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 + 286t + 101. 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: 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: y = e2=²-x %3D

A: Solve the differential

Q: The number of visitors v(t) of a certain park is calculated as a function of the temperature t, in…

A:

Q: The altitude h (in m) of a certain rocket as a function of the time t (in s) after launching is…

A:

Q: A3) Find the equation of the line tangent to the graph of f(x) = 4x³ + 3x? – 2x – 8 at x = -2.

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

A:

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

A:

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: Consider the function y = 1 2r2

A: To find: The horizontal and vertical asymptotes of fx. Given: The function is fx=2xx2-1. Concept…

Q: Find the inflection point, if any, of the function. (If an answer does not exist, enter DNE.) 9(x) =…

A: x= 0 is the inflection point Therefore (x, y) =(0, 0)

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

A: The given function for the revenue from sale of x no. of car seats for infants is R(x)=28x-0.010x2…

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

A:

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

A:

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

A:

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

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: The height above ground of an object movingvertically is given bys = -16t2 + 96t + 112,with s in…

A: Given function for height - s = -16t2+96t+112Differentiating on both sides with respect to t - dsdt…

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

A:

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

A: From given the volume function is fx=x3.

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

A:

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

A:

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: An accessories company finds that the cost and revenue, in dollars, of producing x belts is given by…

A:

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

A: The maximum of a function can be obtained by equating the first derivative of the function to 0. The…

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

A:

Q: The size P of a small herbivore population at time t​ (in years) obeys the function P(t)=700e0.24t…

A:

Q: tổ approximate the change in profit corresponding to an increase in sales (or production) of one…

A: Given that: P=-0.1x3+400x-60, x=50and dx=∆x=1

Q: Solve the Problem. Approximate the curve of the given function f. f(x) = 2x3 – 18x?

A: I am going to solve the given problem by using some simple calculus to get the required result of…

Q: A ball is thrown into the air with an initial upward velocity of 48 ft/s. The height () of the ball…

A: Given, initial upward velocity = 48 ft/s h(t)=-16t2+48t+4

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.