The first equation in the following system gives a company's income, in dollars, for selling x baseball caps. the second equation gives the cost of making x baseball caps. y = 8x y = -0.01 x2 + 4x + 3,200 the solution of the system is (400, 3,200). how would you interpret this solution?

The solution of the system is the point where the graphs intersect, or have the same x and y values. This means that the company's cost to produce 400 caps is the same as the income made from selling 400 caps. Therefore, the company will not make a profit.

The cost to produce 400 caps is the same as the income made from selling 400 caps.

The company will break even when it sells 400 caps; it will not make a profit.

Step-by-step explanation:

Step-by-step explanation:

Given that company's income for selling x baseball caps is

y=8x.  this implies that selling price per baseball cap= 8 dollars.

Next is given the cost equation

y =

Any company will have objective to minimize the cost

Consider the profit equation P = income - cost

i.e. P(x) =

It is that of a parabola.

x intercept is when P =0

x = 400 or -1000

x cannot be negative

Hence for x =400, profit =0

and income = 8(400) = 3200

SO solution of the system is (400,3200)

When 400 units are produced and sold the company makes zero profit, and if units go beyond 400 units profit would be earned.

geometric series converge the common ratio r has magnitude less than one.

which is equivalent to

for the example we need

|2-x| < 1

-1 < 2-x   and 2-x < 1

x < 3 and x > 1

we can write that

answer: 1 < x < 3

1a. common ratio r=250/25=10 > 1     diverges

1b.   r=50/100=1/2 converges

when these converge they converge to

where a is the first term.

answer: 200

1c. r=-1   so it's not the case that |r| < 1.     diverges

2a. x is the common ratio so we converge when |x|< 1

2b.   r=-10x / -2 = 5x.

we converge when

|5x| < 1

|x| < 1/5

2c.   r=3-2x

-1 < 3-2x and 3-2x < 1

-4 < -2x and 2 < 2x

x < 2 and 1 < x

1 < x < 2

2d. [/tex] r=-48x^3/12 = 4x^3[/tex]

|4x^3| < 1

|x^3| < \frac 1 4

|x| < 4^{-1/3}