For matrices A and B, the inverse of the product AB is given by:
(AB)⁻¹ = B⁻¹A⁻¹
A matrix A is symmetric if its transpose equals itself, i.e., A^T = A.
This means the elements are mirrored across the main diagonal.
Given y = 2/x
Let's find the first and second derivatives:
dy/dx = -2/x²
d²y/dx² = 4/x³
Now, let's evaluate y + 1/2 * d²y/dx²:
y + 1/2 * d²y/dx² = 2/x + 1/2 * 4/x³
= 2/x + 2/x³
= (2x² + 2)/x³
= 2(x² + 1)/x³
= 2(1 + x²)/x³
The X-axis and Y-axis intersect at the point (0, 0), known as the origin.
It is the central reference point in the coordinate plane.
Step 1: Convert binary numbers to decimal for easier calculation
(101)2 = 1 × 2^2 + 0 × 2^1 + 1 × 2^0 = 4 + 0 + 1 = 5
(110)2 = 1 × 2^2 + 1 × 2^1 + 0 × 2^0 = 4 + 2 + 0 = 6
Step 2: Add the decimal values
5 + 6 = 11
Step 3: Convert the sum back to binary
11 = 8 + 2 + 1 = 2^3 + 2^1 + 2^0 = (1011)2
LCM of two prime numbers is their product, since they have no common factors other than 1.
So, LCM(a, b) = a × b when both a and b are prime.
To find the median, let's arrange the weights in order:
27, 29, 30, 32, 33, 35, 37, 47, 48
Since there are 9 values (an odd number), the middle value is the median:
The median is the 5th value: 33
The argument of the product of two complex numbers is the sum of their arguments.
This property comes from the multiplication of complex numbers in polar form.
Step 1: Add the two equations to eliminate y
(x + y) + (x - y) = 10 + 10
2x = 202x = 10
Step 2: Solve for x
x = 20/2x = 10
A quadratic equation has the form ax² + bx + c = 0, and it typically has two roots.
These roots can be real or complex, and they can be distinct or repeated (in the case of a double root).