12. A company is constructing a cylindrical can for a new product. They want to keep the cost of producing the can low and have decided, based on the cost of materials, that the can will have a total surface area of 24 square inches. Use calculus to determine the maximum volume of the can. Round to the nearest hundredth. Include units. SA = 2πr² + 2πrh V = πr²h

Q: Evaluate the definite integral. NOTE: Enter the exact answer. 12 5.² 11 |ti + t²j||dt 0 = =

A:

Q: A model for the spread of a rumor is given by the equation p(t)= 1/1+ae^(-kt), where p(t) is the…

A: Given problem:- A model for the spread of a rumor is given by the equation p(t)= 1/(1+ae-kt)…

Q: Use the method of cylindrical shells to find the volume V of the solid obtained by rotating the…

A: Given problem:- Use the method of cylindrical shells to find the volume V of the solid obtained by…

Q: A county's statistics indicate that the number of white-collar crimes is growing according to the…

A:

Q: 3. Solve the following equations by using variation of parameters methods: a) y" - 2y' + y = e* ln x

A: As per our guidelines we can answer only 1 question so kindly repost the remaining questions…

Q: Find the particular solution to the differential equation. 2233 Y and y = 4 when x = 0. y(x) = DNE *…

A:

Q: A ball is thrown vertically upward from the ground with an initial velocity of 64 ft/sec. If the…

A:

Q: (8x4 − 5x2 + 2)dx evaluate indefinite anti-differentiation

A:

Q: Find the length of the curve 3y = 2(x² + 1)2 from x = 0 to x = 3.

A:

Q: s x3 √1-x² V dx

A: Given: I=∫x31-x2dx   ...1   As we know that; The Power rule; ∫xndx=xn+1n+1+C

Q: Write √x+y²+2x-y=3 +y²+2x−y=3 as a polar equation r = f(0).

A: Write in Polar equation

Q: Decide if the limit exists. If it exists, find it. x²-25 a. lim b. lim X-5 x+5 x²-36 x-5 x-5

A:

Q: Consider the function g defined as g(x) = { Evaluate the following limits. 1.) lim g(x) 3x+2 X-2…

A: limit of a function f(x) at a point x=a exists iff limx→a-f(x)=limx→a+f(x)

Q: andard fencing

A:

Q: Consider the following. y 5 4 3 y = x + 2 y = x² -3 -1 1 2 (a) Find the points of intersection of…

A:

Q: ∫ sinx √cosx dx

A:

Q: 2. If the Profit function for producing x units is P(x) = 0.0035x³ + 120x, then the marginal profit…

A:

Q: Show that the integral is independent of the path, and use the Fundamental Theorem of Line Integrals…

A:

Q: List all possible rational zeros given by the Rational Zeros Theorem (but don't check to see which…

A:

Q: √1² +25 -2 I dt

A:

Q: Evaluate fff (3x + 2y)dV, where S is the solid bounded above by the plane z=4, below by plane z=0…

A: ∫∫∫(3x + 2y) dV=∫∫∫(3x + 2y) dxdydz = ∫z = 04∫y = -13∫x =-11(3x + 2y) dxdydz = ∫z = 04∫y = -134y…

Q: Evaluate (sin² (sin² x cos x)(1+ sin z cos x) dx.

A: Use substitution method

Q: x2 (x− 1)(x4 +8x²+16) dx- S

A:

Q: 3. Use Green's Theorem to find the area of the region enclosed by one arch of the cycloid x = t -…

A:

Q: Solve the problem. A business estimates that the salvage value V of a piece of machinery after t…

A:

Q: Consider the following. y = √x 4 X = 8 y = 2-x -6 -8 (a) Form the integral that represents the area…

A:

Q: 4 P = 80x-2x²-xy-3y² +100y + X(12-X-Y) FinD Px, Pxx, Py, Pyy, Pxy = Pyx, fino x And y Fine Fine P

A: Here's the solution.... please have a look at it...

Q: Find the following using the table below. x 1 2 3 4 4 2 f(x) 1 3 f'(x) 2 3 4 1 g(x) 13 4 2 g'(x) 2 4…

A: Chain Rule of differentiation : fgx' = f'gx .g'(x)

Q: Consider the solid torus (the donut-shaped solid shown in the figure) with radii 5r and 6R. a = 6 b…

A: We have to find the integral and volume.

Q: = ||r' (t) x r"(t)|| ||r' (t)||³ to find k(t). r(t) = 11 cos(t)i + 11 sin(t)j + 6tk Use the formula…

A:

Q: Paramount Electronics has an annual profit given by P = -100,000 + 5,000q - 0.25q² dollars, where q…

A:

Q: 10 F [TOF If f(x) dx = 16 and 5 Isro f(x) dx 10 f(x) dx = 5, find the following. S

A:

Q: Solve the differential equation in Higher order differential equations (D^2-D-2)y= cosx PLEASE…

A:

Q: lars) from the production and sale of x units of a product is

A:

Q: ∫ sin4x dx

A:

Q: Verify Green's Theorem by evaluating both integrals √ y² dx + x² dy = √ √ ( Ox (ON-OM) c for the…

A: Here we have to verify the Green's theorem.

Q: The Bernoulli's form of the differential equation x³ydx+(3x4 - y³dy=0 is

A:

Q: ∫10x9−12x3−5 dx Evaluate indefinite anti-differentiation

A:

Q: 1) Find the average value of the function f define by f(x)=√√√49-x²³² On the interval [0, 7] 2) Find…

A: We can use the equation to find average value of a function in an interval.

Q: Find the equation of the tangent line to the graph of f(x) = x'e- at x = 0.

A: The given function is f(x)=x9e-x at x=0.

Q: Sketch the region of integration for the following integral. π/4 3/cos(0) f(r, 0) r dr de The region…

A: We have to sketch the region of given integral

Q: 1. Determine the following using the graph off provided below. If the value is infinite, specify oo…

A: x→a+ means; x approaching to value a from the right side.Equation of straight line:(-7, 3) and  (1,…

Q: Use the given derivative to find all critical points off, and at each critical point determine…

A:

Q: Determine whether the sequence converges or diverges. If it converges, find the limit. If it…

A:

Q: Answer (A) & (B) A- Find the integrating factor of the following D.E (2 cos y + 4x²)dx (x siny) dy…

A: Integrating factor of the differential equation: Consider  Mdx+Ndy=0 be the differential equation.…

Q: Obtain the Lagrange interpolating polynomial for a certain function f of which we know that: f (-1)…

A: Lagrange interpolating polynomial: The Lagrange interpolating polynomial is a degree polynomial that…

Q: F = 3 x 10-4³-4.4 x 10-³w²+3.93w+0.221

A: Given :

Q: The graph of g consists of two straight lines and a semicircle as shown in the figure. y 20 y = g(x)…

A:

Q: S sin (3x) 1+cos² (3x) dx

A: The detailed solution is given below Thank you

Q: A company producing jigsaw puzzles has fixed costs of $7000 and variable costs of $4 per puzzle. The…

A: