### Find the area of the parallelogram with vertices A(-3, 0), B(-1, 5), C(7, 4), and D(5, -1)

The aim of this problem is to get us familiar with the area of a very common quadrilateral known as a parallelogram. If we recall, a parallelogram is a pretty simple quadrilateral with two couples of parallel-faced sides. The opposite lengths of a parallelogram are of equal dimensions and the opposing angles of a parallelogram […]

### Find a vector function that represents the curve of intersection of the cylinder and the plane.

[Cylinder x^2+y^2=4] [Surface z=xy] The aim of this question is to find the vector function of the curve that is generated when a cylinder is intersected by a surface. The basic concept behind this article is the Vector-Valued Function and representation of different geometrical figures in parametric equations. A vector-valued function is defined as a […]

### Let P(x,y) be the terminal point on the unit circle determined by t. Then find the value for sin(t), cos(t) and tan(t).

The aim of this question is to find sin t, cos t, and tan t for a given point P=(x,y) on the unit circle which is determined by t. For this, we will be utilizing the Cartesian Coordinate system and Equation of Circle. The basic concept behind this question is the knowledge of the circle and its […]

### A boat is pulled into a dock by means of a winch 12 feet above the deck of the boat.

The rope is pulled by a winch at 4 feet per second. When 14 feet of rope is out, what will be the speed of the boat? As the boat inches closer to the dock, what happens to its speed? 4 feet per second is a constant speed at which the boat is moving. When […]

### Find the volume of the solid generated by revolving the shaded region about the y-axis.

This article aims to find the volume of the solid formed by rotating the shaded region about the y-axis. The article uses the concept of volume of the solid. The volume of the solid generated by a region under $f(x)$ bounded by the y-axis and vertical lines $y=a$ and $y=b$, which is […]

### Evaluate the double integral y^2 dA, D is the triangular region with vertices (0, 1), (1,2), (4,1)

This article aims to find the double integral of the triangular region with vertices. This article uses the concept of double integration. The definite integral of a positive function of one variable represents the area of the region between graph of the function and the $x-axis$. Similarly, the double integral of a positive function of two […]

### What is 10∠ 30 + 10∠ 30? Answer in polar form. Note that the angle is measured in degrees here.

This question aims to split the given polar form into cartesian coordinate form. This question uses the concept of splitting the given polar form into its cartesian coordinate form. Cartesian coordinate form is the sum of the squared values of the difference between the x coordinate and the y coordinate of the two specified points and […]