Question

The company also discovered that it costs $15.50 to produce 3 widgets, $23.50 to produce 7 widgets, and $56 to produce 12 widgets. What is the total cost producing 5 widgets?

Answer 1

It's a quadratic function, and you have three given points.

The form of a quadratic function is

ax2+bx+c=0

You have three given (x, y) points:

(3, 15.50)
(7, 23.5)
(12, 56)

Insert each of the three points in the equation.
You will get three equations in three unknowns, a, b, and c.
Solve the system of equations for a, b, and c.
Then insert a, b, and c in the quadratic equation above.

Finally, evaluate it for x = 5.

Answer 2

yeah i know those points. but i dont know which variable to plug them into.

Answer 3

@wrstlr3232

Answer 4

@SolomonZelman

Answer 5

\[9a+3b+c = 15.5\]
\[49a+7b+c=23.5\]
\[144a+12b+c=56\]
solve the system

Answer 6

a= 1/2
b= -3
c= 20 ????

Answer 7

a and b are right. I got 19.5 for c

Answer 8

how ?

Answer 9

its 20.. i just calculated it

Answer 10

Now substitute 5 into the quadratic equation:
1/2(25)+-3(5)+20 = ? The cost to produce 5 widgits

Answer 11

i dont get that part..

Answer 12

\[ax ^{2}+bx+c=0\]

Answer 13

1/2(5^2)+-3(5)+20=0
12.5-15+20 = 17.50 so it costs 17.50 to produce 5 widgits (5, 17.50)

Answer 14

a=1/2
b=-3
c=20 substituted those values for a, b, c...used 5 for the x value since that's what we're looking for

Answer 15

thanks can you help me with one more problem?

Answer 16

sure

Answer 17

Looks very similar to last problem

Answer 18

any idea ?

Answer 19

4a+2b+c=45
16a+4b+c=143
100a+10b+c=869 solve the systems

Answer 20

Let me know what you got for a, b, & c...I've determined those

Answer 21

Is there any more to the question?\[c(x)=9x ^{2}-5b+19\]

Answer 22

a= 9
b= -5
c= 19

Answer 23

Yes...Great.

Answer 24

yeah i have to find the total cost of producing 1 calculator

Answer 25

substitute a 1 in for x in the c(x) equation I showed up a few

Answer 26

c(x)=9x2−5b+19
c(x) = 9(1)-5(1)+19 =

Answer 27

23?

Answer 28

yes