2. The school PTA is sponsoring a dance. They decide to price student tickets at $6.00. It will cost the PTA $250.00 to put on t
2 answers:
Answer:
The PTA must sell 42 tickets to make a profit.
Step-by-step explanation:
To solve this problem, we will have to construct an inequality in which $250 is less than our solution.
Let = student tickets
Since each student ticket is priced at $6.00, the money raised by the student tickets can be represented by the expression:
Since it will cost the PTA $250.00 for the dance, the profit will have to be equal to anything greater than $250.00.
Set up your inequality:
Divide both sides of the inequality by the coefficient of , which is
:
As you can see, we are left with a decimal, but we will have to round to the nearest whole number as the tickets can only be represented as whole numbers:
Therefore, the PTA must sell 42 tickets in order to make a profit.
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You can check your work by substituting the solved value for the tickets into the inequality:
And since $252 is greater than $250 (represents a $2 profit), our solution is correct.
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Answer:
The maximum error in the calculated surface area is approximately 8.3083 square centimeters.
Step-by-step explanation:
The circumference (), in centimeters, and the surface area (
), in square centimeters, of a sphere are represented by following formulas:
(1)
(2)
Where is the radius of the sphere, in centimeters.
By applying (2) in (1), we derive this expression:
(3)
By definition of Total Differential, which is equivalent to definition of Linear Approximation in this case, we determine an expression for the maximum error in the calculated surface area (), in square centimeters:
(4)
Where:
- Measure circumference, in centimeters.
- Possible error in circumference, in centimeters.
If we know that and
, then the maximum error is:
The maximum error in the calculated surface area is approximately 8.3083 square centimeters.