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Additive inverse of -2/3 is

We know that the additive inverse of x is -x. Here, x = -⅔. Hence, the additive inverse of -⅔ is ⅔.... View Article

Which of the following differential equation y= c1e^x + c2e^-x as a general solution?

(a). (d2y/dx2) + y = 0 (b). (d2y/dx2) - y = 0 (c). (d2y/dx2) + 1 = 0 (d). (d2y/dx2) - 1 = 0 Solution: Correct Answer: Option (b) (d2y/dx2) -... View Article

_×_= 29

Since 29 is a prime number, it has only two factors such as 1 and 29. Hence, the positive and negative pair factors of 29 are (1, 29) and (-1,... View Article

What acts as a boundary for all the other parts of abacus?

The frame acts as a boundary for all the other parts of the abacus. The abacus has 17 rods, and each rod has 5 beads. The upper and lower part of... View Article

What is divisibility rule in Math?

A divisibility rule is a type of shortcut that allows us to determine whether a given number is divisible by a divisor by looking at its digits... View Article

What is 3 to the power of -1?

3 to the power of -1 means 3-1. 3-1 is written as ⅓ Hence, ⅓ = 0.333. Therefore, 3 to the power of -1 is 0.333.... View Article

If the curves y=2e^x and y=ae^−x intersect orthogonally, then a=?

Given: y = 2ex Hence, dy/dx = 2ex = m1 Also, given that y= ae-x dy/dx = -ae-x = m2 Two curves intersect orthogonally when m1. m2 = -1... View Article

The graph of the function y=f(x) passing through the point (0, 1) and satisfying the differential equation (dx/dy)+ycosx=cosx is such that

(a) It is a constant function (b) It is periodic (c) It is neither an even nor an odd function (d) It is continuous and differentiable for all... View Article

Integrate cos2x cos4x cos6x dx

Given: ∫cos2x cos4x cos6x dx We know that cos A cos B = ½ [ cos (A+B) + cos (A-B)] Thus, ∫cos2x cos4x cos6x dx = ∫cos2x .... View Article

The line x+y=1 meets the lines represented by the equation y³−xy²−14x²y+24x³=0 at the points A,B,C. If O is the origin, then OA²+OB²+OC² is equal to

Given equation: y3−xy2−14x2y+24x3=0 y3-xy2-14x2y+24x3=0 y3-2xy2 + xy2-2x2y-12x2y+24x3=0 y2(y-2x) +xy(y-2x) -12x2(y-2x)=0... View Article

What is the factorial of a number?

Factorial of a number, say k is equal to the product of all numbers such as 1 × 2 × 3 × 4 . . . × (k – 1) ×... View Article

What are decimal numbers?

Decimal numbers are one of the types of numbers, which has a whole number and the fractional part separated by a decimal point. For example,... View Article

What is the inverse of a matrix?

If A and B are two square matrices such that AB = BA = I, then B is the inverse matrix of A and is denoted by A-1, and A is the inverse of B. In... View Article

Find the area of the parallelogram formed by vectors A = [3, 2] and B = [-3, 7].

Given, Therefore, the area of parallelogram is 27 sq.units.... View Article

Two statements, s1 and s2, are given below, followed by a question. s1: 114 < x < 126, where x is a natural number. s2: x is a factor of 169. Question: Is x a prime number?

From the first statement:s1: 114 < x < 126, where x is a natural number. x = {115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125}From... View Article