What are integral equations? [MSc Mathematics]

* Linear operation cannot be performed on the integral equations (3) and (4).

Rationalise the denominator 1÷(7+5√2).

 Given that 1÷7+5√2

= 1/(7+5√2)

Multiplying numerator and denominator by

7-5√2 , we get,

{1×(7-5√2)}/{(7+5√2)(7-5√2)}

=(7-5√2)/{7²-(5√2)²}.  

[By using (a+b)(a-b)=a²-b²]

=(7-5√2)/(49-50)

=(7-5√2)/(-1) = -(7-5√2) =-7+5√2.  Ans.

What is the sum of following: 2+2²+2³+…+2¹²=?

 

If y=f(x),which is dependent and independent variable in this expression?

 

Solve the following system of linear equations 7x - 2y = 5 and 8x + 7y = 15 and verify your answer. [10th cbse2024]

A = 60° and B = 30 deg verify that: sin(A + B) = sin A * cos B + cos A * sin B. [cbse10th 2024]

 

Show that 5×11×17+3×11 is a composite number. [[cbse2024]

 

Evaluate 2√2 cos 45°sin 30°+ 2√3cos30° [cbse 10th 2024]

 

The sum of first and eighth terms of an A.P. is 32 and their product is 60. Find the first term and common difference of the A.P. Hence, also find the sum of its first 20 terms. [cbse2024]

 

In an A.P. of 40 terms, the sum of first 9 terms is 153 and the sum of last 6 terms is 687. Determine the first term and common difference of A.P. Also, find the sum of all the terms of the A.P. [cbse 10th 2024]

 

Find the distance between two points (acosα, sinα), and (acosβ, asinß).

 

If secx+tanx=p, prove that sinx = (p² - 1)/(p²+ 1)