome.

:P

Not old for work yet ;)

Do math, jump in the pool, play videogames, play my cello, try to make time as slow as possible so that the next school year doesn't come by quickly

I would say around a year for the basics of everything but at least 3 if you really want to get in depth.

Parallel means that the lines never touch, and for that to happen, they must have the same slope.

The slope of -2 means that an equation is y = -2x+4. In fact, the y-intercept doesn't matter because they are all parallel.

You are very welcome!

:P