Math: Calculus
posted by Anonymous .
The max. weight M that can be supported by a beam is jointly proportional to its width w and the square of its height h, and inversely proportional to its length L.
a) write an equation that expresses the proportionality.
b) determine the constant of proportionality if a beam is 4 in. wide, 6 in. high, and 12 ft long can support a weight of 4800 lb.
c) if a 10ft beam, made of the same material is 3 in. wide and 10 in.high, what is the max. weight it can support?

M = k(w)h^2/l
b)4800 = k(4)(36)/12
solve for k
c) now that you have the full equation, just sub in the values given to find M 
a)M=k(w)h^2/l
b)4800=k(4)(6)^2/144
k=4800 first change the unit of the length from feet to inch and use the expression that i used above.Unit conversion between in and feet is 1ft=30.48cm and 1in=2.54cm
c)since u have the equation all u have to do is plug in the values to the equation
Respond to this Question
Similar Questions

Calculus
A rectangular beam is cut from a cylindrical log of radius 30 cm. The strength of a beam of width w and height h is proportional to wh^2. Find the width and height of the beam of maximum strength. Is the width 45 and the height 20. 
Math
The maximum weight M that can be supported by a beam is jointly proportional to its width w and the square of its height h, and inversely proportional to its length L. a. Write an equation that expresses this prportionality b. Determine … 
physics
If two different masses have the same kinetic energy, their momenta are: 1. inversely proportional to their masses 2. inversely proportional to the square roots of their masses 3. proportional to the squares of their masses 4. proportional … 
Physics
If two different masses have the same kinetic energy, their momenta are: a. proportional to the squares of their masses b. proportional to their masses c. proportional to the square roots of their masses d. inversely proportional to … 
calculus
A rectangular beam is cut from a cylindrical log of radius 25 cm. The strength of a beam of width w and height h is proportional to wh2. (See Figure 4.70.) Find the width and height of the beam of maximum strength. 
physics
if a stone at the end of a string is whirled in a circle, the inward pull on the stone A) is known as the centrifugal force B) is inversely proportional to the speed of the object C) is inversely proportional to the square of the speed … 
Algebra
Suppose that the maximum weight that a certain type of rectangular beam can support varies inversely as its length and jointly as its width and the square of its height. Suppose also that a beam 6 inches wide, 2 inches high, and 12 … 
Algebra
Suppose that the maximum weight that a certain type of rectangular beam can support varies inversely as its length and jointly as its width and the square of its height. Suppose also that a beam 6 inches wide, 2 inches high, and 12 … 
Mathematics
Suppose that the maximum weight that a certain type of rectangular beam can support varies inversely as its length and jointly as its width and the square of its height. Suppose also that a beam 4 inches wide, 3 inches high, and 18 … 
Math Ratios
Suppose A is directly proportional to B, B is inversely proportional to C and C is inversely proportional to D. Determine whether A and D are directly proportional, inversely proportional, or neither.