Study Plus Life

Search This Blog

on October 12, 2024

Get link
Facebook
X
Pinterest
Email
Other Apps

Question 1:

What is the square root of 25?

Show Solution

The square root of 25 is 5.

Get link
Facebook
X
Pinterest
Email
Other Apps

Comments

Orbiting Velocity Calculation

Derive the formula for orbital velocity (\(v_o\)) for a satellite of mass \(m\) around a planet of mass \(M\) and at distance \(r\) from center of planet. Solution. To find it's solution we need to equate the gravitational force with centripetal force. \(G\dfrac{Mm}{r^2}=\dfrac{m{v_o}^2}{r}\) From above we'll get, \(v_o=\sqrt{\dfrac{GM}{r}}\)

QPD #002 - Mathematics | Special Series

Question: Find the sum \(S_n\) and \(S_\infty\) of given series: \(\frac{1}{1 \cdot 3} + \frac{1}{3 \cdot 5} + \frac{1}{5 \cdot 7} + \cdots + \frac{1}{(2n-1)(2n+1)}\) Solution: These types of series are considered as “special series”. We can definately find a pattern among terms but we can't find sum by general formulas (as we do in AP and GP). So, here we need to modify the given series and hence we will reach to the solution. Given: \(\frac{1}{1 \cdot 3} + \frac{1}{3 \cdot 5} + \frac{1}{5 \cdot 7} + \cdots + \frac{1}{(2n-1)(2n+1)}\) This can be written as: \(\frac{1}{2}(\frac{3-1}{1 \cdot 3}) + \frac{1}{2}(\frac{5-3}{3 \cdot 5}) + \frac{1}{2}(\frac{7-5}{5 \cdot 7}) + \cdots\) \(+ \frac{1}{2}(\frac{(2n+1)-(2n-1)}{(2n-1)(2n+1)})\)

Graphing the Quadratic Equation

Graphing of Quadratic Equation Introduction to graphs Graphs, make the mathematics visual. Without graphs, mathematics is just numbers, symbols and alphabets. Which is very difficult to analyse intuitively. Graphs make it simple to visualise any geometrical problem. Graphs do not exist solely. It exists as a complementary of another branches of mathematics, like, algebra, trigonometry, geometry, statistics, probability. The relation of graphs and algebra is so strong. Any algebraic expression (or function) becomes very realistic and visual when we plot it’s graph. When you’re reading this, it is expected that you are well aware about graphing of an equation. To revise, we know that in a co-ordinate plane, the horizontal line is known as \(x\)-axis and the vertical line is \(y\)-axis. From our knowledge of functions, we know that, in general, a function is written as \(y=f(x)\) where \(x\) is domain and \(y\) is range of function. A graph basically works as: 1. We define the domain of...

Powered by Blogger

Question 1:

Comments

Post a Comment