Question

PLEASE HELP.

Answer 1

Answer:

The total cost of producing 6 widgets is $231.

Step-by-step explanation:

Given : Widget wonders produces widgets. They have found that the cost, c(x), of making x widgets is a quadratic function in terms of x.

To find : The total cost of producing 6 widgets.

Solution :

Cost is given by $c (x) = ax^2 + bx + d$

• Cost $23 to produce 2 widgets,

$c(2) = a(2)^2 + b(2) + d$

$23= 4a+2b+d$ .........[1]

• Cost $103 to produce 4 widgets,

$c(4) = a(4)^2 + b(4) + d$

$103= 16a+4b+d$ ............[2]

• Cost $631 to produce 10 widgets.,

$c(10) = a(10)^2 + b(10) + d$

$631= 100a+10b+d$ ...........[3]

Now, we solve equation [1], [2] and [3]

Subtract equation  [2]-[1]  and [3]-[2]

[2]-[1] →  $12a+2b=80$  ........[4]

[3]-[2] →  $84a+6b=528$  .......[5]

Solving equation [4] and [5] by elimination method,

Multiply equation [4] by 3 and subtract from [5]

$84a+6b-3(12a+2b)=528-3(80)$

$84a+6b-36a-6b=528-240$

$48a=288$

$a=6$

Put in equation [4]

$12(6)+2b=80$

$72+2b=80$

$2b=8$

$b=4$

Substitute the value of a and b in [1] to get d

$23= 4a+2b+d$

$23= 4(6)+2(4)+d$

$23= 24+8+d$

$23= 32+d$

$d=-9$

Substitute a=6,b=4,d=-9 in the cost equation,

The required equation form is $c(x) = 6x^2 + 4x-9$

The total cost of producing 6 widgets.

Put x=6

$c(6) = 6(6)^2 + 4(6)-9$

$c(6) = 216+15$

$c(6) =231$

Therefore, The total cost of producing 6 widgets is $231.

Answer 2

Quadratic
y = ax^2 + bx + d
c (x) = ax^2 + bx + d
c (3) = a (3^2) + b (3) + d
c (3) = 9a + 3b + d = 15.50

c (7) = a (7^2 + b (7) + d

c (7) = 49a + 7b + d = 23.50

c (12) = a (12^2) + b (12) + d
c (12) = 144a + 12b + d = 56

solve using simultaneous equations... to get a b and d

use that to solve for x = 5

hope this helps?