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Calculus
A rectangular open box is have a square base, and its volume is to be 125 inches^3. The cost Per in^2 Of the material for the bottom Is 8$ and for the sides is 4$.
A. Find the mathematical model Expressing The total cost Of the material As a function of the edge Lenght Of the square base.
B. What is the total cost If the square Base has edge Lenght of 4 inches
Calculus
A normal window with a perimeter of 20 units has the shape of a rectangle surrounded by a semi circle. If its base is x units long and the height of rectangle is y units long, write a mathematical model for its area in term of x
Calculus
A right-circural cone is inscribed in a sphere having a fixed radius of 10 in. Express the volume of the cone as a function of its radius.
Calculus
A cable hangs in a parabolic arc between two columns 100 feet apart. The columns are 40
feet high and the lowest point on the suspended cable is 10 feet above the ground.
a. Find the equation of the arc if the vertex is the lowest point of the cable.
b. Find the height of the cable from the ground at a point 30 feet from the lowest point of the
cable.
feet high and the lowest point on the suspended cable is 10 feet above the ground.
a. Find the equation of the arc if the vertex is the lowest point of the cable.
b. Find the height of the cable from the ground at a point 30 feet from the lowest point of the
cable.
Calculus
A tent in the shape of a pyramid with a square base is to be constructed from a piece of material having a side of length 5 meters. In the base of the pyramid, let x be the distance from the center to a side (see figure below). Find a mathematical model expressing the volume of the tent as a function of x. (The volume of a pyramid is V = Bh, where V, B and h are the volume, base area and height of the pyramid respectively).
Calculus
\int \:xsinxdx
Calculus
\int \:xcosxdx
Calculus
\int \:xe^e dx
Calculus
\int \:\frac{x+sinx}{1+cosx}dx
Calculus
\int \:\frac{xe^x}{\left(1+x^2\right)}dx
