A ball projected upwards with a velocity on 128 feet per minute from a height of 5 feet above the ground is modelled by the function h(t) = -16t + 128t + 5

Q: If an archer shoots an arrow straight upward with an initial velocity of 160ft/sec from a height of…

A: If the arrow reaches the ground then h(t)=0…

Q: NASA launches a rocket at t=0 seconds. Its height, in meters above sea-level, as a function of time…

A: Given, NASA launches a rocket at t=0 seconds. Its height, in meters above sea-level, as a function…

Q: The growth of a certain bacteria can be modelled by the function, f(x)=250e^ .0614t , where t is the…

A: The explanation of the solution as follows:

Q: nd the points where the function f(x) = (x² – 1)³ is decreasing, -

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Q: The height of a ball thrown across a field, f(x), in feet, can be modeled by f(x) = -0.005x² + x +…

A: Maxima or minima: Let f(x) is any function. 1) Evaluate f'(x) = 0 for critical point. 2) Evaluate…

Q: Find the formula for a function of the form y=be^((-(x-a)^2)/2) with its maximum at the point (0,5).…

A:

Q: A ball is projected off of a 400-ft-tall building at a velocity of 45 ft/sec. The function f (x) =…

A:

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

A:

Q: If a baseball is projected upward from ground level with an initial velocity of 128 feet per second,…

A: Given height as a function of time S= -16t2+128t Here, A= -16 B= 128, C=0

Q: The cubic function that is the best fit for the data, with y equal to the number of millions of…

A: Given,            The cubic function that is the best fit for the data, with y equal to the number…

Q: If the position function of a moving object is 5(t) t-3t +2 meters from zero in t seconds, then

A: Consider the position of a particle is given by the function x(t). The average velocity of the…

Q: Find an equation for the line tangent to the graph of f(x) = -6xe" at the point (a, f(a)) for a = 2.

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Q: A3) Find the equation of the line tangent to the graph of f(x) = 4x° + 4x² – 3x – 3 at x = -4.

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Q: Find the point on the graph of the function that is closest to the given point. f(x) = Vx - 6, (15,…

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Q: Find the equation of the line tangent to the graph of f(x)=5x^{3}+6x^{2}-6x-3

A: This question is related to functions, We will solve it using given information.

Q: The population of wolves in a wildlife reserve can be modelled by the function f (x) = 1000+600x…

A: The given population of wolves is given as fx=1000+600x10+0.6x The domain of the function is defined…

Q: Find the points of inflection of the function f(x)=e−x2.

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Q: The us population can be modeled by the function y=165.6x^1.345 where y is in thousands and x is the…

A: The US population is modeled by the function, y=165.6x1.345 where y is in thousands and x is the…

Q: the temperature of a pot of coffee after brewing can be determined by the function…

A: Given temperature function is: F(t)=104e-0.0245t+76

Q: The path of a diver is modeled by 24 *+ 13 f(x) = - where f(x) is the height (in feet) and x is the…

A:

Q: The number of White Sturgeon in thousands can be modeled by f(x) = 170(0.82)*in a particular region,…

A: givenf(x)=170(0.82)x when f(x)=7then7=170(0.82)x(0.82)x=.041taking log on both…

Q: The point of the given function at (2, -7) is found to be y = x3 – 2x2 – 4x + 1

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Q: 1. Find the intercepts of the function. f(x)-x* +2 а.

A: Given data÷

Q: The gates of an amusement park are closely monitored to determine whether the number of people in…

A: We will find what (e-l) (4) means in this situation as following.

Q: Find the slope of the secant line between x=−1 and x=2 on the graph of the function f(x)=−2x3 +3.

A: Given lines are x = –1 and x = 2. Given function is

Q: Find an equation of the line tangent to the graph of f(x)=4/x at (-8,-1/2)

A: Given: fx=4x  , -8,-12 Formula Used: Equation of tangent line is given by y-y1=f'x1x-x1

Q: Where is the function y =4x/x-3 concave downward? Show mathematical work to clearly answer this…

A: For a given function y=f(x) the curve is concave downward in an interval I when the second…

Q: The slope of the secant line of the square root function at x-4 and x-9 is and the y-coordinate of…

A: The function f(x) is a rule that associates or fixes a number to the particular point x. If y=f(x),…

Q: Find the point on the graph of the function that is closest to the given point. f(x) = Vx - 4, (15,…

A:

Q: The number of daily users for Japan’s Line messaging service (in millions) can be approximated by…

A: The approximating function that represents the given scenario is: g(x)=53.1+63.1 ln(x) where x…

Q: If a baseball is projected upward from ground level with an initial velocity of 160 feet per​…

A:

Q: If a baseball is projected upward from ground level with an initial velocity of 32 feet per​…

A: When we throw a ball upwards, that ball goes and goes up, at a certain level of height, the thing is…

Q: Find the point on the curve g(x) = x² – 2 that is closest to the point (3,-2)

A: We can represent all the points on the curveg(x) = x2-2 as (x, x2-2)Now we will use the distance…

Q: If a projectile is fired straight upward from the ground with an initial speed of 128 feet per​…

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Q: If a baseball is projected upward from ground level with an initial velocity of 64 feet per second,…

A: Consider the provided function.

Q: There is a bacteria cell in a Petri dish that is reproducing at a rate of              r(t) = 2t^2+1…

A: Solution:

Q: g(t)=15.18(1.047)t​,

A: gt=15.181.047t The year 2010 corresponds to t=10.

Q: A ball is thrown vertically upward. After t seconds, its height h (in feet) is given by the function…

A: A ball is thrown vertically upward. After t seconds, its height h (in feet) is given by

Q: The height, h, of a projectile above the ground t seconds after liftoff is given by the function,…

A: The height is given as :- h(t)=-3t2+72t   for 0≤t≤24 Time when the projectile reach its maximum…

Q: The function f(x) = 4ᴫx2 describes the surface area, f(x), of a sphere of radius x inches. If the…

A: Given: The surface area of a sphere is, fx=4πx2 . Radius of the sphere is, x=6 inches. The…

Q: The height of the corn stock in inches over the first eight weeks of growth could be roughly model…

A: The height of the corn stock in inches over the first eight weeks of growth could be roughly model…

Q: Find the equation of the function f whoseg 3 f'(x) = (0, 4) %3D -- 1 + e

A:

Q: Write the equation of the line tangent to the graph of f (x) = -3x² + 5x + 1 at x = 1 and use it to…

A: We have to find the tangent line equation and also we have to approximate f(1.2).

Q: The number of mosquitos, M(x), in millions, in a certain area of Florida depends on the June…

A:

Q: Find the point on the graph of the function that is closest to the given point. f (x) = Vx - 3 (18,…

A:

Q: Express the area A of a right triangle as a function of the height h if the base of the triangle is…

A:

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.