any math wizards? help please

[csuf_gambler]

please explain to me how to solve each of these

1. solve for X. 3x^2-4x^3 = 0


2. find the slope of the line Y = f(x) = 4, then draw a graph. what is f(3). (dont even understand this one)


3. given demand and supply functions D(x) = (x-5)^2 and S(x) = x^2+x+3 , find the equilibrium point (xE,pE)


thanks

[Homer]

1. solve for X. 3x^2-4x^3 = 0

x^2(3-4x)=0

x^2 = 0 or 3-4x = 0

x = 0, 3/4

2. find the slope of the line Y = f(x) = 4, then draw a graph. what is f(3). (dont even understand this one)

Y = f(x) = 4 is a horizontal line. The value of the function is 4 for all values of x (f(3) = 4) and the slope is 0.

3. given demand and supply functions D(x) = (x-5)^2 and S(x) = x^2+x+3 , find the equilibrium point (xE,pE)

Set the functions equal to each other:

D(x) = S(x)

(x-5)^2 = x^2+x+3

x^2-10x+25 = x^2+x+3

11x = 22

x = 2

Next time if you want me to do your homework it'll cost you.

-- Homer

[bigpooch]

Do you expect someone to do your homework for you? /images/graemlins/laugh.gif
You must be pretty desperate, n'est ce pas?


1. For any polynomial zeros, simply keep factoring out
either (x-k) for some k or (x^2+ax+b) where the latter has
complex roots (but no real roots):

3x^2-4x^3 = x^2(3-4x) so right away you see that 0 is a
double root and the other root is that which solves 3-4x=0
or x=3/4.

A few comments: if there is no constant term, 0 is a root;
if the sum of coefficients is 0, 1 is a root.

2. If this is all you are given, f(x) is just a constant
function, so you should know the slope is 0 and f(anything)
is just 4.

In general, if f(x)=mx+b, the slope is m and the y-intercept
is b.

3. If D and S are the demand and supply functions, the
equilibrium is where the curves intersect, so for D(x)=S(x),
x^2-10x+25 = x^2+x+3 so therefore, x+3 = -10x+25 which gives
x=2 and so D(2)=S(2)=9 and the point of interception is just
(2,9).

Review:
quadratic equation: do you know it? It's important!

Interesting question: suppose a sales tax is placed on a
good in question (say 10%); who actually pays for it? For
example, here in Canada there is something called the GST
(goods and services tax) and technically/legally the
consumer pays for it. But if the demand, supply curves for
a product are usual, the consumer doesn't foot the entire
bill: do you see why?


By the way, if you should ever enter grad school in a field
like economics, don't, until your mathematics is much much
better! You'll have to not only pick up statistics, but
even Lebesgue measure and integration. Better yet, think
of the social "sciences" other than economics!

[csuf_gambler]

thanks guys. i understand it now. except number 1. i messed up the equation, its actually:

2x^4-4x^3=0

[csuf_gambler]

this isnt really homework. school just started and im in math 135:business calculus. this is just a little "gateway" quiz. unfortunatly i forgot most of what i learned in math 115 during the long winter break. and i just cant click with polynomail equations for some reason. i get most of the other stuff. and no i dont think im ever going to grad school.

[Homer]

Factor out the common stuff (x^3), then solve. You should get 0 and 2.

-- Homer

[Ed Miller]

How did algebra 1 all of a sudden become a college course?

[southerndog]

You'd be surprised.