Suppose that income is a function of age. The following function represents the relation between average annual income I and age a.   I(a)=-54a^2 +5,119a -54,421   ​(a) For what age does average income I equal $40,000? ​(b) For what age does average income I equal $50,000?

Q: Express the gross salary G of a person who earns $14 per hour as a function of the number x of hours…

A: Given: Earning per hour = $14       To determine: Gross salary as a function of the number of…

Q: A photocopy service has a fixed cost of $2000 per month (for rent, depreciation of equipment, etc.)…

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Q: Differentiate the functions.

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Q: The relationship between the amount of time a car is parked, in hours, and the cost of parking, in…

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Q: . Sketch the graph of the amount of a particular brand of coffee sold by a store as a function of…

A: To Sketch The graph of the amount of a particular brand of coffee sold by a store as a function of…

Q: During a nine-hour snowstorm, it snows at a rate of 1 inch per hour for the first 2 hours, at a rate…

A: Explanation: Given that,  Rate of snowstorm first two hours = 1 inches/hours Rate of snowstorm next…

Q: How to form a piecewise function by using linear function?

A: The piecewise function can be formed using linear functions as shown below.

Q: The price of 1 gallon of unleaded gasoline at the pump dropped to $2.19 on January 1, 2015, and…

A: As the price of  1 gallon of unleaded gasoline is decreasing  4 cents per month starting from…

Q: of function

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Q: If the monthly consumption of water is less the 2800 gallons then $9.48 is charged and if 2801-5500…

A: Given: Amount charged if the monthly consumption of water is less than 2800 gallons = $9.48 Amount…

Q: Suppose that the height (in centimeters) of a candle is a linear function of the amount of time (in…

A: The height(cm) of the candle is a linear function of the amount of time (in hours) it has been…

Q: (0, 3) 2 1- (2.0)

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Q: Try to draw a vertical line on the graph so it intersects the graph in more than one place. If you…

A: Given graph :

Q: FX) = Secx

A: Given function to be differentiated is : F( X ) = sec X2 In order to differentiate above function,…

Q: Suppose the function f(x) = 0.035x represents the number of U.S. dollars equivalent tox Russian…

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Q: What can you conclude about the inverses of functions whose graphs are lines parallel to the line y…

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Q: Differentiate the function.

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Q: According to the National Center for Health Statistics, in 1990, 28% of babies in the United States…

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Q: Can the graph of a one-to-one function intersect a horizontal line more thanonce? Explain.

A: A one-to-one function f(x) is defined as, Thus, we can infer from the above definition of a…

Q: Write a function rule for the total cost in dollars of gasoline if a gallons of gasoline for $3 per…

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Q: Differentiate the function

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Q: What can you conclude about the inverses of functions whose graphs are lines perpendicular to the…

A: If a graph of a function is perpendicular to the line y=x, then the reflection of the line on y=x…

Q: Write the length L of the rectangle as a function of y.

A: The length L is bounded by two graphs x=2  &  x=2y3

Q: Explain how the vertical line test is used to detect functions.

A: Vertical line test: Draw a vertical line on the graph of the given equation. If the line passes…

Q: homeowner's insurance in a particular year can be described by the function ​f(x)=414.84(1.033)x​,…

A: Given query is to find after how many years average homeowners premium will be 1500.

Q: The number of ATV-related deaths for people of all ages from 1999 to 2009 can be modeled by the…

A: Given the number of ATV-related deaths for people of all ages from 19999 to 2009 can be modeled by…

Q: Suppose that the revenue from selling x washingmachines isr(x) = 20,000(1 - 1/x)dollars. Use the…

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Q: How can you tell from the graph of a function whetherit is one-to-one?

A: Concept: The calculus helps in understanding the changes between values that are related by a…

Q: A rectangular plot of ground is to be enclosed by a fence and then divided down the middle by…

A: Given:length of the force down the middle=x feetcost of the fence down th middle=php 36.00 per foot…

Q: What is the midline equation for the function

A:

Q: during typhoo Ambo, PAGASA tracks the amount of accumulating rainfall. For the first three hours of…

A: For first three hours, the rain fell at a rate of 25 mm per hour.  So for time 1≤t≤3 the rate was 25…

Q: What are the Piecewise-Defined Functions?

A: Piecewise function is a function which has multiple sub-functions. Each sub-functions has different…

Q: Describe what is the relationship between differentiability and continuity of a function.

A: To explain: The relationship between differentiability and continuity of a function. Explanation:…

Q: Based on past experiences, a homeowner estimates that appliances lose 35% of their resale value each…

A:

Q: How can I tell if a graph is the function of x?

A: HOW TO: GIVEN A GRAPH, USE THE VERTICAL LINE TEST TO DETERMINE IF THE GRAPH REPRESENTS A FUNCTION OF…

Q: What will be the orientation of the curve of the graph of the function f(x) = on (-3,0)? A.…

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Q: would it make sense for a function to pass through (0,100)? Why?

A: Topic:- function and geometry

Q: rectangular plot of ground is to be enclosed by a fence and then divided down the middle by another…

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Q: what is increasing or decreasing function

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Q: Determine the end behavior of the graph of the function. 1 f (x) = -x°- 2x* -x° +7 As x - -00, f (x)…

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Q: How can we represent a function ?

A: Function is the relation in which each element of the domain is related with exactly one element in…

Q: Sketch the graph of the function with the given rule. if x < 3 5- x 3x - 7 if x 2 3 y

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Q: Identify the relations which are also functions.

A:

Q: During a nine-hour snowstorm, it snows at a rate of 1 inch per hour for the first 2 hours, at a rate…

A: Given that: Rate of fall of snow for the first 2 hours = 1 in/hrRate of fall of snow for the next 6…

Q: Explain the difference between a relation and a function

A: A relation is a set of inputs and outputs that are related in some way.

Q: What is the Horizontal Line Test for One-to-One Functions?

A: we have to define the horizontal line test for One-to-One Functions.

Q: Explain in your own words what a function is. How is a function different from a relation?

A: A function is a relation between two sets that associates to each element of the first set exactly…

Q: Use function notation to represent that your annual salary after working five years at your job is…

A: We will find the required function as following.