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M.Sc @ Regional Engineering College ,Warangal

I like playing chess , doing paintings, making art pieces etc

Abstract/Modern Algebra, Algebra, Algebra Basics, Applied Mathematics, Arithmetic, Basic Geometry, Basic Operations, Basic Statistics, Bessel Functions, Decimals

I can teach mathematics from basics so students would be able to solve all problems for themselves .Have 17 years of math tutoring experience at various levels.

- Abstract/Modern Algebra
- Algebra
- Algebra Basics

Question: Simplify and find the value of Sin30cos60+cos30sin60 Solution:Sin30cos60+cos30sin60= sin(30+60) (using sin(A+B)= sinAcosB+cosAsinB formula) (Here A= 30 and B= 60) = sin(90) = 1

Question:- x^3 − x^2 − 9x + 9 Let us try to factor the first two and second two separately: x^2(x−1) − 9(x−1) Now we have x-1 on both the terms , so let us use that: (x^2−9)(x−1) And x^2−9 is a difference of squares so that can be done using the formula a^2-b^2= (a+b)(a-b) (Here a = x and b= 3) (x−3)(x+3)(x−1) This is the final answer

Question: -Solve the equation below using the method of completing the square. x^2-9x+14=0 Solution:-Move the constant to the right side of the equation, while keeping the x-terms on the left. This can be done by subtracting both sides by 14. x^2-9x=-14------(1) After subtracting we have this.Now consider the coefficient of x which is 9 Take half of that and square it Which is (9/2)^2= 81/4 Now add 81/4 on both sides of the equation (1) above x^2-9x+81/4=-14+81/4 (x-9/2)^2 = 25/4 Taking square roots on both sides x-9/2 = +- 5/2 solutions are x-9/2 = 5/2 and x-9/2 = -5/2 On simplifying we get x= 7 and x= 2

Question: Find the probability of getting a numbered card when a card is drawn from the pack of 52 cards. Solution:-Total Cards = 52. Numbered Cards = (2, 3, 4, 5, 6, 7, 8, 9, 10) so 9 from each suit 4 × 9 = 36 P (E) = 36/52 = 9/13

Question:-Solve the following equations for the unknown x 5= 7x-16 Solution:-Given that 5 = 7x − 16, add 16 to both sides to get 7x = 21. Now divide both sides by 7 to get x = 3. Checking, we see that 7(3) − 16 = 21 − 16 = 5

Example : f(x) = 3x^2-2x+1 Solution: Given, f(x) = 3x^2-2x+1 Differentiating both sides, we get, f’(x) = 6x – 2, where f’(x) is the derivative of f(x) (Here I used the formula d/dx(x^n) = nx^(n-1))

Question : The sum of two numbers is 50, and their difference is 30. Find the numbers. Solution:-Let the numbers be x and y. Now, as per the given situation, x + y = 50……………………(i) and x – y = 30………………(ii) We can write, x = 50-y, from eq.(i), Therefore, putting the value of x in eq(ii), we get, 50 – y – y = 30 50 -2y = 30 2y = 50-30= 20 y = 20/2 = 10 and x = 50 – y = 50-10 =40 Therefore, the two numbers are 40 and 10.

Example Find the mean of the following data set: 56, 35, 45, 67, 12, 24, 48, 55, 58, 30 Solution:- To find the mean add all the numbers given and divide the sum with the number of items in the list. (56+35+45+67+12+24+48+55+58+30)/10= =430/10=43 The mean=43

0, 5, 10, 15, 20, 25, ... Number pattern Here, we get the numbers in the pattern by skip counting by 5. Given are the steps to identify a number pattern. To solve the problems of number pattern, we need first to find the rule being followed in the pattern. To find out the rule, we need to see the first few numbers in the series. Try to see the difference between consecutive numbers, it will help us understand the relationship between the numbers. Example : · 11, 17, 23, 29, 35, 41, 47, 53 Example In this pattern, we see that every term in the sequence has grown or increased by 6 or the difference between any two consecutive numbers is 6. So, we can get the next term by adding 6 to the previous term.

Question : Solve 25+5(27÷3)-9 Solution: 25 + 5(27 ÷ 3) – 9 ⇒ 25 + 5(9) – 9 ⇒ 25 + 45 – 9 ⇒ 70 – 9 = 61

4/7 of a number is 84. Find the number. Solution: According to the problem, 4/7 of a number = 84 Number = 84 × 7/4 [Here we need to multiply 84 by the reciprocal of 4/7] 84*(7/4) = 21 × 7 (since 4 divides 84 21 times) = 147 Therefore, the number is 147.

1. Maria purchased 24 m 25 cm rope and Nancy purchased 17 m 15 cm rope. What is the total length of ropes both of them purchased? Solution: Length of ropes purchased by Maria = 24 m 25 cm Length of ropes purchased by Nancy = 17 m 15 cm Total length of ropes purchased by them = 24 m 25 cm + 17 m 15 cm = 41 m 40 cm

Question:-A water pitcher weighs 0.64 kg when empty and 1.728 kg when filled with water. How much does the water weigh? Solution:-Solution It is given that a water pitcher weighs 0.64 kg when empty and 1.728 kg when filled with water. We have to find the weight of the water. To find the weight of the water, we need to subtract the weight when the pitcher is empty from the weight of the pitcher when it is filled with water. 1.728 -0.64 ---------- 1.088 ----------- Hence, the weight of the water is 1.088 kg.

Question :- Find the Greatest Common Factor (GCF) of 24,60,66 Solution:-The factors of 24 are 1, 2, 3, 4, 6, 8, 12 and 24 The factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30 and 60 The factors of 66 are 1, 2, 3, 6, 11, 22,33 and 66 Look for the greatest factor that is common to all three numbers - thus 6 is the GCF of 24, 60 and 66.

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