What is the equation of three bisecting solid rods centered at the origin?

Hello, What is the equation of three bisecting solid rods centered at the origin? Given 3 solid rods of length 3 and diameter 1. One rod is on the x-axis One rod is on the y-axis and One rod is on the z-axis Each is centered at the origin and is perpendicular to the other rods in each axis. Need equation in rectan ...continues

Explaination for derivatives

Explaination for derivatives related to exponential and logarithmic functions ,formulae used to solve them and solutions to some problems. All problems are in the solution file

Exponential growth and decay

A leaking oil tank has a capacity of 500 000 liters of oil. The rate of leakage depends on the pressure of oil remaining in the tank and the pressure depends on the height of oil. When the tank is half-full, it loses 20L/min. How long goes it take to lose 15 000L from half-full?

Velocity and acceleration

On another planet, Jim throws a ball directly up into the air. The velocity of this ball is a linear function of t. He finds that the velocity of the ball at 1 second is 44 meters/second. At 4 seconds, it is -49 meters/second. a.) Find v(t), the velocity of the ball at time t seconds. b.) Find a(t), the acceleration of t ...continues

Calculating rates of change in a loan situation.

The formula for the loan one can get with a payment of $P paying monthly for 15 years at an interest rate of r is: L=(12P/r)[1-(1+(r/12))^(-180)] a.) Find dL/dt, the rate of change of the loan with respect to time. (Here, t is the time that is passing, not the t in the original function if you know the loan. Trea ...continues

Minimization problems dealing with lengths.

A rectangular page is to contain 24 square inches of print. The margins at the top and bottom of the page are to have 1.5 inches, and the margins on the left and right are to be 1 inch. What should the dimensions of the page be so that the least amount of paper is used.

Working with infinite sequences and series.

If series Sum(an) and Sum(bn) with positive terms are convergent, is the series Sum(an*bn) converegent? Note: 1. Sum replaces the symbol for summation 2. an and bn are nth elements of the two series

First and second derivatives

Find the first and second derivatives of the function y=((1-x)/x^2)^3

Infinite sequences and series

In the figure (see attachment) there are infinitely many circles approaching the vertices of an equilateral triangle, each circle touching other circles and sides of the triangle. If the triangle has sides of length 1, find the total area occupied by the circles.

Washer and shell methods

find the volume of the solid generated when the region bounded by y = sqrRoot(x-1); y = 0 and x = 5 is rotated about the line y = 3. Use both methods, washer and shell, showing that both methods yield the same answer