All Answers 356067 Answers

If  y³  varies inversely with  z^1/3,  then you can use the formula:  y³  =  a / z^1/3  where a is the proportionality constant.

To find the value of a, use the information that  y = 2  when  z = 1:     

     --->     y³  =  a / z^1/3     --->     (2)³ =  a / (1)^1/3     --->      8  =  a / 1     --->     8 = a

So, the formula is:  y³  =  8 / z^1/3  

     --->     find the value of  z  when  y = 4     --->     (4)³  =  8 / z^1/3     --->    64  =  8 / z^1/3​  

     --->     multiply both sides by  z^1/3     --->     64z^1/3  =  8

     --->     divide both sides by  64    --->     z^1/3  =  8/64     --->     z^1/3  =  1/8

     --->     cube both sides     z  =  1/512 

C=√7/LA, solve for L

C=√7/LA square both sides
C^2=7/LA cross multiply
C^2LA = 7
L=7 / [C^2A]

2GB x 10^6=2 x 10^6 KB

[2 x 10^6] / 8 =250,000 =2.5 x 10^5 pages-the maximum number that the USB Drive can hold.

-12x-9+7x=26

-12x + 7x =26 + 9

-5x = 35 divide both sides by -5

x = 35 /-5

x= -7

42.6 billion, how many noughts is that?

42,600,000,000 =4.26 x 10^10 in scientific notation.

starts with 1

There is one 1, so 11

There are 2 ones, so 21

There is one 2, and one 1, so 1211

etc.

so after 312211 would be

13112221.

-6x ≥ -20    divide both sides by -6    and reverse the inequality sign

x ≤ -20 / -6

x ≤  10 / 3

8 / (2/5)  =

(8/1)  / (2/5)     invert the second fraction and multiply

(8/1) * (5/2)   =

40/2  =

20

.x^2 + y^2 -4x-14=0 at the point (-1,-3) 

correction sir it is *-14 not -17

OK....so we have

2. .x^2 + y^2 -4x-14=0 at the point (-1,-3) (pre calc)

Using implicit differentiation again, the slope at any point is :

2x + 2yy'  - 4 - 0 = 0

2yy' =  4 - 2x    divide through by 2

yy'  = 2 - x      divide by y

y '  = [ 2 - x] / y        so.....at (-1, -3 ), the slope  is     [2 - (-1)] / [ -3]  =  3/-3  = -1

So.......using the point-slope form, we have

y - (-3)  = -1 [ x - (-1) ]

y + 3 = -1 [ x + 1]

y + 3   = -x - 1     subtract 3 from both sides

y = -x - 4

Here's thje graph :  https://www.desmos.com/calculator/m4qjkfosbw

Amps x Volts = Watts

500 x 10^4 =5,000,000 =5 x 10^6 Watts.

I=Do you go to AoPS?

it is -14 im sorry

1. x^2 + y^2 +6x-10y+17=0

Using calculus, the tangent at any point on the circle can be found using implicit differentiation....so we have...

2x + 2yy'  + 6 -10y' + 0 = 0

y' [ 2y - 10y ]  =  - [2x + 6 ]

2y' [ y - 5]  =  -2 [ x + 3 ]     divide both sides by 2

y' [ y - 5]  =   - [x + 3]   

y'  = [ x + 3]  / [ 5 - y]

2. .x^2 + y^2 -4x-17=0 at the point (-1,-3) (pre calc)

Notice that the point (-1,-3)  doesn't lie on the graph of this circle : https://www.desmos.com/calculator/z6kse7svjo

????

If it's tangent to the x axis at (2,0)  and touches the line y = 6, the diameter must be 6, so the radius must be 3

And, it must touch the line y = 6 at the point (2,6)

Then, the midpoint of (2,0) and (2,6)  must be the center -1/2 of the diameter -, so we have  the center as :

 ([ 2 + 2] /2 , [6 + 0]/2 )   = (4/2 , 6/2 ) =  ( 2, 3)

So....the equation of the circle is    (x - 2)^2 + (y -3)^2  = 9

Here's a graph :   https://www.desmos.com/calculator/z4nkt0mtbr 

Since  2x + 10  can be factored as:  2(x + 5),

(2x + 10)⁷  =  [ 2(x + 5) ]⁷  =  2⁷(x + 5)⁷  =  128(x + 5)⁷

Therefore:     (2x + 10)⁷ / (x + 5)⁶  =  128(x + 5)⁷ / (x + 5)⁶  =  128(x + 5)

Centre (2,3) radius3

(X-2)^2+(y-3)^2=9

what 22% as a whole number 

yes

Hayley1

you would know

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cuz i sukd et

(x-2)f(x)=x^3 - 4x^2 - 11x + 30

I believe that we want to find "f(x)"    ......we can do this using polynomial long division

             x^2   - 2x      -15 

x - 2  [   x^3   - 4x^2   - 11x   + 30  ]

             x^3   - 2x^2

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

                     -2x^2   -   11x

                     -2x^2   +     4x

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

                                    -15x    + 30  

                                    -15x   +  30

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

                                                 0

So....f(x)   =  x^2 - 2x  - 15

And notice that this can be factored as ( x -5) (x + 3)

So

x^3 - 4x^2 - 11x + 30  = (x -2) f(x)   =  (x -2) ( x^2 - 2x - 15)   =  (x -2) (x -5) (x + 3)

Divide both sides by (x-2)

to get

f(x) = x^2-2x-15    or  f(x) = (x-5)(x+3)