Solve the given problem.

A farmer has a thousand feet of fence to enclose a rectangular area. What dimensions for the rectangle result in the maximum area enclosed by the fence?

A farmer has 1000 feet of fence to enclose a rectangular area. What dimensions for the rectangle result in the maximum area enclosed by the fence?

For the beam and loading shown, determine (a) the equation of the elastic curve, (b) the slope at end $A,(c)$ the deflection at point $C$.

For the beam and loading shown, find (a) the equation of the elastic curve. (b) the deflection at the midpoint C.

For this exercise, consider the function $P(x)=2 x^2-6 x-8$.

Determine analytically the $y$-intercept of the graph of $P$.

The bicycle has a velocity v=4 ft / s, and at the same instant the rear wheel has a clockwise angular velocity $\omega=3 rad / s$, which causes it to slip at its contact point A. Determine the velocity of point A.

If the forklift's rear wheels supply a combined traction force of $F_A=300 lb$, determine its acceleration and the normal reactions on the pairs of rear wheels and front wheels. The forklift has a weight of 2000 lb, with center of gravity at $G_1$, and the load weighs 900 lb, with center of gravity at $G_2$. The front wheels are free to roll. Neglect the weight of the wheels.

One or more zeros are given for this polynomial. Find all remaining zeros.

$P(x)=x^3-x^2-4 x-6 ; 3$ is a zero.

Solve the given equation for $x$ and then for $y$.

$$3 y^2+4 x y-9 x^2=-1$$

The W $10 \times 45$ is made of A- 36 steel and is used as a column that has a length of $15 \mathrm{ft}$. If the ends of the column are fixed supported, can the column support the critical load without yielding?

The W $10 \times 45$ is made of A-36 steel and is used as a column that has a length of 15 ft. If the ends of the column are fixed supported, can the column support the critical load without yielding?

Two satellites are placed in orbit, one about Mars and the other about Jupiter, such that the orbital speeds are the same. Mars has the smaller mass. Is the radius of the satellite in orbit about Mars less than, greater than, or equal to the radius of the satellite orbiting Jupiter?

Solve the given equation for $x$ and then for $y$.

$$4 x^2-2 x y+3 y^2=2$$

Determine a cubic polynomial function $f(x)$ in standard form having real coefficients with zeros of $4$ and $2 i$, such that $f(1)=-15$.