A company sells widgets. The amount of profit, y, made by the company, is related to the selling price of each widget, x, by the given equation. Using this equation, find out what price the widgets should be sold for, to the nearest cent, for the company to make the maximum profit. y=-34x^2+1542x-10037

In order to maximize profit, the company should sell each widget at $22.68.

Step-by-step explanation:

The amount of profit y made by the company for selling widgets at x price is given by the equation:

And we want to find to price for which the company should sell in order to maximize the profit.

Since our equation is a quadratic with a negative leading coefficient, its maximum will occur at the vertex point.

The vertex of a quadratic is given by the formulas:

In this case, a = -34, b = 1542, and c = -10037.

Find the x-coordinate of the vertex:

So, in order to maximize profit, the company should sell each widget at $22.68.

Extra Notes:

In order to find the maximum profit, substitute the price back into the equation:

the first dot plot best represents the data

plzplzplzplz mark brainliest and have a good day

step-by-step explanation: so we look at the formula un = a + (n-1)d

un is the amount of seats

n is the nth term aka row number

a is the original sequence/row number

d is the difference between each term

so in this a=22 d=6 and n can remain as n because we are simply formjng a rule

lets put these in the equation

un=22+(n-1)(6)

this is your answer to part a

however

lets double check that this is correct, we'll try putting it into the second term

un=a+(n-1)d

u2=22+(2-1)(6)

u2=22+6

u2=28

as the question said the second row has 28 seats so now we know the formula we made is correct.

as for part b

un=a+(n-1)

its asking us to find a row with 100 seats.

remember un was the amount of seata so all we do is substitute this in.

un=100 a=22 d=6

un=a+(n-1)d

100=22+(n-1)(6)

so now we simplify to find n which is the row number.

100-22=22+(n-1)(6)-22

78=(n-1)(6)

78/6=(n-1)(6)/6

13=n-1

13+1=n-1+1

14=n

so now we know that in the 14th row there is 100 seats.

hope this and that you understood! its my first time using the app or anyone out on here : p its also me to revise so a bunch! ask more questions if you dont understand ☺