cientists sometimes use the formula f(t) = a sin(bt + c) + d to simulate temperature variations during the day, with time t in hours, temperature f(t) in °C, and t = 0 corresponding to midnight. Assume that f(t) is decreasing at midnight. The high temperature is 10°C, and the low temperature of −10°C occurs at 4 A.M. (a) Determine values of a, b, c, and d that fit the information. a =       b =       c =       d =       (b) Sketch the graph of f for 0 ≤ t ≤ 24.

Q: I find (fo g)(x) by replacing each occurrence of x in the equation for – with,

A: To find:                    (f o g)(x):   We know that this is the composite function;   So,…

Q: F is directly proportional to a. If F=24 when a=8 find, a when F=18

A:

Q: Let f (x) = x3 – 3x2 – 1, x 2 2. Find the value of df-1 at the point x = -1 = f (3). dx -

A:

Q: Use Newton-Raphson's Method to approximate the real solution of the following function. f(x) = e-x –…

A:

Q: find an equation for the inverse fuction

A: Fin the inverse of the function f (x) = ln (x + 3). First replace f (x) with y as y = ln (x + 3)…

Q: The temperature in Edmonton, over the course of a year, can be approximated using the sinusoidal…

A: The given sinusoidal function is: Tx=16.11sin0.51x-1.75+9.14   ......(1)where T is the temperature…

Q: A mass m is accelerated by a time-varying force exp(-ßt)v², where v is its velocity. It also…

A:

Q: The driver of a car traveling at 48 ft/sec suddenly applies the brakes. The position function of the…

A: Topic- application of derivatives

Q: Suppose an object is launched straight up so that its position (in feet) above the ground after 1…

A: Position of an object above the ground after t seconds is given as ft=-16t2+16t Velocity after t…

Q: (b) Given f(x)=9x – 6x² + x. Find F(x) dx in the form a In|g(x) + h(x)], where a is a constant

A:

Q: The size P of a small herbivore population at time t (in years) obeys the function P(t)=600e^0.27t…

A:

Q: A mass m is accelerated by a time-varying force exp(-ßt)v², where v is its velocity. It also…

A: .

Q: For each of the given functions f(x), find the derivative (f-1)'(c) at the given point c, first…

A: Please see the explanation below

Q: Differentiate the expression with respect to x, assuming that y = f (x). ey/x

A: Given, y=eyx

Q: Find a solution f(x) to the equation (D³ – D² + D – 1)f(x) = 0 | such that f(0) = 1, f'(0) = 0, ƒ(^)…

A: Use the given information.

Q: A. Find the derivative of the function at o P in the direction of A f(x, у) — х — V3sec-1(2xy)at…

A:

Q: For function f(x,y) to have no extremum value at (a,b) is? 1) rt - s>0 2) rt – s?<0 3) rt - s? = 0…

A: To select: The condition for the function f(x, y) to have no extreme value at (a, b).

Q: The depth d of the water in a harbour, measured in meters, t hours after midnight, can be…

A: Form an inequality representing this scenario. Solve that inequality to yield the result.

Q: , v(0) = and Find the position function, F(1), given that F(0) = a(t) = .

A: We have to find position vector

Q: Use Definition 3.2.3 to find f'(x) and then find the equation of the tangent oʻI+*p = o y = Vx+1, a…

A:

Q: Given the function below f(x)=3√405x^3+324 Find the equation of the tangent line to the graph of…

A: Given:405 x3+324f(x)=3        at x=1

Q: The rate of change of the temperature of an object is given by T (t)=t·eª -0.1t min (a) Use the…

A:

Q: In an electric circuit containing a resistor and a capacitor with an initial charge qo, the charge q…

A: Given

Q: Q3. A particle moved according to the relation (S = sin 2t – 5t). Find the velocity and acceleration…

A: S=sin(2t)-5t

Q: Q2) Find the values of c1 and c2 so that the following function will satisfy the prescribed…

A:

Q: Plot the function f(t) 5 sin(x)3x for -5 <xs 10. 5 1. x+e-0.75x

A: Since you have asked multiple questions, we will solve first question for you. If you want any other…

Q: If f is an odd function, why is S, f(x) dx = 0?

A:

Q: Find the fourth derivative, f(4) (æ) for the function, f(x) = x6 – 16x3 %3D 6x5 - 48a? O 120r3 12022…

A:

Q: Assuming that y is defined implicitly b equation x2 – y? = 17, the derivative (7, 12) is O 0.58 O 38…

A: We have to choose the correct answer from the given option according to the given condition

Q: LET F(X) = SIN(2X). TO FIND OPTIMUM STEP SIZE, M VALUE WILL BE: а. 4 b. 1 с. 2 d. 3

A: The value of sin(x) range from -1 to 1.   Thus, maximum value of f(x) = sin(2x) is 1.

Q: The value of b for which the function f (x) = sin x- bx + c is decreasing for x E R is given by (a)…

A: Given function is f(x)=sinx-bx+c differentiating with respect to x we have, f'(x)=ddx(sinx-bx+c)…

Q: The size P of a small herbivore population at time t​ (in years) obeys the function P(t)=1000e0.18t…

A:

Q: A. Find the derivative of the function at o P in the direction of A f(x, y) = x V3sec-1(2xy)at P.…

A: To find the derivative of given function means we have to find the directional derivative of the…

Q: Consider M(x, y)+ N(x, y) · = 0. M and Fy (a) Suppose we can find a function F example of such an…

A: As per our guidelines, we are supposed to solve only first question. Kindly repost other question as…

Q: Q:A- Find for the following functions: - 1+x* 1- 1+secy

A: Given: xy21+secy=1+x4 For finding dydx, we simplify given expression then differentiate it

Q: acceleration, in ft/sec2, of a truck at time t seconds is given by a(t) = 6 – 1.5t. The net change…

A: The acceleration, in ft/sec2, of a truck at time t seconds is given by a(t) = 6 – 1.5t. The net…

Q: ,determine f(t−a)for the given function f and the given constant a. Q. f(t)=e−t sin2t, a =π/6.

A:

Q: In winter, cold wind blows from North to South which brings dramatic decrease in temper- atures in…

A: According to the given data in question you try to solve this problem

Q: (a): Find the derivative of the 8х + 5 function y = 4x and simplify the answer: 2 - (b): The…

A:

Q: Find (f1) (a). f(x) = tan-(x) 6x2, a = 0 (F-1)'(a) = Additional Materials

A: We use the property of function and inverse function and differentiate both sides with respect to x.…

Q: Find f"(0) for the function f(x) = (x+1)e².

A: Given query is to find the Indicated derivative

Q: For which value(s) of x does f(x)=2x3−19x22+19x+2 have a tangent line of slope 5? Select all correct…

A: f(x)=2x3−19x + 2 have a tangent line of slope 5

Q: In the diagram, FG is tangent to OD at F, GH is tangent to at H, FG = 71, and GH = 9x+ 8. Find the…

A:

Q: Find a function ø(x, y) that is harmonic in the wedge < 0 on the left side and ø = 2 on the right…

A: Here, we need to find a function φx, y that is harmonic in the wedge π3&lt;θ&lt;2π3. Note: We will…

Q: A mass m is accelerated by a time-varying force exp(-ßt )v², where v is its velocity. It also…

A:

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

A:

Q: For which value(s) of x does f(x)=−7x22+6x−3 have a tangent line of slope −7? Select all correct…

A: we have to find value of x at which slope of tangent line to f(x)=-7

Q: C-the derivative is y = 0³ e 28 cos 50

A:

Q: The velocity, v of a body as a function of time, t is given as v(t) = 5e4+4, where t is in seconds,…

A: Since, we have been given that v(t)=5e-2t+4-(i), where t is in secondsand v is in m/s.Our Aim is to…

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.