1)It has been conjectured that a fish swimming a distance of L ft at a speed of V ft/sec relative to the water and against a current flowing at the rate of U ft/sec (u<v) expends a total energy given by: E(v)= aLv^3/v-u

where E is measured in foot-pounds (ft-lb) and a is a constant. Find the speed V at which the fish must swim in order to minimize the total energy expended.

2) By cutting away identical squares from each corner of a rectangular piece of cardboard and folding up the resulting flaps, an open box may be made. If the cardboard is 15in long and 8 in wide, find the dimensions of the box that will yield the maximum volume,

3) In an open box has a square base and volume of 108 cubic inches, and is constructed from a tin sheet, find the dimensions of the box, assuming a minimum amoun o material is used in construction.

4) A grain silo has the shape of a right circular cylinder surronded by a hemisphere. If the Silo is to have a capacity of 504*PI cubic feet, find the radius and height of the silo that requires the least amount of material to construct.
(The volume of the silo is pi*r^2*h + 2/3*pi*r^3, and the surface area, including the floor, is pi(3*r^2 + 2*r*h)

... 3x106 Solving for v: v = +13.38x106 m/s A. Speed of the ... a nap in a canoe and wakes up to find the canoe ... the length of the canoe at 0.46 m/s, relative to the ...

... b. Find the velocities of the stone and the ball ... Their directions relative to the positive direction of the x ... 30° to the horizontal with an initial speed of 24 ...

...Find the coefficient of kinetic friction between the block ... The speed relative to the water is the velocity of ... is running boat is having both speeds rowing and ...

...Find the resultant (or sum) displacement vector by (a) the graphical method and (b) the ... 65. A swimmer maintains a speed of 0.15 m / s relative to the ...

... into the formula the known values to find that F ... gravity (which is what determines the speed) just simplifies ... itself, in which case the speeds relative to the ...

... 65% reputation is next 23% and speed is last ... weighted sum vector elements by associated relative priority value. ... of the values (denoted by lmax) found from Step ...

... to find the location of this black hole relative to earth ... 3. Solve the equation found in Question 1 for each of the ... to form the black hole c. the speed of light. ...

...Find value of r and value of y ... The rowing speed of the girls's boat and a set of possible orientations of her boat(relative to still water) are shown in the ...