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3C =37.40F

37.40 - 11 =26.40 F

I just don't get the -16, +16 and the -9, +9 ...

Original answer by geno3141:

f(x)  =  4 - sqrt(16 + 6x - x2)

For ease of calculation, I am replacing  f(x)  with  y:

                                                                  y  =  4 - sqrt(16 + 6x - x2)

Subtract 4 from both sides:                  y - 4  =  - sqrt(16 + 6x - x2)

Multiply both sides by -1:                    -y + 4  =  sqrt(16 + 6x - x2)

Simplify left side:                                   4 - y  =  sqrt(16 + 6x - x2)

Square both sides:                            (4 - y)2  =  16 + 6x - x2

Multiply out:                                16 - 8y + y2  =  16 + 6x - x2

Subtract 16 from both sides:           - 8y + y2  =  6x - x2

Rewrite:                                              y2 - 8y  =  -x2 + 6x

Factor:                                                y2 - 8y  =  -(x2 - 6x)

Complete the squares:    [ y2 - 8y + 16 ] - 16  =  [ -(x2 - 6x + 9) ] + 9

Simplify:                                   [ y2 - 8y + 16 ] =  [ -(x2 - 6x + 9) ] + 25

Factor:                                               (y + 4)2  =  -(x - 3)2 + 25

Rewrite:                              (x - 3)2 + (y + 4)2  =  25  

Analysis:  this is the equation of a circle with center  (3, -4)  and  radius = 5.

But:  the initial equation is only the lower half of this circle; thus, an arc from  (-2,4)  through  (3,-1)  to  8,4).

 -3(4x-5y+6)+8x-9 =    [distribute the "-3"  across the terms in parentheses  ]

-12x + 15y - 18 +  8x   - 9    combine like terms

-4x + 15y - 27

You can only add like radicals.......be careful though.......some may be in "diguised" form......Example :

√2   + √8   =

√2   + √[ 4 * 2]   =

√2   +  √4 * √2   =

√2   +    2 √2   = 

3 √2

Lesson :  Simplify all radicals, first  !!!!!

r= 5sin 0

r = 5 [ y/r ]     multiply both sides by r

r^2  = 5y

x^2 + y^2 =  5y

x^2 + y^2 - 5y  = 0    if we wish, we can put this in standard form by completing the sqaure on y

x^2 + (y - 5/2)^2 = 25/4

r= sin 0+ cos 0

r = y/r + x/r     multiply through by r

r^2 = y + x

x^2 + y^2  = y + x

x^2 - x + y^2 - y = 0          complete the square on x  and y

(x - 1/2)^2  + (y - 1/2)^2 =  1/2

Per cent  just means ' hundredths' in Latin.     82 per cent of something is just 82 hundredths of it. 

So 82 per cent of  215  is just 82 hundredths of 215.  So you need to find

82/100     x     215.   

( A centurion was a Roman commander in charge of one hundred soldiers.)

Thank you!

1. The set of rational numbers between 0 and 10

Infinite....here's a simple example........consider the set of rational numbers between 0 and 1

Let's say we have the two rational .55   and .56

Note......that I could add an ending 5 to the fiirst number and get another rational between these two. And adding another 5 to the end of this would give me another rational between .555 and .56

And adding another 5 to the end of this would give me a rational between  .5555 and .56...and so on.....in fact, we have more rationals between 0 and 1 then there are integers on the number line.......they are infinite.....so.......the set of rationals between 0 and 10 is also infinite

One method.......just factor out a negative and add as normal.....Example

( -5 )  +   ( - 3 )   =

- [5 + 3 ] = 

-8

r = -2sec0

r  = -2 [ r / x ]        divide through by r

1 = -2 / x      multiply both sides by x

x = -2

If the points are (0, 31) and (20, 151)   .........the y value at x = 0 gives the y intercept.....and notice, that when x = 0, y = 31

So......this is the y intercept

to solve this question:

1st square root both sides

and then you will have what V is equal to.

Post the problem.....we'll take a look......!!!!

Assuming a circular table, the area  = pi * (radius)^2    = pi * (50 cm)^2   = 2500pi cm^2 ≈   7853.98  cm^2

to get the answer u do 8/15=5.333333333333333333333333333333333333333333333333333333

f=ma  

a=m/f      Is that what you are looking for?

Whatsm 1+1?

8/15   of a potato each

Just type it straight in.......

the first term and fourth term of a geomtric series are 256 and 2048 respctively

i) what is the value of the common ratios

ii) given the sum of the first n terms is 261888 find the value of n,

1)   We have

2048  = 256r³          divide both sides by 256

2048/256  = r³   

8 = r³      take the cube root of both sides

8^1/3 = 2 = r

2)   We can use the sum formula for a geometric series here :

Sum = [First term ] * [ 1 - common ratio^term number ] / [ 1 - common ratio ]

261888  = 256 [ 1 - 2ⁿ ] /  [1 - 2]      divide both isdes by 256

1023 = [1 - 2ⁿ  ] / -1

1023  = 2ⁿ - 1    add 1 to both sides

1024 = 2ⁿ   take the log of both sides

log 1024 = log 2ⁿ    and we can write

log 1024 = n log 2      divide both sides by log 2

log 1024 / log 2 =  n

10 = n

(-9)⁴ =  (-9)² * (-9)²   = 81 * 81   =  6561