The elevation of a valley above sea level (in feet) is modeled by the function f(x, y) = -2000 +0.004(x – 1000)² + 0.001(y + 1000)²

Q: Find the slope of the graph of the function at the given point.                         f(x) = 3x2 −…

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Q: Differentiate the function using the three step rule. Show your solution. f(x)=(x)/(√(x-4))

A: You must have idea about three step differentiation method.

Q: The line y= -3x+b is tangent to the function y=x3-3x2. What is the value of b? -2 -1 1 2

A: At the point of tangency the slope of the curve and that of the line should be equal. Slope of the…

Q: In the equation x= y3-10 is y a function of x?   I have no idea what this is asking me?

A: Rewrite the given as follows.

Q: A contractor is to build a warehouse whose rectangular floor will have an area of 4000 square feet.…

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Q: A company estimates the profit for selling a certain commodity by the given function, P(x) = -x2…

A: We will find out the required value.

Q: The revenue from the sale of a product is given by the function R= 324x-x. Selling how many units…

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Q: A parachutist is falling with speed 176 ft/s when his parachute opens. If the Wv? lb, where W is the…

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Q: The area of a rectangular garden is 125 square feet. The garden is to be enclosed on three sides by…

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Q: S-x-1 x-2

A: Given function

Q: A toy company can make a doll worth 55 pesos for christmas season. If the production manager plans…

A: We will solve the problem

Q: The area of a rectangular floor is 1000 square feet. Express the perimeter of the floor, P, as a…

A: Let x be the width and y be the length of the rectangular floor. Given that the area of a…

Q: On a recent scuba diving trip, Kate and Kara reached a depth of 130 feet. Six-and-a-half minutes…

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Q: A 1 lb sponge initially contains 5 lb of water. As it is lifted up from the ground, the sponge loses…

A: Answer is option d here decrement in water is linearly (as constant rate)

Q: The y-intercept of the function is

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Q: How do you determine if an equation in x and y defines y as a function of x?

A: To Determine: If an equation in x and y defines y as a function of x. Explanation: If in any…

Q: The function C(x)=300x+6,000 represents the cost to produce x number of items. How many items should…

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Q: Differentiate the function.

A: The given differential equation is y=x2e-1x Apply the product rule f·g'=f'g+g'f to differentiate the…

Q: The percentage of gross domestic product​ (GDP) in a state going toward health care from 2007…

A: Given, the modelled function f(x) = 1.3lnx + 14.7, where f(x) is the percentage of gross domestic…

Q: A parachutist is falling at speed of 176 ft/s when his parachute opens. If the air resistance is…

A: Solution is in step 2

Q: The revenue from the sale of a product is given by the function R= 289x -x. Selling how many units…

A: To find the number of products to be sold for positive revenue

Q: It costs $3 per hour to park in a parking lot, with a maximum cost of $12. Explain why the amount of…

A: Authoring guidelines: As per the authoring guidelines, we can solve only the first question.Please…

Q: Is the function y = -4x + 2 linear or nonlinear? a Linear Nonlinear

A: To determine :- If y = -4x + 2 is linear or non-linear.

Q: A team of researchers finds that there is a relationship between the overall health of a forest…

A: We need to find maximum number by drawing graph.

Q: Find the points of intersection of the graphs of the functions y = x2 + 1 and y = 4x

A: Given functions:                     y = x2+1   ... (1)                     y = 4x      ... (2)

Q: Consider the function f(x) = 4/¤ + 2 on the interval [4, 5].

A: Given function is, f(x)=4x+2

Q: The number of concurrent users of a social networking site has increased dramatically since 2001. By…

A: The function P(t)=2.8291.484t, where t is the number of years after 2001,models this increase in…

Q: Describe the x-values at which the function is differentiable. x2 y = x² - 4

A: Given: y=x2x2-4, To find: The value of x at which the function is differentiable.

Q: A store owner estimates that by charging x dollars each for a certain lamp, he can sell 40 – x lamps…

A: Given  number of lamps sell each week by charging x dollars each = 40-x

Q: How do you prove step by step that this equation: y=2x+1 is a function?

A: The solution are next step

Q: What does it mean for a function to be defined implicitly by an equation?

A: An implicitly defined function is a function that is presented as the solution of some equation or…

Q: The height of a right triangle is 44 feet more than three times the length of its base. Express the…

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Q: According to an experimental study, the lifespan of a hamster is a function of the time the hamster…

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Q: YOUR TURN!! Given the function f (x) (x + 5) + 8, ax² + %3D What is the equation of the function…

A: fx=x+52+8

Q: Find the value of the function f(-x)=?

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Q: i. Find the equation of a power function through the points (2, ) and (, 8). y ii. Now, find the…

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Q: Express the perimeter P of a rectangle as a function of the width W if the length of the rectangle…

A: According to the given information:P is defined as the perimeter of the rectangleW be the width of…

Q: A downtown parking lot charges $5 per hour for the first 2 hours, then $2.50 per hour after that.…

A: Given:  The parking lot charges $5 per hour for the first 2 hours, then $2.50 per hour after that.…

Q: In 1990, the population of Bend, Oregon was 722. In 2000, the population had grown to 977.  Using…

A: Let us denote t= years after 1990  So, 1990 means t=0 and 2000 means t=2000-1990=10 So the…

Q: The number of people afflicted with the common cold in the winter months dropped steadily by 25 each…

A: As ‘C’ denotes the number of people afflicted with common cold and let ‘t’ be the years after 2002…

Q: Sketch the curve. Show your solutions. f(x) = x4 - 6x2

A: Consider the given: fx=x4−6x2Apply exponent rule:     ab+c=abacfx=x2x2−6x2Factor out common term…

Q: downtown parking lot charges 5 per hour for the first 2 hours, then 2.50 per hour after that. Which…

A: A downtown parking lot charges 5 per hour for the first 2 hours, then 2.50 per hour after that. To…

Q: A paper airplane was thrown from the top of a 9 meter tall house and falls at a rate of 3 meters…

A: Given  The height of the paper airplane above the ground can be found using  the function  y  =…

Q: find horizontal and vertical intercept of f(x)= -2|x+1|+6 and graphing the function

A: The given function:

Q: What does it mean to find the zero of a function?

A: Given :  Zero of a function

Q: The number of concurrent users of a social networking site has increased dramatically since 2001. By…

A: The given question has been solved in detail

Q: 5. Find the range of the function y = 7x -1 when the domain is {-1, 0, 1}

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Q: The length of a rectangle is 3 inches more than the width. Which of the following represents the…

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Q: A downtown parking lot charges $5 per hour for the first 2 hours, then 2.50 per hour after that.…

A: Given that for first 2 hours parking charges = $5 per hour and after 2 hours parking charge = $2.50…

Q: The function f (x) = 15,000(0.88)* represents the value of a car over x years. What is the most…

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