Applicaitions of cubics + quadratics look at this :p

[dagg3r]

1. A student wants to construct an open box with a base area 35 cm2 from a rectangular piece of cardboard measuring 9 cm by 7 cm.
Find x, where x cm is the length of the side of the square which must be removed from each corner of the cardboard.

this is what i did, i went (9-2x)*(7-2x)=35, then i get it in a form of a quad or cubic, then find the x-intercepts?



2. From a rectangular sheet of metal, ABCD, the part ABP is cut, and the area of the remaining part is 114 cm2.
Find the value of x.


i am totally lost i don't know what to do here



3. The demand, x units of a certain product is given by x = 400 - 0.25p per month
where p is the selling price per unit. The cost, $C, to produce x units is given by
C = 9600 + 1200x
a) Express p in terms of x.

yeah this one i did. p=4 (400 - x)



b) The revenue obtained is a result of selling a number of units at a certain price.
Express the revenue, R, in terms of x.

totally lost, do i just use the x= 400 - 0.25p , and sub p from previous example in?



d) Determine the number of units that must be produced and sold each month :



i) in order to break even

i have to use the c= formula and find the x-intercepts?

ii) if the profit is to be $300 per month.

totally lost here



c) Express the profit, P, in terms of x.

profit... how do i do that?

 

[Mulder]

#1 - is there anything that says you have to cut out squares? You can cut out rectangles and still form a box, so you want x and y, say.

edit; ok if it does have to eb squares, won't you want 5 * (9-2x)(7-2x)? Try drawing it again.

#2, which length is 'x'?

 

[tacman]

1. To construct the open box, you need to cut out squares of size x from each corner of the cardboard. This will create flaps on each side that can be folded up to form the sides of the box. The length and width of the base will be (9-2x) and (7-2x) respectively. Since the base area is 35 cm2, we can set up the equation (9-2x)*(7-2x)=35 and solve for x by finding the x-intercepts. Once we have the value of x, we can cut out the squares and fold up the flaps to construct the box.

2. In this problem, we are given the area of the remaining part after cutting out triangle ABP, but we don't know the dimensions of the remaining part. To find the value of x, we can set up the equation for the area of the remaining part as (9-x)*(7-x)=114 and solve for x by finding the x-intercepts.

3. a) To express p in terms of x, we can rearrange the demand equation to solve for p. We get p = (400-x)/0.25.

b) Revenue, R, is given by the product of the number of units sold (x) and the selling price (p). So we can express R as R = px = p(400-x).

d) i) To break even, the cost of producing x units should be equal to the revenue obtained by selling x units. So we can set up the equation C = R and solve for x by finding the x-intercepts of the equation (9600 + 1200x) = (p(400-x)).

ii) To make a profit of $300, the revenue obtained from selling x units should be $300 more than the cost of producing x units. So we can set up the equation R = C + 300 and solve for x by finding the x-intercepts of the equation (9600 + 1200x + 300) = (p(400-x)).

c) Profit, P, is given by the difference between the revenue (R) and the cost (C). So we can express P as P = R - C = (p(400-x)) - (9600 + 1200x).