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V_cone  =  3.14 * (radius)^2 * height / 3

V_cone = 3.14  (5)^2 * 6  / 3  =      157 m^3

So....the total cost is    157 * 25   =  $3925

It is a monomial because it contains a single term.

It is 3rd degree because the sum of the exponents of the free variables is 3

\(x^2 y = x^2 y^1\\ 2+1=3\)

\(TP(p) = -15p^2 + 195p - 450\)

\(a) \text{find }TP(4.5)\)

\(b) \text{at this intersection }TP(p) = 0\\ \text{This is a simple quadratic equation. Solve it for it's roots. }\\ \text{Use the quadratic formula if you have to}\)

\(c)~\text{0 profit means why bother}\)

\(d)~\text{We want to find the maximum value of TP.}\\ \text{As }TP(p) \text{ is a quadratic equation it's graph will be a parabola}\\ \text{In this case as the coefficient of the }p^2 \text{ term is negative it will be facing downwards}\\ \text{and thus the maximum value will occur at the vertex of the parabola}\\ \text{A quick formula for the }x \text{ coordinate of the vertext of }a p^2 + bp + c \\ \text{is }p = -\dfrac{b}{2a} \text{, in this case }p = -\dfrac{195}{2(-15)} = \dfrac{13}{2}\\ \text{Plug this value into }TP(p) \text{ and read off the maximum profit that can be achieved}\)

h = hours

temp starts at 50

decreases by four each hour     - 4 h

< 32

50 - 4h < 32   solve for h.....subtract 50 from both sides of the equation

-4h < -18    divide both sides by -4 (remember when you multiply or divide an inequality by a negative the <> reverses)

h> 4.5 hours

-13x = 78    divide BOTH sides of the equation by -13

x = - -6     Ta - Da !!

The hole in the graph occurs when the denominator = 0   (undefined point)

    this occurs at x = 3

The NUMERATOR factors in to  (x-3)(x+3)     this reduces to  (x+3) when you 'cancel out' with the denominator (x-3)

     this value at x = 3          is (x+3) = 6

so the point of the hole is    3,6

-13x = 78      divide both sides by -13

x = -6

Wellllll...since it is between 1.8 and 1.9   let's pick   1.85  and substitute that into the equation and look at the result to see if it = 1

1.85      1.85^3 - 3(1.85) = .7816     Kinda close, lets try  1.86

1.86                                =  .8548   closer...try 1.87

1.87                                =  .9292   getting there ....try 1.88

1.88                                = 1.0046     BINGO !   

1.88   to 2 decimal places  is a solution to  x^3 - 3x = 1

which is the solution to this equation

-13x=78

We are trying to find the x that makes x^3 -3x - 1 = 0

We can use "divide and average" to find this

Le/t suppose that the answer of x = 1.85 =  0

So   (1.85)^3 -3(1.85) - 1  =   -.218

The root must be between  1.85 and 1.9

Average ths   [ 1.85 + 1.9] /2 = 1.875

Put this into the function

 (1.875)^3 -3(1.875) - 1   =  -.033                

The root must be between   1.875 and 1.9

Average these =  [ 1.875 + 1.9 ] / 2  = 1.8875

Put this value into the function

 (1.8875)^3 -3(1.8875) - 1   = .062

The root must be between 1.875 and 1.8875

Average these  = [ 1.8875 + 1.875 ] / 2 = 1.88125

Put thiis into the function

 (1.88125)^3 -3(1.88125) - 1  = .014

The root must be between 1.875 and 1.88125

Average these = [ 1.88125 + 1.875 ] / 2  = 1.878125

Put this into the function ≈  -.009       (1) 

The root must be between  1.878125 and 1.88125

Average these = 1.8796875

Put this into the function =  .002

The root must be between   1.878125 and 1.8796875  

Average these = 1.87890625

Put this into the function = -.0036     ......This agrees with (1) to 2 decimal places

So....the approximate root is  ≈  1.87

[ Note....the true root is ≈ 1.8794 ]

Changing the denomintor from   x-3    to x+4      shifts LEFT by   7

changing the +1   to  +3    shifts UP   2 

5t+4 >19     subtract 4 from both sides of the equation

5t > 15         divide both sides by 5

t>3            Answer A

  Actually the equation SHOULD read 5t+4 >= 19   because if he rides EXACTLY 3 loops and to-from the park it would be exactly 19 miles

Divide both sides of the equation by 26.

Actual Mechanical Advantage is a more realistic number than IMA , as  AMA accounts for friction etc.

80N x 1m = 80 N*m    (torque)    the work 'in'

Output   150 N * .5 m = 75 N* m   the work 'out     (so some of your input is lost in the form of friction, sqeaks,slippage etc)

AMA =   output F / input F  =   150/80 =  1.875      ( I have not seen this subject in a long time......pretty sure of my answers though)

(2^37)mod 60 =  32     min  after the hour

So

[2^37 - 32] / 60 =   2290649224

(2290649224 ) mod 24 =   16     hrs after 1700  hrs

The time shown on the clock will  be    16 hr 32 min  after   1700  hrs    (5PM)  = 9:32 AM =  0932 hrs

IMA = Ideal Mechanical Advantage  = force multiplier

280 N out is the input force multiplied by 7     so the input force is  280n/IMA = 280/7 = 40 N

Ah ok. I thought it could be that but then confused myself.

Thanks

3^m   *    3ⁿ    = 3^m+n

^sooooooo....

3^m+n  = xy

I'll give ya partial credit.....  1/2 of a heart.    Haha  

Not exactly sure what you are asking, but I will go with this:

8x=140   divide both sides of the equation by 8

x = 17.5 degrees

Maybe   8x + 140 = 180   ??    subtract 140 from both sides

              8x = 40                       divide both sodes by 8

                 x = 5

Thank you much! I will check out the desmos graphing system as well. It could come in handy for understanding problems like these!!