A grocer sells 30 loaves of bread a day. The cost is $2.50 per loaf. The grocer estimates that for each $0.50 increase in cost,
2 fewer loaves of bread will be sold per day. Let x represent the number of $0.50 increases in the cost of a loaf of bread.For what number of $0.50 increases in the cost of a loaf of bread will the grocer's generated revenue be greater than zero?
A. The grocer's generated revenue will be greater than zero for any number of $0.50 increases greater than 20.
B. The grocer's generated revenue will be greater than zero for any number of $0.50 increases less than 20.
C. The grocer's generated revenue will be greater than zero for any number of $0.50 increases greater than 15
.
D. The grocer's generated revenue will be greater than zero for any number of $0.50 increases less than 15.
A. The grocer's generated revenue will be greater than zero for any number of $0.50 increases greater than 20.
B. The grocer's generated revenue will be greater than zero for any number of $0.50 increases less than 20.
C. The grocer's generated revenue will be greater than zero for any number of $0.50 increases greater than 15
.
D. The grocer's generated revenue will be greater than zero for any number of $0.50 increases less than 15.
1 answer:
Answer:
none of the above
Step-by-step explanation:
The grocer's revenue will be the product of the number of loaves sold (30-2x) and their price (2.50+0.50x).
Revenue will be positive for values of x between those that make these factors be zero. The number of loaves sold will be zero when ...
... 30 -2x = 0
... 15 -x = 0 . . . . . divide by 2
... x = 15 . . . . . . . add x
The price of each loaf will be zero when ...
... 2.50 +0.50x = 0
... 5 + x = 0 . . . . . . . multiply by 2
... x = -5 . . . . . . . . . . subtract 5
Revenue will be positive for any number of increases greater than -5 and less than 15.
_____
D is the best of the offered choices, but it is incorrect in detail. -5 is a number less than 15, but will give zero revenue.
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Answer:
General Formulas and Concepts:
<u>Calculus</u>
Differentiation
- Derivatives
- Derivative Notation
Derivative Property [Multiplied Constant]:
Derivative Property [Addition/Subtraction]:
Derivative Rule [Basic Power Rule]:
- f(x) = cxⁿ
- f’(x) = c·nxⁿ⁻¹
Derivative Rule [Product Rule]:
Derivative Rule [Quotient Rule]:
Derivative Rule [Chain Rule]:
Step-by-step explanation:
*Note:
Since the answering box is <em>way</em> too small for this problem, there will be limited explanation.
<u>Step 1: Define</u>
<em>Identify.</em>
<u>Step 2: Differentiate</u>
We can differentiate this function with the use of the given <em>derivative rules and properties</em>.
Applying Product Rule:
Differentiating the first portion using Quotient Rule:
Apply Derivative Rules and Properties, namely the Chain Rule:
Differentiating the second portion using Quotient Rule again:
Apply Derivative Rules and Properties, namely the Chain Rule again:
Substitute in derivatives:
Simplify:
We can rewrite the differential by factoring and common mathematical properties to obtain our final answer:
∴ we have found our derivative.
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Learn more about derivatives: brainly.com/question/26836290
Learn more about calculus: brainly.com/question/23558817
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Topic: Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Differentiation
The perpendicular bisector theorem gives the statements that ensures
that and
are perpendicular.
The two statements if true that guarantee is perpendicular to line
are;
Reasons:
The given diagram is the construction of the line perpendicular to line
.
Required:
The two statements that guarantee that is perpendicular to line
.
Solution:
From the point <em>C</em> arcs <em>E</em> and <em>D</em> are drawn to cross line , therefore;
arcs drawn from the same radius.
is perpendicular to line
, given.
Therefore;
by perpendicular bisector theorem.
Learn more about the perpendicular bisector theorem here: