Calculus Answers

A tsunami causes the ocean water at a place to first go down from its normal depth of 9 m to its lowest depth of 1.5 m in a time of 4 minutes. It then rises to its maximum depth of 15.5 m before receding to its normal depth, and thereafter repeating this periodic water movement.

Find the volume of the solid generated by revolving the circle x^2 + y^2 = 4 about the line x = 3. Use the cylindrical shell method.


Note: With sketch please

Eliminate θ from the equations 4x = cos(3θ) + 3 cos θ; 4y = 3 sin θ  sin(3θ)

v(t)= A (1-e^(-t/tmaxspeed))
1.Identify the
●units of the coefficient A
●physical meaning of A
●velocity of the car at t = 0
●Asymptote of this function as t → ∞?
2.Sketch a graph of velocity vs. time.
3.Derive an equation x(t) for the instantaneous position of the car as a function of time. Identify the
●value x when t = 0 s
●asymptote of this function as t → ∞
4.Sketch a graph of position vs. time.
5.Derive an equation for the instantaneous acceleration of the car as a function of time. Identify the
●acceleration of the car at t = 0 s
●asymptote of this function as t → ∞
6.Sketch a graph of acceleration vs. time.
7.Apply your mathematical models to your allocated car. Use the given data for the 0 – 28 m/s and 400m times to calculate the:
●value of the coefficient A
●maximum velocity
Maximum acceleration.

Let P = {0,1/4,1/2,3/4,1} be a partition of [0, 1]
and a function f : [0, 1] —> R be defined by
f(x) = x³ . Find U(P, f).

find the shortest distance between the origin and the surface x ^ 2y-z ^ 2 + 9 = 0

Johnny is designing a rectangular poster to contain 32 inches squared of printing with a 4​-in margin at the top and bottom and a 2​-in margin at each side. What overall dimensions will minimize the amount of paper​ used?

Let f(x)=x−8x+8
f
(
x
)
=
x
−
8
x
+
8
. Find the open intervals on which f
f
is increasing (decreasing). Then determine the x
x
-coordinates of all relative maxima (minima).

A discharging circuit has a voltage across the capacitor of v = V e^((-t)/RC) Determine dv/dt, the rate of change in voltage in the discharging circuit capacitor. Then find dv/dt when t = T.

Make use of binomial theorem to expand binomial expression & show the range of values of x for which expansion is valid? 1. (2-x)^-2 and 2. (1-x)^1/2

^ = to power of