An example of a domain that can be illustrated from the information given will be D(x) = 32.
<h3>Domain and range</h3>
An example based on the information given is "A gas tank in John's car can hold 20 gallons of gas and the car gets 32 miles for every gallon".
John fills up the tank and then goes on a trip. In this case, the distance that will be travelled on one tank will be:
D(x) = 32x
In the above function, it should be noted that the number of gallons can be from 0 to 20. Since he gets 32 miles per gallon, the car can travel 640 miles.
In this case, the domain is the number of gallons that can be used. The number of miles will be the range.
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Answer: The company should produce 7 skateboards and 16 rollerskates in order to maximize profit.
Step-by-step explanation: Let the skateboards be represented by s and the rollerskates be represented by r. The available amount of labour is 30 units, and to produce a skateboard requires 2 units of labor while to produce a rollerskate requires 1 unit. This can be expressed as follows;
2s + r = 30 ------(1)
Also there are 40 units of materials available, and to produce a skateboard requires 1 unit while a rollerskate requires 2 units. This too can be expressed as follows;
s + 2r = 40 ------(2)
With the pair of simultaneous equations we can now solve for both variables by using the substitution method as follows;
In equation (1), let r = 30 - 2s
Substitute for r into equation (2)
s + 2(30 - 2s) = 40
s + 60 - 4s = 40
Collect like terms,
s - 4s = 40 - 60
-3s = -20
Divide both sides of the equation by -3
s = 6.67
(Rounded up to the nearest whole number, s = 7)
Substitute for the value of s into equation (1)
2s + r = 30
2(7) + r = 30
14 + r = 30
Subtract 14 from both sides of the equation
r = 16
Therefore in order to maximize profit, the company should produce 7 skateboards and 16 rollerskates.
X2 - 8x + 15 = 0
(x - 3)(x - 5) = 0
critical points are at 3 and 5
