An object attached to a coiled spring is pulled down a​ distance, a, from its rest position and then released. Assuming that the motion is simple harmonic with period​ T, write a function that relates the​ displacement, d, of the object from its rest position after t seconds. Assume that the positive direction of the motion is up.   |a|=7​; T=8 seconds

Q: Outside temperature over a day can be modeled as a sinusoidal function. Suppose you know the…

A:

Q: A new laptop is purchased and after one year it is worth $713.50, but after two years it is worth…

A: Consider the provided information, A laptop is purchased and after one year its cost reduced and…

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

A:

Q: Let P(x, y) be a point on the graph of y = x2 - 8. Express the distance, d, from P to the origin as…

A: To find the distance from point P (x, y) to the origin (0, 0).

Q: An object dropped from a height of 500 feet has a height, h(t), in feet after t seconds have…

A: To express t as a function of h h=500-16t²

Q: Sketch the following functions (in steps), then find their domains. 1 b) y=- -1 tan

A: See attached file for a step by step explanation.

Q: A chemist working on a flu vaccine needs to mix a 10% sodium-iodine solution with a 60%…

A:

Q: If a football is kicked straight up with an initial velocity of 96 ft/sec from a height of 5 ft,…

A:

Q: The acceleration due to gravity is-9.8 meters per second squared. An object is thrown upward from a…

A:

Q: The amount of a pollutant (measured as parts per million) in a local lake can be modeled by the…

A: ∗Given:-       Amount  of   pollutant,       At=14×2.71-0.016 t ‐‐‐i∗ To  find:-        Time  taken…

Q: An object dropped from a height of 400 feet has a height, h(t), in feet after t seconds have…

A: Given : h(t)=400-16t2   To find : a) t(h)b) time to reach height of 350 feet

Q: Suppose that Nolan throws a baseball to Ryan and that the baseball leaves Nolan's hand at the same…

A: Given : v = 85 ft/s and angle is 45°

Q: 221 writc a formnla for the function y =f cx) whose is shown fig: 2.

A:

Q: Find the first and second derivative of the function. Check to see that your answers are reasonable…

A: find out the first and second derivative.

Q: In the given question , determine whether the statement is true or false. If it is false, explain…

A: To determineTrue or falseslope of the graph of the inverse tangent function is positive for all x.

Q: You are on an island 2 miles from the nearest point P on a straight shoreline, as shown in the…

A: We will be using the formula, Speed = DistanceTime over the course of movement to derive the time,…

Q: A weather balloon is being inflated so that the radius is changing with respect to time according to…

A:

Q: The population P of elephants in a wild animal preserve changes with time (in years) according to…

A: Here, the given differential equation is: dP-0.0005P(190-P)dt=0 Find P as a function of t if there…

Q: Outside temperature over a day can be modelled as a sinusoidal function. Suppose you know the high…

A: Given that: Highest temperature = 75°FLowest temperature, = 65 °F at 3 AMTime taken from mid night.

Q: Suppose that another drug is administered intravenously to an adult patient in a hospital as…

A:

Q: An asteroid is spied by a ground-based telescope, traveling toward the sun. It is noted that the…

A: Given that       An asteroid is spied by a ground-based telescope, travelling towards the sun.  It…

Q: An object dropped from a height of 400 feet has a height, h(t), in feet after tt seconds have…

A: An object dropped from a height of 400 feet has a height, h(t), in feet after t seconds have…

Q: For function, find (a) the equation of the secant line through the points where x has the given…

A: fx=6x,   x=25,  x=36 When x=25,  f25=625=30 When x=36, f36=636=36 a). Equation of the secant line…

Q: Consider the function f(x)=x^3-6x+c, where C is an unspecified constant. Suppose the line 102x-y=609…

A: Since you have posted multiple subparts, as per our policy we will answer first three subparts.…

Q: A power plant sits next to a river where the river is 800 ft wide. To lay a new cable from the plant…

A:

Q: A rocket sled having an initial speed of 152 mi/h is slowed by a channel of water. Assume that…

A: Given that: Initial speed, u=152 mi/hacceleration, a=-μv2Final velocity, v=18 mi/h

Q: A ball is launched directly in the air at a speed of 60 feet per second from a platform located 20…

A: Solution

Q: Outside temperature over a day can be modeled as a sinusoidal function. Suppose you know the high…

A: Given that: Outside temperature over a day can be modelled as a sinusoidal function. Suppose you…

Q: Consider the following function h(r) = -3r - 5x* +20z + 60r. Find the point on the graph of h(r)…

A: Inflection points are the points on the graph of a function where its curvature changes from concave…

Q: Suppose that Nolan throws a baseball to Ryan and that the baseball leaves Nolan's hand at the same…

A:

Q: Suppose that Nolan throws a baseball to Ryan and that the baseball leaves Nolan's hand at the same…

A: The baseball leaves Nolan's hand at the same height at which it is caught by Ryan. To Find: Estimate…

Q: Differentiate the function. g(x) coth-! (2x + 1) Give your answer in exact form. g'(x) =

A:

Q: A cup of coffee has a temperature of 200° ? and is palced in a room that has a temperature of 70° ?.…

A:

Q: Assume the velocity of a person traveling along a straight hiking trail is given by the graph…

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

Q: Consider the function f(x) = 3x – 6. Find the following: a) The average rate of change between the…

A: let fx=3x-6af-1=3-1-6=-3-6=-9f2=32-6=6-6=0points are :-1,-9and 2,0Average rate of…

Q: Yこ cot 2.

A: Given: y=cot-1 x2-2xTo find the derivative of y with respect to xFormula: cot-1x'=-11+x2x'=12x ;…

Q: A stone is dropped into a lake, creating a circular ripple thattravels outward at a speed of 60…

A: (a) Express the radius of this circle as a function of thetime t(in seconds).

Q: The city of New Orleans is located at latitude 30°N. Use the figure below to find a function that…

A: The graph of the length of day light is shown below: We can observe that, the graph is sinusoidal…

Q: you drive from your home to a vacation resort 590 miles away, You return on the same highway. The…

A: Given you drive from your home to vacation resort 590 miles away. you returnon the same highway. The…

Q: Zoom in on a plot of f at the point (a, f (a)) and state whether or not f appears to be…

A:

Q: Find the tangent line of the function ?(?) = (16 /x )− 4√? at x = 4, and the point at which tangent…

A: Given the function

Q: Find the intervals where the function is concave upward or concave downward. Enter "DNE" if it is…

A: Given data:   The given function is f(x)=4/(x2+11).   The first derivative of the given function is,…

Q: Evaluate the function (a) cosh 0 (b) sech 1. If the value is not a rational number, round your…

A: Solution:- Evaluate the hyperbolic function  a) cosh 0  b) sech 1

Q: Let P= (x,y) be a point on the graph of y = x. Express the distance, d, from P to (7,0) as a…

A:

Q: The volume of a rectangular prism with a square base is fixed at 500 cm3 a) Determine the surface…

A: Volume is the measure of the amount of space occupied by a closed surface. A rectangular prism is a…

Q: Suppose that Nolan throws a baseball to Ryan and that the baseball leaves Nolan's hand at the same…

A: A scalar function f(x,y) is a rule that is used to associate a number or quantity with a particular…

Q: The figure shows a page with 1-inch margins at the top and the bottom and half-inch side margins. A…

A: Let the length and width of the printed page be y and x, respectively. Given printed area of page is…

Q: A football player kicks a ball at an angle of 37° above the ground with an initial speed of 20…

A: h=0.75d-0.0192d2 Solution is in next step and final answers are in last step

Q: guy wire is attached to the top of a 90-ft pole and stretched to a point that is d feet from the…

A: Given: By right angle triangle property, tan β=90d⇒ β=tan-190d.