If f and g are functions of time, and at time t=3, f equals 5 and is rising at a rate of 2 units per second, and g equals 4 and is rising at a rate of 5 units per second, then the product fg equals ____ and is rising at a rate of ____ units per second

Q: A car is initially traveling at a rate of 5 feet per second. The acceleration of the car is 9 feet p...

A: Given data,  Initial speed of car (v(0)) = 5 ft/sec Acceleration of the car (A(t)) = 9 ft/sec2  To D...

Q: Express the equation in logarithmic form. (a) 24 = 16 %3D (b) 10-3 = 0.001

A: a)24=16taking log bothside with base 2log2(24)=log2164log22=log2(16)       here  [log22=1]Solog2(16)...

Q: 12-

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Q: Calculus Question

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

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A: Given:  y=0.5x8, x=1, ∆x=dx=0.1 To determine: The value of ∆y and dy.  

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A: we have to draw a linear function in rectangular coordinates for an equation 6x-5f(x)-20=0  The abov...

Q: Find the particular solution of the differential equation that satisfies the initial condition(s). ...

A: f''x=3x2 Integrating with respect to x on both sides, we get ∫f''x dx=∫3x2 dx⇒f'x=3·x33+C1⇒f'x=x3+C1...

Q: Solve for æ: 2x – 11 r2 – 3x – 40 - Identify roots and asymptotes 2x – 11 has a root at æ = т? — Зх ...

A: The given rational function is 2x-11x2-3x-40. Equate the rational function to find the zero of the f...

Q: The problem is on the picture. Show the solution.

A: The Diameter of the Ferris wheel = 190 feet     The Radius of the Ferris wheel = 95 feet            ...

Q: dy (13) Find implicitly and then find the slope of the tangent line to the curve at (2,0): x2 -y = 4...

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Q: A motel finds it can rent 230 rooms when the room rate is $45 per day. For each $1 increase in the r...

A: Given that,   230 rooms are rented at $ 45 per day,   For each $ 1 more increase, two fewer rooms ar...

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A: Given function is, f(x)=x3

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A: Given: Endpoints of minor axis :(1,8) and (1,0) Foci : (-2,4) and (4,4). Here, the y coordinates of ...

Q: dy Find implicitly and then find the slope of the tangent line to the curve at (2,0): x2-y = 4ey dx

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Q: The top of a 10 ft ladder slides down a vertical wall at a rate of 1 ft/sec. How fast is the distanc...

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Q: Please help me figure out how to solve this. I know the answer is -300 in2/hr. But I just don't know...

A: Given   The surface area is decreasing  at a constant rate of  60 square inches per hour dSdt=-60 Th...

Q: + xln\ V 1 – x° | dx

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A: Given: fx=-1gx=4 To Graph: Graph the given functions f and g in the same rectangular coordinate syst...

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A: Given that an=lnn+7n1n. This implies that, an=lnn+7n1nlnan=lnlnn+7n1nlnan=lnlnn+7-lnn1nlnan=lnlnn+7-...

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A: From figure, Let x=5secθ dx=5secθtanθ

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Q: Find all the local minimum/minima, maximum/maxima, inflection points, intercepts, and all asymptotes...

A: Consider the given function, fx=x2+122x+1f'x=ddxx2+122x+1=2x+12x+0-x2+122+02x+12=2x2+x-122x+12f''x=d...

Q: Evaluate the following limit. Use l’Hôpital’s Rule when it is convenient and applicable.

A: We have to evaluate limx→0+x1lnx Let L=limx→0+x1lnx Taking logarithm on both sides, lnL=limx→0+lnx1l...

Q: True or False. Justify your answer. Number 12

A: Given:Inverse function f existsThe graph of f has a y-intercepty-intercept of f is anx-intercept of ...

Q: Find the limit of the sequence if it converges; otherwise indicate divergence. an = (-1)" |1- 1 3 O ...

A: we have  an=(-1)n1-3n

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Q: Darnell deposts $4000 in a bank account which pays 13.39% interest compounded monthly.  How many yea...

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Q: A right circular cylinder has a 4 inch diameter and is filling with water at a constant rate.  The w...

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Q: Let (x) = 1 Find and simplify f(x+h)-f(x) Show and explain all the steps. Explain the significance o...

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Q: Bank D pays 7.289% effective annual yield, on an investment account in which interest is compounded ...

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Q: Solve the equation  e^(x^2+2x+1) = e^-(2x+2)  for x

A: We have to solve for x Given that e(x^2+2x+1)=e-(2x+2) Equating both power( because base is equal) x...

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A: Given: For some positive constant c and D=Drug Dose  T=Patient's temperature change T=C2-D3D2

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A: y'+2=-6x, passes through (8,1)

Q: 6. Let s'+- if + -1 and a # 1 f (æ) if x = -1 if æ = 1 1 (a) Find f (-2). (b) Find f (-1). (c) Find ...

A: Answer and explanation is given below

Q: 4=x^_4 2x²-7xt6 Id the function continuous cut x=23

A: GIVEN FUNCTION : Function y=x2-42x2-7x+6                 TO FIND :  Function is continuous at x=2 A...

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A: given xy2-y-2=0 to find the equation of tangent at x=1

Q: How do I solve this limit.

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Q: I'm confused on this problem, how would I go about solving it?

A: The power series ∑n=1∞(-1)n+1(x-c)nncn. We have to find the interval of convergence.

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A: Given,            The bathtub has a length of 1 meter and its cross-section is a trapezoid with the ...

Q: multivariate calcu;us:   Find the total derivative of V with respect to X. V=3X^3 + 5Y^2 + 6Z Z=4+5X...

A: Consider the provided equation, V=3x3+5y2+6z Find the total derivative of V with respect to X.  

Q: Assume that the sequence converges and find its limit. a 1 = 8, a n+ 1= /8an O 1 O 64 8 -8

A:

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.