An inferior product with a large advertising budget sells well when it is introduced, but sales fall as people discontinue use of the product. Suppose that the weekly sales S are given by 600t S= t2 0 (t + 1)2' where S is in millions of dollars and t is in weeks. After how many weeks will sales be maximized? weeks

Q: 5. The estimated cost per sq.m. of fully furnished house construction in a given site is governed by…

A: For a differential equation of the form: y'=fx, y, Euler's method uses the formula:…

Q: From 2010 through 2019, the revenue per snare fin $) tor stark Industries can be modeled by 2. 2. R…

A:

Q: A particle moves along the x-axis so that at time t > 0 its position is given by x(t) = t – 24t.…

A: This is an application of differential calculus.

Q: Find the supply function x = f(p) that satisfies the initial conditions. dx 10 x = 160 when p = $1…

A:

Q: 2. The growth rate (in inches per year) of the diameter at breast height of a certain tree is given…

A:

Q: A particle moves along a line so that its velocity is given by v(t)=−t^3+2t^2+2^(−t) t≥0. For what…

A:

Q: The approximate value of y(3) for the initial value problem for ' = cost + sint, y (0)=0.5 with h=…

A: Correct option is (b) 2.631 Detailed solution : Given y′=cos(t)+sin(t),y(0)=0.5,h=0.5,y(3)=?Forth…

Q: Q3) Use Euler's method to estimate y(0.02) ey-x 1+ e2y y(0) = 1 ( h=0.01) .What is the error in the…

A: Given ; h = 0.01 y(0) = 1

Q: A particle moves along the x-axis so that at time t 0 its velocity is given by v(t) = -3t2 - 2t +…

A:

Q: The projected rate of increase in enrollment in a new college is estimated by dE/dt= ( at+1)^-1(…

A: Given the projected rate of increase in enrollment in a new college is dE/dt= ( at+1)^-1( a+1). We…

Q: If a ball is given a push so that it has an initial velocity of 5 m/s down a certain inclined plane,…

A:

Q: Maximize Q = xy, where x and y are positive numbers such that x+3y 16. The maximum value of Q is and…

A: Maximize Q=xy, where x and y are positive numbers such that x+3y2=16

Q: 2. For time t > 0, a particle moves along the X-axis, its position is given by the function s(t) =…

A:

Q: Q4/ If z = Vx² – y² and x increasing at 3.5 m/s, determine at what rate y must change in order that…

A: In the question it is asked to determine at what rate y must change so that z shall neither increase…

Q: The velocity of a skydiver 1in m>s2 t seconds after jumping from a plane is v1t2 = 60011 -…

A: Limits are used where the exact value of the function cannot be determined, hence the approaching…

Q: 12. The position of an object at time tis given by x = V3t – 4 ++4, where x is in feet and t is in…

A: (12) The position of an objects at time t is given by  xt=3t-4+1x+4, x is in feet and t is in…

Q: Find the amount of medicine to which the body is most sensitive by finding the value of M that…

A: Given

Q: A particle moves along the y-axis so that at time t≥0 its position is given by y(t)=t3−6t2+9t. Over…

A: A particle is moving along the y-axis its position is given by y(t)=t3-6t2+9t      at…

Q: A particle with velocity at any time t given by v(t)=e't moves in a straight line. How far does the…

A: solve the following

Q: At any time t, the velocity of a particle moving along the y-axis is given by v(t)= 4t - t^2. The…

A:

Q: If the brakes on a car give the car a constant negative acceleration of 2k m/s2, where k is a…

A: use simple velocity,acceration,and distance formula.

Q: Suppose the height of a spacecraft at time 1 is given by f () = 27 E1 for 0 <15 3. Find an…

A:

Q: The position function of a particle is given by s = t3-10.5t2-2t, t (greater than or equal to) 0.…

A: The position of particle is given by- s(t)=t3-10.5t2-2t , t≥0 To find the time when particle reach a…

Q: 2. A rock thrown upward has a height given by s(1) = 49t-9.81 where s is in meters and / is in…

A: Use derivative to solve

Q: A particle moves along the x-axis so that at time t 0 its velocity is given by v(t) = 3t2 – 60t.…

A: v(t)=3t2-60t,    t≥0the particle is moving to the right whenv(t)&gt;03t2-60t&gt;03t(t-20)&gt;0

Q: it is known from experiments that the height (in meter) of a certain plant after t months is given…

A: Given: ht=t-t; 0≤t≤1 for finding given values, first we draw graph of given function on given…

Q: The distribution of P(x,y) on a thin metal plate is given by ²P 2- dx2 = 0 ду? If we use a step size…

A: Given: Distribution of Px,y on a thin metal plate is, 2∂2P∂x2+∂2P∂y2=0 Step size: h=14, k=12   To…

Q: For time t > 0, a particle moves along the x-axis, its position is given by the function s(t) = -t*…

A:

Q: 6. Using the u-substitution u = x2+ 1, solve the initial value problem dy 4.r Vr2 +1 and y(0) = 0 dr…

A:

Q: 3. For time t > 0, a particle moves along the X-axis, its position is given by the function s(t) =…

A: Consider the given position function. st=-t3+3t2-6 Find the double derivative of the position vector…

Q: A traffic engineer monitors the rate at which cars enter a freeway during rush hour. From the data…

A:

Q: Suppose the initial population is Po = 270, the point of inflection is (15,1200), and the time is…

A: Given the initial population is P0=270 and the point of inflection is 15,1200. The inhibited growth…

Q: A particle moves along the x-axis so that at time t ≥ 0, its position is given by x(t) = 2t3 - 3t2.…

A: V(t) = d[x(t)]/dt Put, v(t) &gt; 0.

Q: A particle is moving along the x-axis so that at any time t > 0, its acceleration is given by the…

A: The acceleration of a particle is the rate of changing of velocity at time. When the velocity…

Q: Find the number of units x that produces the minimum average cost per unit C in the given equation.…

A: given

Q: Suppose that the concentration C of a medication in the bloodstream t hours after an injection is…

A: The concentration C of a medication in the bloodstream t hours after an injection is given by:…

Q: 5. Suppose that t hours after the injection of x milligrams of adrenalin the response is R units…

A: We need to find value of x and t.

Q: A particle moves along the x-axis so that at time t > 0 its velocity is given by v(t) = 3t² – 30t –…

A: topic - quadratic equations

Q: For some positive constant C, a patient's temperature change, T, due to a dose, D, of a drug is…

A: As per given by the question, the patient's temperature is given by; . Now, First finding the…

Q: A particle moves along the x-axis with velocity given by v(t) = 6t2 – 18 for time t > 0. If the…

A:

Q: The population of a culture of bacteria has a growth rate given by p'(t) = 210 bacteria per hour,…

A: Given data is: The population of a bacteria growth culture is: p't=210t+1r  The increase in…

Q: 2. The weekly revenue of a newly released film is given by 15t R(t) for t 20, 2+ 10' where R is…

A:

Q: The size of a population x as a function of time y is given by dx/dy=0.02x+9y . Solve for x as a…

A:

Q: ) How many miles did chloe travel from time t=0 to time t=2 b)at time t=3, is chloes speed…

A: Given the motion of Chloe. The speed B and time t table is given. We need to answer some questions.…

Q: A particle moves along the x-axis so that at time t≥0 its position is given by x(t)=2t3+3t2−36t+50.…

A: given, A particle moves along the x-axis so that at time t≥0 its position is given by…

Q: A particle moves along the x-axis with velocity given by v(t) = 6t² + 1 for time t > 0. If the…

A:

Q: A particle moves along the X-axis so that at time t>0 its position is given by x(t)= 2t3 +…

A:

Q: Suppose a person wants to travel D miles at a constant speed of (60 + x) mi/hr, where x could be…

A: Given that speed is  s=(60+x) mi/hour time required to travel D miles is T(x)=60D(60+x)-1 in minutes

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.