A rain drop hitting a lake makes a circular ripple. If the radius, in inches, grows as a function of time in minutes according to r(t)=25t+2−−−−√, find the area of the ripple as a function of time. Find the area of the ripple at t=2.

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: Find the average rate of change of the function f(x) = 2x² + 16x + 28 on the interval [-3, –3 + h].

A:

Q: Given the function h(x) = –x² – 6x + 17, determine the average rate of change of the function over…

A:

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: Pls help, ASAP

A: Consider the given function fx=4x2-10x+3. Obtain the slope of the secant line to the curve…

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: The function f(x) = 4ᴫx3/3 describes the volume, f(x), of a sphere of radius x inches. If the radius…

A: f(x) = 4πx33 Volume of sphere , f(x) = 4πx33 where,  x is the radius of sphere in inches.…

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

A:

Q: A parking lot charges $2 per hour for the first 4 hours, then $3 per hour after that. Which…

A: Given, a parking lot charges $2 per hour for the first 4 hours, then $3 per hour after that. Let the…

Q: The deeper you are under water; the less sunlight reaches you. The percent of sunlight, P, that…

A: We will modern the following question by the function in next step.

Q: For the function f(x) 5x3 – 8x? + 8x, Step 2 of 2: Find the equation of the tangent line at x = 1

A:

Q: Find the slope m and the equation of the tangent line to the graph of the function f at the point…

A:

Q: Between 2006 and 2016, the number of applications for patents, N, grew by about 3.2% per year. That…

A:

Q: The function f(x) = (4/3) πx3 describes the volume, f(x), of a sphere of radius x inches. If the…

A: fx=43πx3 Differentiating with respect to x, we get f'x=ddx43πx3=43π·3x2            ∵dxndx=nxn-1=4πx2

Q: Find the slope of the line tangent to the graph of the function at the given value of x. 12) y = x4…

A:

Q: Given the function​ f, find the slope of the line tangent to the graph of f-1 at the specified point…

A: Obtain the inverse of the given function as follows:

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.

A:

Q: Juanita wishes to have a rectangular garden in her backyard with an area of 64 ft2. Letting x denote…

A: we know that area of rectangle =  length × width

Q: Use differentials to approximate the change in revenue in dollars corresponding to an increase in…

A: The revenue function is: R=90x-0.55x2

Q: The function f(x) = x3 describes the volume of a cube, f(x), in cubic inches, whose length, width,…

A: Given volume function fx=x3 to find instantaneous rate of change of the volume x=4 in

Q: The space vehicles are supplied power from nuclear energy derived from radioactive isotopes. The…

A: Let's find.

Q: Find the slope of the line tangent to the graph of the function at the given value of x. 12) y = x4…

A: The given equation is y=x4+3x3-2x-2, x=-3. Find the slope of the line tangent to the graph of the…

Q: Find an equation for the line tangent to the graph of f(x)=−7xe^x at the point (a,f(a)) for a=2.

A: Given:

Q: Under certain conditions, the wind speed S, in miles per hour, of a tornado at a distance d feet…

A: Given wind speedSa,d,v=av0.51 d2

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

A:

Q: The daily temperature in degrees Fahrenheit of Phoenix in the summer can be modeled by the function…

A:

Q: As a cold front moved through a midwestern city, the temperature dropped at the rate of 3F per hour…

A: Given: Rate of change in temperature between noon and 8 p.m. = -3∘F. At 1 p.m. the temperature was…

Q: If f(x) is the slope of a trail at a distance of x miles from the start of the trail, what…

A: Given that f(x) is the slope of a trail at a distance of x miles from the start of the trail.

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: Determine where the graph of the function is concave upward and where it is concave downward.…

A: The graph is shown below:

Q: The height (in feet) of a stone thrown upward on another planet is given by the function f (t) =…

A:

Q: A parking lot charges $2 per hour for the first 4 hours, then $3 per hour after that. Which…

A:

Q: Given the function h(x) = x² – 7x + 6, determine the average rate of change of the function over the…

A: The rate of change of a function is given by it's derivative.

Q: pressure

A:

Q: When I push the gas pedal to the floor, my speed, in mph, is given by s=13t, where t is the time, in…

A: Given that s=13t  And given that unit of speed is mph = miles/hour t is in seconds  1 hour= 3600…

Q: The height of an arch above the ground is given by the function y=10sinx, for 0 less than or equal…

A:

Q: Find the equation of the line tangent to the graph of f(x) = 4x + 5x? – 4x – 3 at a = -7

A:

Q: For what value(s) of x does the graph of f(x) = 4x3 - 6x2 - 144x - 24, have a horizontal tangent?

A:

Q: The height of an arch above the ground is given by the function y=10sinx, for 0 <= x<= pi .…

A: The given interval is [0,π] So, a=0, b= π

Q: Next, differentiate the given function y = X 8x + 37 and write as a single fraction completely…

A: Derivative of function

Q: The surface area of a hot-air balloon is given by the function S(r) 4Tr", where r is the radius of…

A: NOTE: Refresh your page if you can't see any equations. . the radius is increasing at a rate of…

Q: Given the function f(x) = –x² – 5x + 12, determine the average rate of change of the function over…

A:

Q: Given the function f(x) = -x² – 7x + 19, determine the average rate of change of the function over…

A: Given function is: fx=-x2-7x+19 And the given interval is: -9≤x≤3 At x=-9:…

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: 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 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 rate A (in tons per year) at which a pollutant is being dumped near a city is given by the…

A:

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 slope of the line tangent to the graph of the function at the given value of x. y = x4 + 2x…

A: Given : y = x4+2x3+2x-2