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trasher [3.6K]
3 years ago
11

For what value of c is the relation a function (2,8),(12,3),(c,4),(-1,8),(0,3)

Mathematics
1 answer:
Fittoniya [83]3 years ago
3 0
The value of c is { c | c ∈ R, c ∉ {-1,0,2,12} }.
c is a number such that it is not in the set {-1,0,2,12} else we end up with a domain value having multiple range values, contradicting with the definition of a function.


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Question 2 -of 15 Step 1 of 1No Time LimitA company manufactures two products. One requires 5 hours of labor, 3 poundsof raw mat
elena-14-01-66 [18.8K]

the cost of labour per hour is $7.20

the cost of raw materials per pound is $11.60

Explanation:

For product one:

time = 5 hours of labour

let the cost labour per hour = x

Amount = 3 pounds of raw amterials

let the cost of one pound raw material = y

Cost to produce each product = $70.8

The equation:

time (cost per hour) + amount (cost of one pound of raw material) = Cost to produce each product

5(x) + 3(y) = 70.80

5x+3y=70.8....\mleft(1\mright)

For product 2:

time = 3.5 hours of labour

let the cost of labour per hour = x

Amount = 13 pounds of raw amterials

let the cost of one pound raw material = y

Cost to produce each product = $176.00

The equation:

time (cost per hour) + amount (cost of one pound of raw material) = Cost to produce each product

3.5(x) + 13(y) = 176

3.5x+13y=176\text{   .... (2)}

combining both equations:

5x + 3y = 70.8 ...(1)

3.5x + 13y = 176 ....(2)

Using elimination method:

To eliminate y, we will multiply equation (1) by 13 and equation (2) by 3 so that both coefficient of y become the same

65x + 39y = 920.4 ...(*1)

10.5x + 39y = 528 ...(2*)

subtract equation (2*) from (1*):

65x - 10.5x + 39y - 39y = 920.4 - 528

54.5x + 0 = 392.4

54.5x = 392.4

divide both sides by 54.5:

x = 392.4/54.5

x = 7.2

substitute for x in any of the equations

Using equation 1: 5x + 3y = 70.8

\begin{gathered} 5\mleft(7.2\mright)+3y=\text{ 70.8} \\ 36\text{ + 3y = 70.8} \\ 3y\text{ = 70.8 - 36} \\ 3y\text{ = 34.8} \\  \\ \text{divide both sides by 3:} \\ \frac{3y}{3}=\frac{34.8}{3} \\ y\text{ = }11.6 \end{gathered}

Hence, the cost of labour per hour is $7.20 and the cost of raw materials per pound is $11.60

6 0
1 year ago
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