Explanation

The ratio test and root test are inconclusive when the limit of the ratio (or root) of successive terms is exactly 1.

These tests fail to determine convergence or divergence in this case.

Explanation

Given the product of two complex numbers (x + iy) and (x' + iy') is zero:

(x + iy)(x' + iy') = 0

This implies either (x + iy) = 0 or (x' + iy') = 0.

Therefore, at least one of the complex numbers must be zero.

Explanation

Logarithm of 0 is undefined because there is no exponent you can raise 5 to that results in 0.

In math, log₅(0) has no real value, as logarithmic functions are only defined for positive real numbers.

Explanation

Step 1: Recall the formula for torque

Torque (τ) is related to the change in angular momentum (L) over time (t) by the formula: τ = ΔL / Δt

Step 2: Calculate the change in angular momentum

ΔL = 5L - 2L = 3L

Step 3: Calculate the torque

τ = ΔL / Δt = 3L / 3 = L

Explanation

Given f(t) = 1/t and g(t) = t³

To find gof(t), substitute f(t) into g(t):

gof(t) = g(f(t))

= g(1/t)

= (1/t)³

= 1/t³

Explanation

To find the center of the circle, rewrite the equation in standard form:

45x² - 60x + 45y² + 36y = -19

Divide by 45:

x² - (4/3)x + y² + (4/5)y = -19/45

Complete the square:

(x - 2/3)² + (y + 2/5)² = ...

The center is (2/3, -2/5).

Explanation

Given a ≠ 0, b ≠ 0, and ab = 0:

In this case, a and b are called Zero divisors.

Explanation

The sum of three consecutive numbers is given 2 is the difference between the first and third numbers

***

Let the numbers bex,x+1  and  x+2  Then 

(x+2)−x=2

SH24-8-2023

Explanation

Pythagoras Theorem:

It states that in a right-angled triangle:

c = √(a² + b²)

where c is the hypotenuse, and a and b are the other two sides.

This formula helps calculate the length of the hypotenuse.

Explanation

A function is concave down on an interval if its second derivative is negative over that interval.

Graphically, this means the curve bends downward like an upside-down bowl.