Initial Value Problem. Use Laplace transform.

m''(t) + 6*m'(t) + 25*m(t) = cos(t)

where m(0) = 1 and m'(0) = 1

Use the Disk/Washer Method to find the volume of the solid of revolution formed by rotating the region about each of the given axes.

14. Region bounded by: y=4 - x^2 and y=0.

(a) the x-axis (c) y= -1

(b)y=4 (d) x=2

AND

17. Region bounded by: y=1/ sqrt((x^2) +1), x= -1, x=1 and the x-axis.

Rotate about:

(a) the x-axis (c) y= -1

(b) y=1

Use the Laplace transform to solve the given initial value problem.

y^(4)−256y=0; y(0)=38, y′(0)=64, y′′(0)=320, y′′′ (0)=640

Find the work done by the force field F(x,y) = <2xy-cosx,ln(xy)+cosy> along the path C, where C starts at (1,1)(1,1) and travels to (2,4)(2,4) along y=x^2, then travels down to (2,2)(2,2) along a straight path, and returns to (1,1)(1,1) along a straight path. Fully justify your solution.

Please show all steps, explain in detail, write legibly

y"-6y'+9y = 24t^-5e^3t

^{Find the general solution}

1. How tall and wide would a single giant screen be from combining all the screens on mobile phones in the USA?

Hint: We'll want our giant mobile phone to have the same height/width ratio as a single mobile phone.

Estimate the population of the USA. ?

Estimate the number of mobile devices in the USA. ?

Estimate the area (in meter²) of one mobile phone.

Using your answers above, estimate the area (in meter²) of all mobile phones in the USA. ?

Estimate the height (in meter) of our giant mobile phone. Use the provided hint. ?

Estimate the width (in meter) of our giant mobile phone. Use the provided hint. ?

Let D be a lamina (a thin plate) occupying the region in the xy-plane that is in the first quadrant, between the circles of radius 1 and 4 centered at the origin. Assume D has constant density which you may take as a unit value. Complete these tasks: 1. Draw a graph of D. 2. Compute the mass of D (which will be the same as the area because the density is equal to one). 3. Identify a line of symmetry in D which will help with Step 4, below. 4. Compute the center of mass of D. I recommend that you use polar coordinates. 5. Go back to your graph of D and plot the location of the center of mass you just found.

What is today's label for postulates and common notion?

please don't answer unless you can do all parts, circle answer and show work please part

1)

A 13 foot ladder is leaning against a wall. If the top slips down the wall at a rate of 3 ft/s, how fast will the foot be moving away from the wall when the top is 9 feet above the ground? The foot will be moving at ft/s. 2.87 (I got this but its wrong)

part 2)

Oil spilled from a ruptured tanker spreads in a circle whose area increases at a constant rate of 6 mi2/hrmi2/hr. How rapidly is radius of the spill increasing when the area is 10 mi2mi2? The radius is increasing at 9.38 (This is my answer I got and its incorrect) mi/hr.

part 3)

At noon, ship A is 40 nautical miles due west of ship B. Ship A is sailing west at 18 knots and ship B is sailing north at 15 knots. How fast (in knots) is the distance between the ships changing at 6 PM? The distance is changing at 12.17 (Again my answer but its incorrect) knots. (Note: 1 knot is a speed of 1 nautical mile per hour.)

part 4)

A spherical balloon is inflated so that its volume is increasing at the rate of 3.8 ft3/minft3/min. How rapidly is the diameter of the balloon increasing when the diameter is 1.8 feet? The diameter is increasing at 1.8 (My answer but its incorrect) ft/min.

part 5)

A street light is at the top of a 18 ft tall pole. A woman 6 ft tall walks away from the pole with a speed of 6 ft/sec along a straight path. How fast is the tip of her shadow moving along the ground when she is 40 ft from the base of the pole?

ft/sec

How fast is the length of her shadow increasing?

ft/sec

part 6)

Suppose that for a company manufacturing calculators, the cost, and revenue equations are given by

C=70000+40x,R=400−x^2/30

where the production output in one week is x calculators. If the production rate is increasing at a rate of 500 calculators per week when the production output is 6000 calculators, find each of the following:

Rate of change in cost =

Rate of change in revenue =

Rate of change in profit =

How do I design a correlational study examining the relationship of recall using ITI(inter trial interval), feedback percent, introversion/extroversion and number of digits recalled?

definitions of weak topology and weak star topology with as little jargon as possible.