ElectricPavlov

Again.... what two numbers ADDED together = -17   and multiplied together = 72     (-9   and -8)

(p-9)(p-8)

Find the zeroes of the equation....the distance between them will give you the width

Find the Vertex to know the height....

vertex is given by   - b / 2a   =    - 3.2 / (2*(-.1) ) = 3.2/.2 = 16  feet     (equation parameters were not supplied...hence the ?)

at x = 16     f(x) = -.1(16^2) + 3.2(16) - 3.5    = 22.1 feet (?)   tall

Now we know it is 22.1 feet tall at   x = 16    but we still do not know the width....

Find the zeroes using quadratic equation

-3.2 +- ( sqrt(3.2^2 - 4(-.1)(-3.5)   /  2(-.1)  =  30 .86  - 1.134 = 29.76 feet wide     at the BASE

The train looks like it will fit.......    this equation is a parabola BUT.....at y = 20   is the equation > 10    for the train to fit???

20 = -.1x^2 + 3.2 x - 3.5   ???   Yields   x = 11.417   and  20 .583    which is less than 10 (9.166)

The train may not  fit ! 

A lot of times, you can eliminate a step by assigning 'x' the value you are looking for....

x = larger number

x-1 = the previous number

The difference in these squares = 59

x^2 - (x-1)^2 = 59     expand

x^2 - x^2 + 2x -1 = 59

2x-1 = 59

2x = 60

x = larger number = 30         x^2 = 900

OK..... you have two RIGHT triangles

sine = opp / hypotenuse        (this assumes the angles you gave me are the angles the cables make with the ground)

            =    12/hyp

sine 30 = 12/hyp

.5 = 12/hyp              hyp = 24  for one side

the OTHER side

sin 45 = 12/hyp           hyp = 16.97                          total = 24 + 16.97 = 40.97 m

Sorry ....I edited this several times !!

Area of a circle = pi r ^2          calculate the larger circle area ....then subtract the 13 smaller circle total area form it......

All pretty good, except this is an EXPONENTIAL function....it is not linear month-to-month but is INRASING each month

(I am assuming you do NOT know how to derive   dm/dt   the rate function of this population function)

month 5 = 32.62

month 6 = 39.84

month 7 =  48.66

A little 'narrower' range of months ( rahter than 0 - 6 months) will yield better 'average'

in two months from 5 to 7       (48.66-32.62 ) / 2 = 8.02 rabits per month increase

or from month 5 to month 6   =  39.84 - 32.62  = 7.22 rabbits/month

Let's look at month  5.5 to 6.5  =  44.03   -36.05= 7.98 rabbits/month

Since it is a RIGHT TRIANGLE , you can use the pythagorean theorem to find the other side (the distance from the base of the ladder to the house)  

x^2 + 16^2 = 20^2

x=12 ft    

We need to know the angle of the    wires to the ground    or wires to the pole   to figure this one ,,,,,  

If he does those things in the order listed, the equation looks like this

x  Larry's age

((x+10)/2   - 10 ) * 2 = 30      Solve for x    First divide both sides of the equation by 2

(x+10 )/2  -10 = 15                          add 10 to both sides

(x+10) /2       = 25                      multiply both sides by 2

x+10 = 50                              subtract 10 from both sides

x = 40 y/o = Larry ('the Liar's ' ) age                 

The only reasonable way I can see is to use the quadratic Formula to find the roots....

\(x = {-b \pm \sqrt{b^2-4ac} \over 2a}\)           a = -1    b = -3   c = 90