NASA launches a rocket at t = 0 seconds. Its height, in meters above sea-level, as a function of time is given by h(t) = - 4.9t2 + 238t + 248. Assuming that the rocket will splash down into the ocean, at what time does splashdown occur? The rocket splashes down after seconds. How high above sea-level does the rocket get at its peak? The rocket peaks at meters above sea-level.

Q: Water will be both added to and drained from a bathtub at the same time for 7 minutes. The total…

A: It is given that a bathtub has water added and drained simultaneously for 7 minutes. The total…

Q: After an antibiotic tablet is taken, the concentration of the antibiotic in the bloodstream is…

A: At t= 1.824 hours , concentration will be maximum.....and its value = 0.47 microgram/ mL  For…

Q: The function A = 58t – 0.83t² gives the height of a projectile with an initial velocity of 58 meters…

A:

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

A:

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

A:

Q: After an antibiotic tablet is taken, the concentration of the antibiotic in the bloodstream is…

A:

Q: The quantity of the demand per month of a certain accessory is related to the price (in 500 where x…

A:

Q: The height, h metres, of an object thrown vertically upwards at time t seconds after its release is…

A: Given function represents height of the object at time t.

Q: Y = 0.75X + 0.0042X2 – 0.000023X3 At what level of X, the output will be maximum?

A:

Q: A3) Find the equation of the line tangent to the graph of f(x) = 4x + 3r² – 6x – 4 at x = -3.

A: f(x)=4x3+3x2-6x-4 at x=3,

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

A: Let's find.

Q: A conservation commission estimates the reproduction function for rainbow trout in a large lake to…

A: Given:

Q: Use the position function s(t) = -16t2 + v0t + s0 to solve: A projectile is fired vertically upward…

A: The position vector is given as  s(t)=-16t2+v0t+s0 here v0=48 ft/sec s0 is the height at ground…

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: + iv is analyt: and satisfies the a real constant

A: Since f is analytic in S, it satisfies Cauchy-Riemann equations. Thus,

Q: the height ( in feet) attained by a rocket t sec into flight is given by the function…

A:

Q: The quantity of the demand per month of a certain accessory is related to the price (in 500 where x…

A: The extremum value of a real-valued function is determined through differential calculus. It is one…

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: Consider the population of bacteria grows according to the function f(t) = 500e0.05t, where t is…

A:

Q: The cube root parent function y = Vx has been transformed a) 2.

A: given graph

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

A:

Q: A3) Find the equation of the line tangent to the graph of f(x) = 4x³ + 7x2 – 4x – 3 at z = -5.

A:

Q: A commuter drove to work a distance of 20 miles and then returned again on the same route. The…

A: Let x be the average velocity on the outgoing trip.

Q: Use the position function s(t) = -16t2 + v0t + s0 to solve this problem. A projectile is fired…

A:

Q: A commuter drove to work a distance of 40 miles and then returned again on the same route. The…

A: Let the average velocity on the outgoing trip be x miles per hour. Now since the average velocity on…

Q: Both the front and rear wheels of a motor scooter have a reflector attached to their spokes.  The…

A: Given: The front and rear wheels of a motor scooter have a reflector attached to their spokes. The…

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

A:

Q: Consider the function whose output formula is N = f(t) = 175(2)^T . What is the solution for the…

A:

Q: Differentiate the function.  v = t2 - 1 / fourt root of t3

A: Given function is v=t2-1t34. Power rule of differentiation states that: ddxxn=nxn-1 Differentiating…

Q: Find d3y of the function y=xln1/x.

A: Given: Calculation:

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: Marine ecologists estimate the reproduction curve for swordfish in a fishing ground to be  f(p) =…

A:

Q: The annual amount of energy produced in a country from dry natural gas (in tnillion cubic feet) can…

A: Given function is gt=15.621.041t. Where t =10 represent year 2010. (a) Obtain the amount of dry…

Q: The revenue of a multimillion corporation (in million pesos from 2000 to 2010 is modeled by…

A: In this question, we will find the rate at which the company's revenue is changing in 2008.

Q: After an antibiotic tablet is taken, the concentration of the antibiotic in the bloodstream is…

A:

Q: As machines get older, the cost of maintaining them tends to increase. Suppose for a particular…

A: We get the answer using integrating.

Q: The number of bacteria in a culture is modeled by the function n(t)=30e^rt where t is in hours.…

A:

Q: The revenue (in dollars) from the sale of x car seats for infants is given by the following…

A: R(x)=24x-0.010x20≤x≤2400 To find average change in revenue apply formula…

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: Use the position function below to solve the following problem. A projectile is fired vertically…

A:

Q: Suppose that a vending machine service company models its income by assuming that money flows…

A: *to find:- total income over the first 3 years. *concept:- integration of e^{ax} = (e^{ax})/a.

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

A:

Q: The supply for a particular item is given by the function S(x) = 17 + 0.36x² . Find the producer's…

A:

Q: Q1. Determine whether this is a quadratic spline function T € (-00, 1] f(x) = {-(2 – x)² + T € [1,2]…

A:

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

A:

Q: The yield in bushels from a grove of orange trees is given by Y = x(400 − x), where x is the number…

A: