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Calculus and Analysis

Differential Equation: System of Equations

For this problem state the method you used and show the work required to obtain the answer. Find the general solution for this system: this is a matrix x'= 3y+z y'= x+z+2y z"= 3y+x

Differential Equations

Hi, For this problem please state the method you used and show the work required to obtain the answer. Find the complete solution to this equation problem. y^3 - 2y^2 + y^1 = 2- 24e^(x) + 40e^(5x)

A problem dealing with volume of revolution

A bowl is shaped like a hemisphere with radius R centimeters. An iron ball with radius R/2 centimeters is placed in the bowl and water is poured in to a depth of 2R/3 centimeters. How much water was poured in?

Volume of water poured in to bowl with iron ball.

A bowl is shaped like a hemisphere with radius R centimeters. An iron ball with radius R/2 centimeters is placed in the bowl and water is poured in to a depth of 2R/3 centimeters. How much water was poured in?

Surface area of revolution

How do I find the surface area obtained by revolving the curve y=x-1 from x=1 to x=4 about the line x= -1?

Differential Equations Reduction of Order Methods

Please see the attached file for the fully formatted problems. (i) Consider the differential equation: x. = x^2 , x(0) given x(0)>0 Find the solution of x(t) of this equation in terms of x(0) and show that there is a T, which depends on x(0), such that lim x(t) = infinity t --> T- (ii) Find the solution of the

Working with growth and decay rates and decay rate expressions.

A crude-oil refinery has an underground storage tank which has a fixed volume of 'V' liters. Due to pollutants, it gets contaminated with 'P(t)' kilograms of chemical waste at time 't' which is evenly distributed throughout the tank. Oil containing a variety of pollutants with concentration of 'k' kilograms per liter enters

Differential Equations and Newton's Law of Cooling

At 4:30 PM on Monday, a Virginia criminalist was called to the scene of a homicide. She noted that the body temperature of the deceased was 85.5 deg. while the air temperature was 78 deg. Thirty minutes later, the deceased's body temperature was 82 deg. Assuming the air temperature stayed constant, what is the estimated time of

Interval of Convergence Power Series

I am trying to find the interval of convergence for the attached power series (attached as a gif). I am also supposed to check the endpoints for convergence. I'm not that good with power series and the format of this power series is really throwing me off. So I am looking for the steps to find the interval of convergence (also c

Power Series Representation

I am trying to figure out a powers series representation for the function f(x) = e^x, centered at c = -2. I also need to find the interval of convergence.

Tangent Line to a Curve

Find an equation of the tangent line to the curve, Y = x^3 - 3x^2 + 5x that has the least slope. Make sure to show all of the required steps.

Rectilinear motion: Calculation of velocity

A billiard ball is hit and travels in a line. If s centimeters is the distance of the ball from its initial position at t seconds, then s=100t2 + 100t. If the ball hits a cushion that is 39cm from its initial position, at what velocity does it hit the cushion?

Find the maximum area of a window.

A special window has the shape of a rectangle surrmounted by an equilateral triangle. If the perimeter is 16 feet, what dimensions will admit the most light? (hint: Area of equilateral triangle = the square root of 3/4 times x squared.)