An Indy race car driver makes a pit stop at the beginning of a lap.The time t in seconds that it takes the driver to complete the lap, including the pit stop, can be modeled by t(x) = 12x+9000/x, where x is the driver’s average speed in miles per hour after the pit stop. The driver’s average speed after the pit stop is 210 mi/ℎ. How long does it take the driver to complete the lap,including the pit stop

Q: If a projectile is launched into the air at 29.4 feet per second from a height of 60 feet, its…

A: Answer

Q: use quadratic functions. Suppose that the equation p(x) = -2x2 + 280x - 1000, where x represents the…

A: Use quadratic functions. Suppose that the equation p(x) = -2x2 + 280x - 1000, where x represents the…

Q: The path of a diver is modeled by f(x)= -4/9x2 + 24/9x + 9 where f(x) is the height (in feet) and x…

A: Since, we have been given the path of driver by :-f(X)=Y=-49X2+249X +9 -(i)Our aim is to find the…

Q: The value of China's exports of automobiles and parts (in billions of dollars) is approximately f(x)…

A:

Q: many trees per acre will maximize the profit?

A: Use of derivatives,

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Q: The average cost of tuition and fees at public four-year colleges in the United States can be…

A:

Q: (3) If a projectile is launched into the air at 29.4 feet per second from aheight of 60 feet, its…

A: 3. given that                                                         u=29.4 feet per secondh=60…

Q: The amount of medicine (in milligrams) in a patient's bloodstream tt hours since taking a pill can…

A:

Q: The value of China's exports of automobiles and parts (in billions of dollars) is approximately f(x)…

A: I am attaching image so that you understand each and every step.

Q: A race car driving under the caution flag at 80 feet per second begins to accelerate at a constant…

A: As per the company policy i can answer only first question for you,more than that leads me towards…

Q: A car purchased for $16,000 is expected to depreciate according to the formula f(x) = -2,400x +…

A: The  car purchased for $16,000 is expected to depreciate according to the formula   f(x) = -2400(x…

Q: A population of bacteria is growing according to the equation P(t) = 750e population will exceed…

A: Equation for bacteria growth is given by- Pt=750e0.04t We have to find out when the population of…

Q: ーX -2X +xe t5

A:

Q: A toy rocket is launched vertically from 5 feet above ground level with an initial velocity of 112…

A: A toy rocket is launched vertically from 5 feet above ground level with an initial velocity of 112…

Q: If a projectile is launched into the air at 29.4 feet per second from a height of 60 feet, its…

A: A projectile is launched into the air at 29.4 feet per second from a height of 60 feet, its height…

Q: One parcel of land is worth $100,000 now and is increasing in value at a rate of $3,000 per year. A…

A:

Q: The average cost in dollars of producing x units of golf clubs is C(x) = x2- 18x + 140. Determine…

A: Average cost of golf clubs - C(x) = x2-18x+140Given that,C(x) should be below 75$Then,C(x) <…

Q: use the difference quotient to solve this equation; f(x)= (1/x2)

A: The difference quotient is calculated by . First, evaluate the value of f(x+h).

Q: The profit (P) for a company is given by the equation P=-0.02x^2 + 1.40x + 1500, where x is the…

A: Consider the given profit function: P=-0.02x2+1.40x+1500 Where  x is the number of units sold Here,…

Q: The value of China's exports of automobiles and parts (in billions of dollars) is approximately f(x)…

A:

Q: A company's revenue from selling å units of an item is given as R. = 1500x – x². If sales are…

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Q: When Alexander moved into a new house, he planted two trees in his backyard. At the time of…

A: Given there is two tree named as Tree A and Tree B

Q: Vx - 5 h (x) 2x2 17x +21 -

A:

Q: The value of China's exports of automobiles and parts (in billions of dollars) is approximately f(x)…

A: Use the given value and logarithms to find the value of x

Q: A company's revenue from selling x units of an item is given as R = 1000x - x² dollars. If sales are…

A:

Q: The average cost of tuition and fees at public four-year colleges in the United States can be…

A:

Q: The total number of seats in an auditorium is modeled by f(x) = 2x2 - 6x, where x represents the…

A: Given,          The total number of seats in an auditorium is modeled by fx=2x2-6x, where…

Q: If a toy rocket is launched vertically upward from ground level with an initial velocity of 128 feet…

A:

Q: A video game uses the quadratic equation to determine the height (h) in feet of an object above the…

A: We use second derivative test to find maximum height of the object. So consider,  h'(t) = 0   ⇒…

Q: Find the equation of a quadratic function having the x-intercepts a(-4,0) and b(3,0) and passing…

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Q: The profit P (in dollars) for a company that produces antivirus and system utilities software is…

A: Calculate the derivative for P i.e. P’(x).

Q: The value of China's exports of automobiles and parts (in billions of dollars) is approximately…

A:

Q: The height (feet) of a projectile x seconds after it is launched straight up in the air is given by…

A: We have given the height function f(x) = -16x2 + 458x + 5

Q: use quadratic functions. Suppose that the cost function for a particular item is given by the…

A: We have to use quadratic functions. The cost function for a particular item is given by the…

Q: The height of a rocket is modeled by h(x) = -(4x-8)(4x-24). About how long after reaching maximum…

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Q: rewrite in polynomial function, show your solution. f(x)=(x+3)(x+2)

A:

Q: The height of an object (in feet) propelled upward is given by the equation, h(t) = - 16t +96t + 112…

A:

Q: The total fertility rate in a certain developing country can be modeled according to the equation f…

A: Given, f(x)=0.003x2-0.2x+6.48 Where x is the number of years since 1958.

Q: The profit per acre from a grove of orange trees is given by  x(150 − x) dollars,  where x is the…

A:

Q: A snowplow has maximum speed of 35 miles per hour on a dry highway. Its maximum speed decreases by…

A: Given, a snowplow has maximum speed of 35 miles per hour on a dry highway. Its maximum speed…

Q: The profit of a company in thousands of dollars is given by the quadratic function P(x) = 3000 +…

A: Hello! thank you for the question but as per our honor code, we'll able to solve only the first…

Q: A company's revenue from selling x units of an item is given as R = 1000x - x2 dollars. If sales are…

A: Given that A companys revenue from selling x units of an item is given by  R=1000x-x^2 Sales are…

Q: A duck dives under water and its path is described by the quadratic function y=2x-4x, where y…

A: y=2x2-4x The position of duck to dive down 2 meters y=-2 -2=2x2-4x 2x2-4x+2=0 2(x2-2x+1)=0…

Q: While watching a basketball game, Hanz has a dilemma on finding the peak of the ball every time a…

A: We are given that  the equation of the ball is given by : f(x)=-x2-10x+2 Let it travels x distance…

Q: The height of a stone catapulted into the air is given by h(x)=−1/480x2+3x+2 where x is the…

A: Given:  The height of a stone catapulted into the air is given by h(x)=-1480x2+3x+2 where x is the…

Q: The population of a species is modeled by the equation p(t)= -t4 + 72t2 +225, where t is the number…

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Q: A computer virus is spreading according to the equation A = 0.5(20'), where t is the time in hours.…

A: Consider the given: The number  A of computer viruses spreading according  to the equation…

Q: use graphs to find approximate solutions 2x = 5

A: Given that, 2x=5

Q: A soft-drink vendor at a popular beach analyzes his sales records and finds that if he sells cans of…

A: Given: P(x)=-0.001x2+3x-1800

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.