4. A solid consists of a right-circular cylinder and a hemisphere on each end. The length of the cylinder is twice its radius. Find the rate of change of the volume wrt the radius when r = 2 in.

Q: Differentiate the function with respect to the independent variable. 9 h(t) = -t²- +4 h' (t) =

A:

Q: 2X 4) y = C₁ + c₂e² c + C3 e-3x

A:

Q: 32 *The solution for the following differential equation is dy x-y dx x+y y² + 2xy - x² = c y² + xy…

A:

Q: 1 Suppose that I is a location function of an object, given as L(t) = We will compute the 3t - 7…

A:

Q: € +h (1 g+ dy S

A:

Q: 2. A certain plutonium isotope decays at a rate proportional to the amount present. Approximately…

A: Let  at time t the amount of plutonium is  A(t)

Q: 6 Find the area enclosed by the given curves. * y = x³ and y = 4x

A: Since you have posted multiple questions i can do first question as per our company guidelines…

Q: analyze and sketch the curve y=x² / (x-1)

A:

Q: 3x + 1 Evaluate (x-1) (x+2) dx using Partial fractions.

A: This question can b solved using the concept of partial fractions.

Q: A transportation company sells 2000 bus tickets per day when the price is $10 per ticket. They…

A:

Q: The function f(x) 2x³ 45x² + 300x + 6 has one = local minimum and one local maximum. This function…

A:

Q: Solve the following Differential Equations with Laplace Transforms y" - 6y' + 15y = 2 sin(3t), y (0)…

A:

Q: Convert the following iterated integrals (SET UP ONLY): x² a.) [f dA from Cartesian coordinates to…

A: The simple change polar coordinate...

Q: a) b.) O F+ x dx (x³ +1) ³ 3 Sinx sin 2x dx 2 cos x

A:

Q: Find the arc length of the curve on the given interval x (0) = 0³, y (0) = 0² ; 0 ≤ 0 ≤ 2

A:

Q: Use the integral test to determine which of the following diverges. Α.Σ. ke k k=6 1 Β.Γ. Έk? +1 k C.…

A:

Q: Find the derivative: y = ln(24) 2x-4 O 4x-x² 2x-4 x²-4x 4 4x-x² 4 x²-4x O о O 8

A:

Q: 2. The 2 vectors 4â + 3b and â - 2b are perpendicular. Find the angle between â and b if they are…

A: Given :two vectors :4a^+3b^a^-2b^they are perpendicular

Q: 3 i(z³+1³) lim z→-i_z²+1

A:

Q: e costu(t) e-¹ u(t) Option 3 Option 4 • What is inverse Laplace for 1 (s + 1)² + 1 y (s) = te¹ u(t)…

A:

Q: a b 3. Write the scalar equation of the plane with normal vector = [5,-1,-2] and passing through the…

A:

Q: 3) (11x + 17) dx 2x² + 7x - 4 S

A:

Q: Use the sum and/or difference rule(s) to find the derivative of the following functions: with…

A: We have to find derivative of given function.

Q: Solve the following Differential Equations with Laplace Transforms y" - 6y + 15y = 2 sin (3t), y (0)…

A:

Q: Question 9 Evaluate: lim1 (3-2x)tan (37) O e O None of the choices 01 e 3r O ∞

A:

Q: Given z=x²y+3xy, x=sin(2t), y=cos(t), find dz/dt when t=0

A: ddxcosx=-sinx

Q: Find the acceleration u= 2x² + 3y, v=- - 2xy + 3y² + 3zy, Example the following flow field: W =- at…

A:

Q: Q17) Evaluate L (2 e-2t sin4t - 0.5 cos3t): 8 S 8 - a) b) (s+2)2+16 2s2+18 (S-2)2+16 252418 c)…

A: 17) To evaluate: L(2e-2tsin 4t-0.5cos 3t)

Q: g(x)=x5bx³ +a+c. Use calculus to: St (a) Find the critical points of g(x). (Round the y-value to 3…

A: Given a=15, b=12 & c= 15

Q: 5. Two planes are perpendicular if their nommals: a) have a cross product of zero c) have a dot…

A:

Q: dy ({})y+3

A:

Q: dx sin x tanx

A: Here we have to solve only part b

Q: solve the differential equation for initial value problem using the method of undetermined…

A:

Q: (a) Solve the following: √4x² dx

A: As per rule of bartleby we can solve only one question at a time and we can solve only three subpart…

Q: Find the tangent line, in slope-intercept form, of y=f(x) at the specified point. f(x) = - 5 3 2 -1+…

A: Given function, f(x)=5x-3x+2x2f(x)=5x-3x-12+2x-2

Q: 1) e5ln x+4Lny-Ln z qua

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

Q: Differentiate f(N) = (N) = 0 bN² + N with respect to N. Assume that b and K are positive constants.…

A:

Q: Determine whether the series converges, and if so find its sum. If the series diverges, indicate…

A: We have to find the series is convergent or not and find the sum also.

Q: Q1) L-1 1 s(s²-1)/ a) cosht-1 b) 1-cosht c) (cosh2t - 1) d)/(1-cosh2t) Q2) The general solution of…

A:

Q: A drink can, in the form of a cylinder, needs to have a volume of 750 cm³. The material for the top…

A:

Q: A piece of cardboard measuring 14 inches by 9 inches is formed into an open-top box by cutting…

A:

Q: Describe the type of discontinuity at x = -1, explain your answer. Use the definition of continuity…

A: a. Type of Discontinuity: Removable Discontinuity

Q: The midpoint of AB is at (0, 0). If A = (-5, 4), find B. B is: (

A: Given :A=-5, 4Mid Point of AB=0,0

Q: *.The equation (y"+x3y'+y=sinx)is.............. differential equation Linear,2nd order, Homogenous O…

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

Q: Consider the utility of a consumer consuming two goods, the quantities of which are x and y. His…

A: Let's solve.

Q: Solve the following Differential Equations with Laplace Transforms y" - 6y' + 15y = 2 sin (3t), y…

A:

Q: A cylinder shaped can needs to be constructed to hold 200 cubic centimeters of soup. The material…

A: Given problem:- A cylinder shaped can needs to be constructed to hold 200 cubic centimeters of soup.…

Q: Question 4 (a) Solve the following: √4x² dx (b) Explain with the aid of a sketch how this value can…

A: Let's solve given integral.

Q: 2x² + 3x + 3 (x + 1)³ - dx

A:

Q: Evaluate: S O (1+2√√)¹ 2 O (1+2√)¹ +C 8 O 2(1+2√x) + C O (1+2√)¹ - + C 4 (1+2√x)³ - dx +C

A: