### Find two vectors in opposite directions that are orthogonal to the vector u. U=(-1/4)i +(3/2)j

This question aims to find the $2$ vectors which are orthogonal to the given vector $U = dfrac{-1}{4}i+dfrac{3}{2}j$, and these two vectors should be in opposite directions. This question is based on the concept of orthogonal vectors. If two vectors $A$ and $B$ have a dot product equal to zero, then the said two vectors […]

### Find an equation of the tangent line to the curve at the given point. y = sqrt(x) , (81, 9)

The aim of this question is to deduce the equation of a tangent line of a curve at any point on the curve. For any given function y = f(x), the equation of its tangent line is defined by the following equation: Read moreFind the parametric equation of the line through a parallel to b.[ […]

### Find the area under the given curve over the indicated interval.

– $int_{1}^{6} 2 x ,dx$ The main objective of this question is to find the area of the curve over the indicated interval. Read moreFind the parametric equation of the line through a parallel to b.This question uses the concept of the area under the curve. The area under the curve can be […]

### Find a polynomial with integer coefficients that satisfies the given conditions

– The degree of $Q$ should be $3, space 0$ and $i$. The main objective of this question is to find the polynomial for the given conditions. Read moreFind the parametric equation of the line through a parallel to b.This question uses the concept of the complex conjugate theorem. […]

### At a certain college, 6% of all students come from outside the United States. Incoming students there are assigned at random to freshman dorms, where students live in residential clusters of $40$ freshmen sharing a common lounge area.

How many international students would you expect to find in a typical cluster? With what standard deviation? This question aims to find the expected number of international students in a typical cluster along with their standard deviation. Take into consideration what a random variable is: a collection of numerical values resulting from a random process. […]