This educational page which helps the learners of School grade to improve their subject knowledge.
A triangle ABC is drawn to circumscribe a circle of radius 3cm, such that the segments BD and DC into which BC is divided by the point of contact D are of length 9cm and 3cm respectively. Find the sides AB and AC.
Math Tricks to calculate quickly - Multiply by 11
Square of Two digit number ending in 5
Math Tricks to calculate quickly - Multiply by 9
Math Tricks to calculate quickly - Multiply by 5
Show that the points (-4,-7), (-1,2), (8,5) and (5,-4) taken in order are the vertices of a Rhombus. Find its area.
What is a Logarithm?
1. Logarithms are Just a Way to Ask: “How Many Times Do We Multiply?”
Imagine you know that multiplying a number by itself several times gets you a big number. A logarithm helps you figure out how many times you need to multiply it to reach that big number.
For example, if you want to know how many times to multiply 10 to reach 100, the answer is 2 (since 10×10=100).
2. Let’s Look at a Simple Example
log10(100)=2: This is just asking, “How many times do we need to multiply 10 to get 100?” The answer is 2 because 10×10=100.
3. Another Way to Think About It
If you see something like log2(8), think of it as asking: “How many times do we multiply 2 to get 8?” Since 2×2×2=8, the answer is 3. So, log2(8)=3.
4. Logarithms are Like Reversing Exponents
When you see 10^2=100, you’re saying "10 multiplied by itself 2 times is 100."
A logarithm reverses this question: Given 10 and 100, it asks, “What power of 10 gives me 100?” And the answer is 2, so log10(100)=2.
In simple terms, a logarithm helps us figure out how many times we need to multiply a number to get another number.
A 1.6m tall man is looking at the top of a tower which is 31.6m in height from a point at certain distance. The angle of elevation from his eye to top of the tower increases from 30 degrees to 60 degrees as he walks towards the tower. Find the distance he walked towards the tower.
Construct △ABC in which AB=6cm, ∠A=60 degrees, AC=5cm. Construct a triangle similar to it whose sides are 3/4th of the corresponding sides of △ABC.
Find the median of the data.
Show that 2√3+√7 is an irrational number.