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This was posted here: https://web2.0calc.com/questions/a-police-car-is-located-30-feet-to-the-side-of-a-straight-road-a-red-car-is-driving-along-the-road-in-the-direction-of-the-police-car-and-i

Hope this helped!

Set up equatiojn

with var a and b

(a) * (a + b) * (a + 2b) = 64

Expand

a^3 + a^2*b + a^2*2b + ab^2 = 64

graph it:

https://www.desmos.com/calculator/fkcrxzgdfy

lowest possible value for b is... 4...

4, 4, 4, is an arithmetic sequence with a common difference of 0.

ok bye bye

Nice, Geno!

I don't know how to generate  the  slope  using  the "regular" procedure.....

But....apparently.....this method must work just fine.....

If  1 - √2  is  a root  then so is  1 + √2

Same for  2 + √5

So   we  can find this as

[  x - (1 -√2) ]  [x -(1 + √2) ] [ x - ( 2 + √5) ] [ x - (2 - √5) ]

Taking this in pieces, we have

[x^2  - (1 - √2)x - (1 + √2)x  + ( 1 - √2)(1 + √2) ]  =

[x^2  - x + √2x - x - √2x + 1 - 2]  =

[ x^2 -2x - 1]   (1)

And

[x- (2 + √5) ] [ x - (2 - √5) ]   =

 [ x^2   -(2 + √5)x - (2 - √5)x  + (2 + √5)(2 - √5)  ]  = 

[x^2  -2x - √5x - 2x + √5x  + 4 - 5]  =

[ x^2 - 4x  - 1 ]  (2)

Take  the product of (1) (2)  =

[ x^2 - 2x - 1]  [ x^2 - 4x - 1]  =

x^4  - 2x^3  - x^2

       -4x^3 + 8x^2  + 4x

                 -x^2     +2x     +  1

____________________________

x^4  - 6x^3  + 6x^2 + 6x  + 1

Notice that the coefficient of d decreases:

    2n + 1,  2n,  2n - 1,  2n - 2,  ...   1

The way that the coefficient can become one if the coefficient is   '2n - '

so that  '2n -

If  'something' is '2n - 1'  then  2n - (2n- 1)  =  2n - 2n + 1  =  1. 

I do not see offhand Cal.  (so I am not surprised that Bxtterman does not see either)

I will have to think about it. 

Alright, CPhill! Thanks for the advice!

Try these:    [  'cubrt' means 'cube root'   and   'sqrt' means 'square root' ]

a  =  4·cubrt(2)  -  sqrt(8)·cubrt(2)

b  =  4·cubrt(2)

c  =  4·cubrt(2)  +  sqrt(8)·cubrt(2)

I don't know if this is the smallest value of b, but it works.

Hey, DragonLord...if you  send this  one  to heureka he might know how to fnd the  result mathematically...he's pretty good with this kind of thing.....

That's impossible, guest.....an arithmetic series will have the same  difference between terms......

FWIW....I put this into WolframAlpha......it didn't find any integer solutions for this where all the integers were positive

It  came  back  with

- 8 , -2,  4

Which  has a constant difference  of  6

Maybe someone else  knows  how to find  the positive  solutions.....!!!!

LOL

Cal you were sprung!

It is good that jfan caught you out.  Everything he said is correct.

You must give credit where credit is due.

However, I do believe that you are using this site to learn.

And I do believe that you understood and learned from CPhill's answer.

I know CPhill will be very pleased that you are learning from his answers. 

Oh okay, I was using the wrong formula for the slope I think. My teacher gave us the y2-y1/x2-x1 formula to use. Is there a way to get the same answer but using this formula? Thank you for your help. I greatly appreciate it.

Sorry jfan, I am with Spongebob on this one.

The question is about the cost of dinners.  It is not a theoretical question.

The answer MUST be rounded off to give a dollars and cents answer. 

Exactly how it is rounded may be open to interpretation but it must be rounded. The waitress cannot charge a part of a cent.

Also, I have not looked at your answer thoroughly, but it seems to me that you have allowed the calculator to round anyway.

Your answer does not look exact to me. 

Rounding to 2 decimal would make a lot more sense.,

Here's  the procedure....hang on....there are a few steps here

Take  the  mean of the  x values  = 640

Take  the  mean of  the y values  = 1190

Calculate  the  difference  between  each x value  and  the  mean of the  x values   and do  the same  for the y values

350 - 640  =     -290               2500 -  1190   =  1310                 

450  - 640  =   -190                1450  -  1190  =   260           

600 - 640   =      -40                  800 -  1190   =  -390               

800 -  640   =    160                 1100 - 1190   =   -90              

1000 - 640  =    360                 100 - 1190 =   -1090

Take  the products  of these results  and  add them

(-290)(1310) + (-190)(260) +  (-40)(-390)  + (160)(-90) + (360)(-1090)   =  -820500     (1)

Square  each  value  in the  first column above  and add them together   =

(-290)^2  + (-190)^2  + (-40)^2  + (160)^2  + (360)^2   =  277000     (2)

The slope of  the line =  (1) / (2)  =  - 2.96

The  y  intercept  (b) is  found  as

b = average of  y values  -  (slope  * average of  x values)  

b  = 1190  - ( [-820500/277000] * 640)    = 3085. 74

So....our line  is

y = -2.96x  + 3085.74

Circle O is tangent to AB at A, and angle ABD = 90 degrees. If AB = 12 and CD = 18, find the radius of the circle.

The radius of the circle is:     r = sqrt [(CD/2)² + (AB)²] = 15

BC = 6

The AP is; 2, 4, 8   and b = 4

Whoa, Cal....you were right in the  first place  !!!

I = Prt

96 = 800 * r * 5

96 = 4000 * r    

96 / 4000  = r  = .024 =  2.4%

[   19.2 / 800  = .024  ]  

Check this out: https://web2.0calc.com/questions/i-m-confused-about-this

find the distance   BC using pythagorean theorem   

3250^2  =  3000^2  + BC^2         BC = 1250 km    

SO her total distance travelled  =   3250  +  1250  +  3000 km = ......

thats what i have done but confused now

Our answer will be 96/800, which is interest rate/total.

That will get us 0.12, or 12%

Hope this helped!

Never mind it's wrong lemme try again

96/5= 19.2 he earns each year!

19.2/800 will be our answer :D

Never mind this is wrong

ik that but im confused on the calculations