Explanation

The identity element e should satisfy ae = ea = a for all a in G.

Here, e = 6 works since 26=2, 46=4, 66=6, 86=8.

Explanation

To find the fraction equivalent to 2/5%, first convert the percentage to a decimal:

2/5% = (2/5) × (1/100) = 2/500 = 1/250

Explanation

Every subgroup of a cyclic group is also cyclic.

This is a key result in group theory under abstract algebra.

Explanation

"Annihilate" means to completely destroy, which fits the context of weapons and global threat.

Annihilate means فنا

Explanation

To find the slope of the tangent to the parabola y = 2x^2 - 13x + 5, we need to find the derivative of y with respect to x.

dy/dx = 4x - 13

We want to find if there is a point where the slope of the tangent is -1.

4x - 13 = -1

4x = 12

x = 3

Now, we need to find the corresponding y-coordinate.

y = 2(3)^2 - 13(3) + 5

y = 18 - 39 + 5

y = -16

So, the point of tangency is (3, -16).

The equation of the tangent line is:

y - (-16) = -1(x - 3)

y + 16 = -x + 3

y = -x - 13

Explanation

Explanation

"Exorbitantly" means excessively or unreasonably high, which fits well in the sentence:

"Fares are exorbitantly high in this city."

Explanation

Explanation

Explanation

Calculation:

• Current total age = 80 years

• Three years ago, each person was 3 years younger.

• Since there are three people, the total reduction in age is $3\times 3=9$ years.

So, the total of their ages three years ago is:

$$\mathrm{<b><font\; color="\#0000ff">80</font></b>}<b><font\; color="\#0000ff">-</font></b>\mathrm{<b><font\; color="\#0000ff">9</font></b>}<b><font\; color="\#0000ff">=</font></b>\mathrm{<b><font\; color="\#0000ff">71</font></b>}\text{<b><font color="\#0000ff"> years</font></b>}$$